A z-score value that is three standard deviations away from the mean can be calculated by multiplying three with the standard deviation. The positive or negative result will indicate whether it is above or below the mean, respectively.
To determine a z-score value that is three standard deviations away from the mean, we need to consider the properties of the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. Since the z-score represents the number of standard deviations a particular value is away from the mean, we can calculate the z-score by multiplying the number of standard deviations (in this case, three) by the standard deviation. In this case, since the mean is 0 and the standard deviation is 1, the z-score value that is three standard deviations away from the mean can be calculated as follows: Z = 3 * 1 = 3
Therefore, a z-score value of 3 indicates that the corresponding value is three standard deviations above the mean. Conversely, a z-score of -3 would represent a value that is three standard deviations below the mean.
To learn more about z-score value click here
brainly.com/question/29115764
#SPJ11
Homework: Section 2.1 Introduction to Limits (20) x² - 4x-12 Let f(x) = . Find a) lim f(x), b) lim f(x), and c) lim f(x). X-6 X-6 X-0 X--2 a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim f(x)= (Simplify your answer.) X-6 B. The limit does not exist
The limit of the function f(x) = (x² - 4x - 12)/(x - 6) as x approaches 6 is 8.Taking the limit as x approaches 6 of the simplified function,
To find the limit of the function f(x) = (x² - 4x - 12)/(x - 6) as x approaches 6, we can substitute the value 6 into the function and simplify:
lim f(x) as x approaches 6 = (6² - 4(6) - 12)/(6 - 6)
= (36 - 24 - 12)/0
= 0/0
We obtained an indeterminate form of 0/0, which means further algebraic manipulation is required to determine the limit.
We can factor the numerator of the function:
(x² - 4x - 12) = (x - 6)(x + 2)
Substituting this factored form back into the function, we get:
f(x) = (x - 6)(x + 2)/(x - 6)
Now, we can cancel out the common factor of (x - 6):
f(x) = x + 2
Taking the limit as x approaches 6 of the simplified function, we have:
lim f(x) as x approaches 6 = lim (x + 2) as x approaches 6
= 6 + 2
= 8
Therefore, the limit of f(x) as x approaches 6 is 8.
In summary, the limit of the function f(x) = (x² - 4x - 12)/(x - 6) as x approaches 6 is 8.
To know more about value click here
brainly.com/question/30760879
#SPJ11
Solve the equation. dy dx - = 7x²4 (2+ y²) An implicit solution in the form F(x,y) = C is (Type an expression using x and y as the variables.) 3 = C, where C is an arbitrary constant.
A solution to an equation that is not explicitly expressed in terms of the dependent variable is referred to as an implicit solution. Instead, it uses an equation to connect the dependent variable to one or more independent variables.
In order to answer the question:
Dy/dx = 4(2+y)/3 - 7x2/(2+y)
It can be rewritten as:
dy/(2+y) = (4(2+y)/3) + (7x)dx
Let's now integrate the two sides with regard to the relevant variables
∫[dy/(2+y^2)] = ∫[(4(2+y^2)/3 + 7x^2)dx]
We may apply the substitution u = 2+y2, du = 2y dy to integrate the left side:
∫[1/u]ln|u| = du + C1
We can expand and combine the right side to do the following:
∫[(4(2+y^2)/3 + 7x^2)dx] = ∫[(8/3 + 4y^2/3 + 7x^2)dx]
= (8/3)x + (4/3)y^2x + (7/3)x^3 + C2
Combining the outcomes, we obtain:
x = (8/3)x + (4/3)y2x + (7/3)x3 + C1 = ln|2+y2| + C1
We can obtain the implicit solution in the form F(x, y) = C by rearranging the terms and combining the constants.
ln[2+y2] -[8/3]x -[4/3]y2x -[7/3]x3 = C3
, where C3 = C2 - C1. C3 can be written as C = 3 since it is an arbitrary constant. Consequently, the implicit response is:
ln[2+y2] -[8/3]x -[4/3]y2x -[7/3]x3 = 3
To know more about Implicit Solution visit:
https://brainly.com/question/31481624
#SPJ11
Let V be an inner product space, and let u, V EV. We will construct an alternative proof of the Cauchy-Schwarz inequality. (a) Show that if u = 0, then (u, v)| = || | || v ||. (b) Let u = 0. Show that since projuv and v- proj, v are orthogonal, Pythagoras' theorem implies ||projuv||2 < ||v||2. (c) Again assuming u #0, show that ||projuv ||* = (u, v) 2/||u1|12. (d) Conclude that (u, v)|| < || | || vil. (e) Prove that equality holds iff u and v are parallel.
The line "u" is parallel to the line "v".
(a) Let u = 0Then, (u, v) = 0 since the inner product of two vectors is zero if one of them is zero.
Also, we know that modulus of any vector is greater than or equal to zero, so,|| v || ≥ 0
Multiplying the two equations, we get||(u, v)|| = || u ||*||v||... equation (1)
(b) Since u = 0, we can write projuv = 0
Also, we can write v = projuv + v - projuv
Now, by using Pythagoras theorem, we can write as ||v||2 = ||projuv||2 + ||v - projuv||2
Since, projuv and v - projuv are orthogonal, the equation can be simplified to ||v||2 = ||projuv||2 + ||v - proj uv||2...(2)
Since u = 0, by using definition of proj uv, we get(u, v) = 0...(3)
Now, by using (1) and (3), we get
||projuv||* = (u, v) / ||u||*||v|| = 0...(4)
From (2) and (4), we can write ||projuv||2 < ||v||2...(5)
(c) Again assuming u ≠ 0, by using definition of pro juv and (1), we get
||projuv||* = (u, v) / ||u||*||v||...(6)
Now, squaring the equation (6), we get
||projuv||2 = (u, v)2 / ||u||2||v||2...(7)
(d) Using (7), we get||(u, v)|| = ||projuv||*||u||*||v|| ≤ ||u||*||v||...(8)
Now, we can write|(u, v)| ≤ ||u||*||v||... equation (9)
(e) Equality holds when proj uv is parallel to v.
Therefore, u is also parallel to v. Hence, the proof is completed.
To learn more about Pythagoras theorem, visit the link below
https://brainly.com/question/21926466
#SPJ11
In a class of 32 students, there are 14 students that play on a sports team and 12 students that play in one of the school bands. There are 8 students that do not play a sport or play in a band. Some play on a team and play in one of the bands. What is the probability that a student chosen at random will play on a sports team or play in one of the school bands?
The probability that a student chosen at random will play on a sports team or play in one of the school bands is 75%. The number of students who play both in a sports team and in one of the school bands is 24 students.
There are two ways to find out the number of students who play both in a sports team and in one of the school bands:1.
We can use a Venn diagram or2. Use the formula, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
Let us use the Venn diagram approach to find out the number of students who play both in a sports team and in one of the school bands.
A Venn diagram is a graphical representation of the relationships between sets.
The sample space, which is the set of all possible outcomes, is represented by a rectangle.
Each set is represented by a circle or an oval. The overlapping region represents the intersection of two or more sets.
The non-overlapping regions represent the sets themselves and their complements (the elements that do not belong to the set).
Here,14 students play on a sports team,12 students play in one of the school bands, and8 students do not play a sport or play in a band.
To find n(A ∩ B), we can use the formula,n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
Here, n(A ∪ B) represents the total number of students who play on a sports team or play in one of the school bands.n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
So, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)= 14 + 12 - (32 - 8)= 24 students.
Therefore, the number of students who play both in a sports team and in one of the school bands is 24 students.
Total number of students who play in a sports team or play in one of the school bands = n(A ∪ B)= n(A) + n(B) - n(A ∩ B)= 14 + 12 - 24= 26 students
Hence, the probability that a student chosen at random will play on a sports team or play in one of the school bands is P(A)
= (Number of favorable outcomes) / (Total number of outcomes)
= (26 + 24) / 32= 50 / 64= 75%.
To know more about probability visit :-
https://brainly.com/question/31828911
#SPJ11
A cell phone plan has a basic charge of $35 a month. The plan includes 500 free minutes and charges 10 cents for each additional mi
To determine the cost of the cell phone plan given the number of minutes used, we can break it down into two scenarios: when the number of minutes is within the 500 free minutes, and when it exceeds the 500 free minutes.
If the number of minutes used is within the 500 free minutes:
In this case, the cost of the cell phone plan is only the basic charge of $35 per month.
If the number of minutes used exceeds the 500 free minutes:
In this case, the cost of the additional minutes is calculated at a rate of 10 cents per minute. Let's denote the number of additional minutes as x. The cost of the additional minutes can be represented as 0.10x.
Therefore, the total cost of the cell phone plan, including the basic charge and any additional minutes, can be expressed as:
Total cost = Basic charge + Cost of additional minutes
Given that the basic charge is $35, we can write:
Total cost = $35 + 0.10x
To summarize:
If the number of minutes used is within the 500 free minutes, the total cost is $35.
If the number of minutes used exceeds the 500 free minutes, the total cost is $35 + 0.10x.
Note: It's important to consider any additional charges or fees that may be applicable to the cell phone plan. The given information states the basic charge and the charge for additional minutes, but other factors such as taxes or surcharges may also affect the total cost.
know more about scenarios: brainly.com/question/15367590
#SPJ11
Find a surface parameterization of the portion of the tilted plane x-y + 2z = 2 that is inside the cylinder x² + y² = 9.
To find a surface parameterization of the portion of the tilted plane x - y + 2z = 2 that is inside the cylinder x² + y² = 9, we can use cylindrical coordinates.
Let's first parameterize the cylinder x² + y² = 9. We can use the parameterization:
x = 3cosθ
y = 3sinθ
z = z
where θ is the azimuthal angle and z is the height.
Now, let's substitute these parameterizations into the equation of the tilted plane x - y + 2z = 2 to find the parameterization for the portion inside the cylinder. 3cosθ - 3sinθ + 2z = 2 Rearranging the equation, we have:
z = (2 - 3cosθ + 3sinθ)/2
Therefore, the parameterization for the portion of the tilted plane inside the cylinder is:
x = 3cosθ
y = 3sinθ
z = (2 - 3cosθ + 3sinθ)/2
This parameterization describes the surface points that satisfy both the equation of the tilted plane and the equation of the cylinder, representing the portion of the tilted plane inside the cylinder.
Learn more about surface parametrization here: brainly.com/question/11983917
#SPJ11
1. Solve for the sample size with the assumption that the confidence coefficient is 95% and second, the population proportion is close to 0.5. a. Suppose the school has the following population per year level: First year - 205 Second year - 220 Third year- - 180 Fourth year 165 Use the appropriate probability sampling for this population. Population Sample size = First year: n = Second year: n= Third year: n = Fourth year: n=
To calculate the sample sizes for each year level with a 95% confidence level and assuming a population proportion close to 0.5, we can use the formula for sample size calculation: [tex]n = (Z^2 \times p \times (1 - p)) / E^2[/tex]
[tex]n = (Z^2 \times p \times (1 - p)) / E^2[/tex]
Where:
n = sample size
Z = z-score corresponding to the desired confidence level
p = estimated population proportion
E = margin of error
Since we assume a population proportion close to 0.5, we can use p = 0.5.
For a 95% confidence level, the corresponding z-score is approximately 1.96 (for a two-tailed test).
Let's calculate the sample sizes for each year level:
First year:
[tex]n = (1.96^2 \times 0.5 \times (1 - 0.5)) / E^2[/tex]
E is not specified, so you need to determine the desired margin of error to proceed with the calculation.
Second year:
[tex]n = (1.96^2 \times 0.5 \times (1 - 0.5)) / E^2[/tex]
Again, you need to specify the desired margin of error (E).
Third year:
[tex]n = (1.96^2 \times 0.5 \times (1 - 0.5)) / E^2[/tex]
Specify the desired margin of error (E).
Fourth year:
[tex]n = (1.96^2 \times 0.5\times (1 - 0.5)) / E^2[/tex]
Specify the desired margin of error (E).
Learn more about margin of error here:
https://brainly.com/question/29419047
#SPJ11
Let {u1, U2, U3} be an orthonormal basis for an inner product space V. If v=aui + bu2 + cuz is so that || v || = 115, v is orthogonal to uz, and (v, u2) = -115, find the possible values for a, b, and c. = —
According to the given condition is: [tex]v'uz = 0[/tex] or [tex][a b c] * [0 0 1]'[/tex]. The possible values of a, b, and c are 0, -115, and 0.
The set {u1, U2, U3} is an orthonormal basis for an inner product space V.
Also, [tex]v=aui + bu2 + cuz[/tex] is so that [tex]|| v || = 115[/tex], v is orthogonal to uz, and
[tex](v, u2) = -115[/tex].
The given v can be written in matrix form as:
[tex]v = [ui, u2, u3] * [a b c][/tex]'
As given, [tex]|| v || = 115[/tex], then
v[tex]'v = || v ||^2v'v \\= [a b c] * [a b c]' \\= a^2 + b^2 + c^2 \\= 115^2[/tex] ----(1)
It is given that v is orthogonal to uz.
As {u1, U2, U3} be an orthonormal basis, then the vectors are mutually orthogonal and unit vectors.
Hence, [tex]uz = [0 0 1]'[/tex].
Thus, the given condition is: [tex]v'uz = 0[/tex]
or [tex][a b c] * [0 0 1]' = 0c = 0[/tex] ----(2)
Given, (v, u2) = -115
or [tex][a b c] * [0 1 0]' = -115b = -115[/tex] ----(3)
Substituting (2) and (3) in (1),
[tex]a^2 + (-115)^2 + 0^2 = 115^2[/tex]
[tex]a^2 = 115^2 - 115^2[/tex]
[tex]a^2 = 115^2 * (1-1)a = 0[/tex]
Therefore, a = 0, b = -115, and c = 0.
Hence, the possible values of a, b, and c are 0, -115, and 0.
To know more about orthogonal, visit:
https://brainly.com/question/32196772
#SPJ11
find from the differential equation and initial condition. =3.8−2.3,(0)=2.7.
The particular solution to the given differential equation `dy/dx = 3.8 - 2.3y` with initial condition `(0) = 2.7` is `y = 1.65 + 2.15e⁻²°³ˣ`.
Given differential equation `dy/dx = 3.8 - 2.3y` and the initial condition `(0) = 2.7`.
We are required to find the particular solution to the given differential equation using the initial condition. For this purpose, we can use the method of separation of variables to solve the differential equation and get the solution in the form of `y = f(x)`.
Once we get the general solution, we can substitute the initial value of `y` to find the value of the constant of integration and obtain the particular solution.
So, let's solve the given differential equation using separation of variables and find the general solution.
`dy/dx = 3.8 - 2.3y`
Moving all `y` terms to one side, and `dx` terms to the other side,
we get: `dy/(3.8 - 2.3y) = dx`
Now, we can integrate both sides with respect to their respective variables:`
∫dy/(3.8 - 2.3y) = ∫dx`
On the left-hand side, we can use the substitution
`u = 3.8 - 2.3y` and
`du/dy = -2.3` to simplify the integral:`
-1/2.3 ∫du/u = -1/2.3 ln|u| + C1`
On the right-hand side, the integral is simply equal to `x + C2`.
Therefore, the general solution is:`-1/2.3 ln|3.8 - 2.3y| = x + C`
Rearranging the above equation in terms of `y`, we get:`
[tex]y = (3.8 - e^(-2.3x - C)/2.3`[/tex]
Now, we can use the initial condition `(0) = 2.7` to find the constant of integration `C`.
Substituting `x = 0` and `y = 2.7` in the above equation, we get:
[tex]`2.7 = (3.8 - e^(-2.3*0 - C)/2.3`[/tex]
Simplifying the above equation, we get:
[tex]`e^(-C)/2.3 = 3.8 - 2.7` `[/tex]
[tex]= > ` `e^(-C) = 1.1 * 2.3`[/tex]
Taking the natural logarithm of both sides, we get:`
-C = ln(1.1 * 2.3)`
`=>` `C = -ln(1.1 * 2.3)`
Substituting the value of `C` in the general solution, we get the particular solution:`
[tex]y = (3.8 - e^(-2.3x + ln(1.1 * 2.3))/2.3`\\ `y = 1.65 + 2.15e^(-2.3x)`[/tex]
Therefore, the particular solution to the given differential equation
`dy/dx = 3.8 - 2.3y` with initial condition
`(0) = 2.7` is[tex]`y = 1.65 + 2.15e^(-2.3x)`.[/tex]
Know more about the particular solution
https://brainly.com/question/30466117
#SPJ11
A set of data has a normal distribution with a population mean of 114.7 and population standard deviation of 79.2. Find the percent of the data with values greater than -19.9. E Identify the following variables: : σ. I: 2 = The percent of the population with values greater than-19.9 is Enter your answers as numbers accurate to 2 decimal places.
The percentage of the population with values greater than -19.9 is approximately 57.35%. To find the percent of the data with values greater than a certain value in a normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.
First, we need to standardize the value -19.9 using the formula:
z = (x - μ) / σ
where z is the standardized value, x is the given value, μ is the population mean, and σ is the population standard deviation.
For the given value x = -19.9, population mean μ = 114.7, and population standard deviation σ = 79.2, we can calculate the standardized value:
z = (-19.9 - 114.7) / 79.2
z = -0.1904
Next, we can use the standard normal distribution table or a calculator to find the area under the curve to the right of z = -0.1904. This represents the percentage of data with values greater than -19.9.
Using a standard normal distribution table, we can find that the area to the left of z = -0.1904 is approximately 0.4265. Therefore, the percentage of data with values greater than -19.9 is:
1 - 0.4265 = 0.5735
Multiplying by 100 to convert to a percentage, we get:
57.35%
So, the percentage of the population with values greater than -19.9 is approximately 57.35%.
Identifying the variables:
σ: Population standard deviation = 79.2
2: The percent of the population with values greater than -19.9 = 57.35
learn more about mean here: brainly.com/question/31101410
#SPJ11
77. Find the inverse of the nonsingular matrix -4 1 6 -2]
The inverse of the nonsingular matrix [-4 1; 6 -2] is [1/2 1/2; -3/4 -1/4].
To find the inverse of a matrix, we follow a specific procedure. Let's consider the given matrix [-4 1; 6 -2] and find its inverse.
Step 1: Calculate the determinant of the matrix.
The determinant of the matrix is found by multiplying the diagonal elements and subtracting the product of the off-diagonal elements. For the given matrix, the determinant is:
Det([-4 1; 6 -2]) = (-4) * (-2) - (1) * (6) = 8 - 6 = 2.
Step 2: Determine the adjugate matrix.
The adjugate matrix is obtained by taking the transpose of the matrix of cofactors. To find the cofactors, we interchange the signs of the elements and compute the determinants of the remaining 2x2 matrices. For the given matrix, the cofactor matrix is:
[-2 -6; -1 -4].
Taking the transpose of this matrix, we get the adjugate matrix:
[-2 -1; -6 -4].
Step 3: Calculate the inverse matrix.
The inverse of the matrix is obtained by dividing the adjugate matrix by the determinant. For the given matrix, the inverse is:
[1/2 1/2; -3/4 -1/4].
Learn more about: nonsingular matrix
brainly.com/question/32563516
#SPJ11
The equation 15/x + 15/y + 5/z – 5 = 0 defines z as a function of x and y. Find dz/dx and dz/dy at the point (9, 48,2).
Dz/dx|(x,y,z)=(9,48,2)=
Dz/dy|(x,y,z)=(9,48,2)=
Given equation: 15/x + 15/y + 5/z – 5 = 0 defines z as a function of x and y.
It can be written as: 5/z = 5 – 15/x – 15/y
Therefore: z = 1/(1/x + 1/y – 1)
Differentiate w.r.t. x:z
[tex][x^2y/xy(y-x)]dx/dx -[xy^2/xy(x-y)]dy/dx/[xy(y-x) + xy(x-y)]^2z[/tex]
= y(y–x)/[x+y–xy]²Dz/dx|(x,y,z)=(9,48,2)
= 48(48 – 9)/[9+48 – 9×48]²= – 216/(29)²
Differentiate w.r.t. y:z
[tex]= [xy^2/xy(x-y)]dx/dy -[x^2y/xy(y-x)]dy/dy/[xy(y-x) + xy(x-y)]^2z \\= x(x-y)/[x+y-xy]^2Dz/dy|(x,y,z)=(9,48,2)= 9(9-48)/[9+48 - 9*48]^2\\= 216/(29)^2[/tex]
Therefore, dz/dx|(x,y,z)=(9,48,2)
= -4.09, dz/dy|(x,y,z)=(9,48,2)= 4.09.
To learn more about Differentiate visit:
brainly.com/question/24062595
#SPJ11
12:49 PM Fri May 20 < ☆ J T 3. One solution of 14x²+bx-9=0 is -- 2 Find b and the other solution. RO +: 13% U +
the other solution is x = 1/2 and the value of b is 64.
Given, One solution of [tex]14x²+bx-9=0 is -2[/tex]
To find: Value of b and other solution.
Step 1: Let's find the two solutions of [tex]14x²+bx-9=0.[/tex]
We know that the quadratic equation has two solutions and the sum of the roots of the equation -b/a and the product of the roots of the equation is c/a.
The equation is given as;[tex]14x²+bx-9=0[/tex]
Here, a = 14, b = b and c = -9.
We know that sum of the roots of the equation is -b/a.
Thus, (1st root + 2nd root) = -b/a.
Now, we need to find the 1st root of the equation.14x² + bx - 9 = 0It is given that one root of the quadratic equation is -2.
Thus, (x+2) is a factor of the quadratic equation.
Using this, we can write the quadratic equation in the factored form;[tex]14x² + bx - 9 = 0(7x + 9)(2x - 1) \\= 0[/tex]
Now, we can find the second root of the quadratic equation using the factor form of the equation.
[tex]2x - 1 = 0x \\= 1/2[/tex]
Now, the two roots of the quadratic equation are; x = -2 and x = 1/2.
Step 2: To find the value of b we will substitute the value of x from either of the two solutions in the equation.
[tex]14x²+bx-9=0[/tex]
Putting, x = -2 in the above equation
[tex]14(-2)² + b(-2) - 9 = 0b =\\ 14(4) + 18 \\= 64[/tex]
Substituting the value of b and the two solutions in the equation.[tex]14x² + 64x - 9 = 0[/tex]
Thus, the other solution is x = 1/2 and the value of b is 64.
Know more about equations here:
https://brainly.com/question/29174899
#SPJ11
Let
f(x) = 6x^2 - 2x^4
(A) Use interval notation to indicate where f(x) is increasing
Note: Use INF' for [infinity], INF for-[infinity], and use 'U' for the union symbol.
Increasing: _____________
(B) Use interval notation to indicate where f(x) is decreasing.
Decreasing: _______________
(C) List the values of all local maxima of f| if there are no local maxima, enter 'NONE' x1 values of local maximums = ______________
(D) List the an values of all local minima of f| If there are no local minima, enter NONE. x1 values of local minimums = _________
To apply the Mean Value Theorem (MVT), we need to check if the function f(x) = 18x^2 + 12x + 5 satisfies the conditions of the theorem on the interval [-1, 1].
The conditions required for the MVT are as follows:
The function f(x) must be continuous on the closed interval [-1, 1].
The function f(x) must be differentiable on the open interval (-1, 1).
By examining the given equation, we can see that the left-hand side (4x - 4) and the right-hand side (4x + _____) have the same expression, which is 4x. To make the equation true for all values of x, we need the expressions on both sides to be equal.
By adding "0" to the right-hand side, the equation becomes 4x - 4 = 4x + 0. Since the two expressions on both sides are now identical (both equal to 4x), the equation holds true for all values of x.
Adding 0 to an expression does not change its value, so the equation 4x - 4 = 4x + 0 is satisfied for any value of x, making it true for all values of x.
To learn more about equations click here, brainly.com/question/29657983
#SPJ11
Calculus Consider the function f(x, y) = (x² - 1)e-(z²+y²),
(a) This function has three critical points. Verify that one of them occurs at (0,0), and find the coordinates of the other two.
(b) What type of critical point occurs at (0,0)?
Separated Variable Equation: Example: Solve the separated variable equation: dy/dx = x/y To solve this equation, we can separate the variables by moving all the terms involving y to one side.
A mathematical function, whose values are given by a scalar potential or vector potential The electric potential, in the context of electrodynamics, is formally described by both a scalar electrostatic potential and a magnetic vector potential The class of functions known as harmonic functions, which are the topic of study in potential theory.
From this equation, we can see that 1/λ is an eigenvalue of A⁻¹ with the same eigenvector x Therefore, if λ is an eigenvalue of A with eigenvector x, then 1/λ is an eigenvalue of A⁻¹ with the same eigenvector x.
These examples illustrate the process of solving equations with separable variables by separating the variables and then integrating each side with respect to their respective variables.
To know more about equation:- https://brainly.com/question/29657983
#SPJ11
Use Shell method to find the volume of the solid formed by revolving the region bounded by the graph of y=x³+x+l, y = 1 and X=1 about the line X = 2₁"
To calculate the flux of the vector field F = (x/e)i + (z-e)j - xyk across the surface S, which is the ellipsoid x²/25 + y²/5 + z²/9 = 1, we can use the divergence theorem.
The divergence theorem states that the flux of a vector field across a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface.
First, let's calculate the divergence of F:
div(F) = (∂/∂x)(x/e) + (∂/∂y)(z-e) + (∂/∂z)(-xy)
= 1/e + 0 + (-x)
= 1/e - x
To calculate the surface integral of the vector field F = (x/e) I + (z-e)j - xyk across the surface S, which is the ellipsoid x²/25 + y²/5 + z²/9 = 1, we can set up the surface integral ∬S F · dS.
To know more about theorem:- https://brainly.com/question/30066983
#SPJ11
Which of the following is NOT a type of non-probability sampling? Select one: a. Consecutive sampling O b. Panel sampling O c. Snowball sampling O d. Convenience sampling O e. Quota sampling. f. Strat
The option that is NOT a type of non-probability sampling is: f. Stratified sampling.
What is Stratified sampling?Not non-probability sampling but stratified sampling is a sort of probability sampling. A random sample is drawn from each stratum once the population has been split into various subgroups or strata. This makes it a type of probability sampling by guaranteeing that each subgroup is represented in the sample.
Non-probability sampling techniques on the other hand, do not use random selection and do not ensure that each member of the population has an equal chance of being selected for the sample.
Therefore the correct option is f.
Learn more about Stratified sampling here:https://brainly.com/question/20544692
#SPJ4
(iii) For the 2 x 2 matrix A with first row (0, 1) and second row (1,0), describe the spectral theorem. (iv) For a linear transformation T on an IPS V, show that Ran(T)+ = Null(T*). Hence show that for a normal T, V = Ran(T) + Null(T). (v) Find all 2 x 2 matrices that are both Hermitian and unitary.
The spectral theorem states that every normal matrix can be written as a unitary matrix multiplied by a diagonal matrix of eigenvalues. The range of a normal matrix is the entire space, and the null space of a normal matrix is the set of all vectors that are orthogonal to the eigenvectors of the matrix.
The only 2x2 matrices that are both Hermitian and unitary are the identity matrix and the matrix with 1 on the diagonal and -1 on the diagonal.
(iii) The spectral theorem states that every normal matrix can be written as a unitary matrix multiplied by a diagonal matrix of eigenvalues. In the case of the 2x2 matrix A with first row (0, 1) and second row (1,0), the eigenvalues are 1 and -1. The unitary matrix is simply the identity matrix, and the diagonal matrix of eigenvalues is the matrix with 1 on the diagonal and -1 on the diagonal.
(iv) The range of a linear transformation T is the set of all vectors that can be written as T(v) for some vector v in the domain of T. The null space of a linear transformation T is the set of all vectors that are mapped to the zero vector by T.
The spectral theorem states that every normal matrix can be written as a unitary matrix multiplied by a diagonal matrix of eigenvalues. The range of a unitary matrix is the entire space, and the null space of a diagonal matrix is the set of all vectors that are orthogonal to the columns of the matrix. Therefore, the range of a normal matrix is the entire space, and the null space of a normal matrix is the set of all vectors that are orthogonal to the eigenvectors of the matrix.
(v) A 2x2 matrix is Hermitian if it is equal to its conjugate transpose. A 2x2 matrix is unitary if its determinant is 1 and its trace is 0. The only 2x2 matrices that are both Hermitian and unitary are the identity matrix and the matrix with 1 on the diagonal and -1 on the diagonal.
Learn more about spectral theorem here;
brainly.com/question/30001842
#SPJ11
Suppose the demand for oil is P=1390-0.20. There are two oil producers who form a cartel. Producing oil costs $9 per barrel. What is the profit of each cartel member?
The profit of each cartel member is $16592.84 and $21659.59 respectively.
What is it?Where, P = Price per barrel
Q = Quantity of oil produced and,
Cost of producing one barrel of oil = $9.
The total cost of producing Q barrels of oil is TC = 9Q.
So, profit per barrel of oil = P - TC.
Substituting TC in terms of Q,
Profit per barrel of oil = P - 9Q.
Now, the cartel has two producers, so we can find the total quantity of oil produced, say Q_Total
Q_Total = Q_1 + Q_2.
We need to find profit per barrel for each of the producers.
So, let's say Producer 1 produces Q_1 barrels of oil.
Profit_1 = (P - 9Q_1) * Q_1
The second producer produces Q_2 barrels of oil,
so Profit_2 = (P - 9Q_2) * Q_2.
Now, we need to find values of Q_1 and Q_2 such that the total profit of the two producers is maximized.
Thus, Total Profit = Profit_1 + Profit_2
= (P - 9Q_1) * Q_1 + (P - 9Q_2) * Q_2
= (1390 - 0.20Q_1 - 9Q_1) * Q_1 + (1390 - 0.20Q_2 - 9Q_2) * Q_2
= (1390 - 9.2Q_1)Q_1 + (1390 - 9.2Q_2)Q_2.
So, we can find the values of Q_1 and Q_2 that maximize total profit by differentiating Total Profit w.r.t. Q_1 and Q_2 respectively.
We will differentiate Total Profit w.r.t. Q_1 first.
d(Total Profit)/dQ_1 = 1390 - 18.4Q_1 - 9.2Q_2
= 0=> Q_1 + 0.5Q_2
= 75.54
(i) Similarly, d(Total Profit)/dQ_2 = 1390 - 9.2Q_1 - 18.4Q_2
= 0=> 0.5Q_1 + Q_2
= 75.54
(ii)Solving the above two equations, we get,
Q_1 = 31.8468,
Q_2 = 43.6932.
Thus, total quantity of oil produced = Q_
Total = Q_1 + Q_2 = 75.54.
Profit_1 = (P - 9Q_1) * Q_1
= (1390 - 9(31.8468)) * 31.8468
= $16592.84
Profit_2 = (P - 9Q_2) * Q_2
= (1390 - 9(43.6932)) * 43.6932
= $21659.59
Hence, the profit of each cartel member is $16592.84 and $21659.59 respectively.
To know more on Profit visit:
https://brainly.com/question/31117493
#SPJ11
for all equations, writ the value(s) of the bariable that makes the denominator 0. Solve the equations
2/X +3 = 2/ 3x +28/9= 3/x-2+2=11/X-2 4/x
=4 + 5/x-2 =30/(x+4)(x-2)
In summary, for equations 1, 5, and 6, the denominators do not have any values that make them zero. For equations 2, 3, 4, and 7, the denominators cannot be zero, so we need to exclude the values x = 0, 2, -4 from the solution set.
To find the values of the variable that make the denominator zero, we need to set each denominator equal to zero and solve for x.
2/X + 3 = 0
The denominator X cannot be zero.
2/(3x) + 28/9 = 0
The denominator 3x cannot be zero. Solve for x:
3x ≠ 0
3/(x-2) + 2 = 0
The denominator (x-2) cannot be zero. Solve for x:
x - 2 ≠ 0
x ≠ 2
11/(X-2) + 2 = 0
The denominator (X-2) cannot be zero. Solve for x:
X - 2 ≠ 0
X ≠ 2
4/x = 0
The denominator x cannot be zero.
4 + 5/(x-2) = 0
The denominator (x-2) cannot be zero. Solve for x:
x - 2 ≠ 0
x ≠ 2
30/((x+4)(x-2)) = 0
The denominator (x+4)(x-2) cannot be zero. Solve for x:
(x+4)(x-2) ≠ 0
x ≠ -4, 2
To know more about equations,
https://brainly.com/question/29109059
#SPJ11
For the function S() 20 2013r? 125, what is the absolute maximum and absolute minimum on the closed interval ( 2,4]?
Absolute maximum of S(x) on the closed interval (2, 4]: -92
Absolute minimum of S(x) on the closed interval (2, 4]: -105
The given function is:
[tex]S(x) = 20 + 13r^3 - 125[/tex]
The function S(x) is continuous on the closed interval [2, 4].
Thus, the absolute extrema of S(x) on the closed interval [2, 4] occur at the critical numbers and endpoints of the interval.
Firstly, let's find the critical numbers, if any, of S(x) on (2, 4).
S'(x) = 0 is the necessary condition for S(x) to have a local extrema at
[tex]x = c.S'(x) \\= 0[/tex]
=>
[tex]S'(x) = 39r^2 \\= 0[/tex]
=> r = 0 (Since r³ is always positive)
However, r = 0 doesn't lie on the given closed interval [2, 4].
Thus, S(x) doesn't have any critical number on (2, 4).
So, we need to evaluate S(x) at the endpoints of the closed interval [2, 4].
At x = 2,
[tex]S(2) = 20 + 13(0) - 125 \\= -105[/tex]
At x = 4,
[tex]S(4) = 20 + 13(1) - 125\\ = -92[/tex]
Thus, S(x) has an absolute maximum of -92 at x = 4 and an absolute minimum of -105 at x = 2 on the given closed interval (2, 4].
Hence, the required values are as follows:
Absolute maximum of S(x) on the closed interval (2, 4]: -92
Absolute minimum of S(x) on the closed interval (2, 4]: -105
To Know more about absolute maximum, visit:
https://brainly.com/question/31585619
#SPJ11
Solve the following Bernoulli equation dy/dx + y/x-2 = 5(x − 2)y¹/². Do not put an absolute value in your integrating factor.
The solution to the Bernoulli equation dy/dx + y/x - 2 = 5(x - 2)y^(1/2) involves an integral expression that cannot be simplified further. Therefore, the solution is given in terms of the integral.
To solve the given Bernoulli equation, we will follow these steps:
Write the equation in standard Bernoulli form.
Identify the integrating factor.
Multiply the equation by the integrating factor.
Rewrite the equation in a simpler form.
Integrate both sides of the equation.
Solve for the constant of integration, if necessary.
Substitute the constant of integration back into the solution.
Let's solve the equation using these steps:
Write the equation in standard Bernoulli form.
dy/dx + (y/x - 2) = 5(x - 2)y^(1/2)
Identify the integrating factor.
The integrating factor for this equation is x^-2.
Multiply the equation by the integrating factor.
x^-2 * (dy/dx + (y/x - 2)) = x^-2 * 5(x - 2)y^(1/2)
x^-2(dy/dx) + (y/x^3 - 2x^-2) = 5(x^-1 - 2x^-2)y^(1/2)
Rewrite the equation in a simpler form.
Let's simplify the equation further:
x^-2(dy/dx) + (y/x^3 - 2/x^2) = 5(x^-1 - 2x^-2)y^(1/2)
Integrate both sides of the equation.
Integrate the left-hand side with respect to y and the right-hand side with respect to x:
∫x^-2(dy/dx) + ∫(y/x^3 - 2/x^2)dy = ∫5(x^-1 - 2x^-2)y^(1/2)dx
x^-2y + (-1/x^2)y + C = 5∫(x^-1 - 2x^-2)y^(1/2)dx
Solve for the constant of integration, if necessary.
Let C1 = -C. Rearranging the equation, we have:
x^-2y - (1/x^2)y = 5∫(x^-1 - 2x^-2)y^(1/2)dx + C1
Substitute the constant of integration back into the solution.
x^-2y - (1/x^2)y = 5∫(x^-1 - 2x^-2)y^(1/2)dx + C1
The integral on the right-hand side can be evaluated separately. The solution will involve special functions, which may not have a closed form.
Thus, the equation is solved in terms of an integral expression.
To learn more about Bernoulli equation visit : https://brainly.com/question/15396422
#SPJ11
(c ).Find the real-valued fundamental solution. x₁₂' = 3x₁, x₂ = 3x₂ - 2x₂₁x₂² = x₂ + x3z² [6 marks]
To find the real-valued fundamental solution, we need to find the eigenvector corresponding to the real eigenvalue.
From the previous calculations, we found that the eigenvalues are complex:
λ₁ = (-1 + i√7) / 2
λ₂ = (-1 - i√7) / 2
Since we're looking for real-valued solutions, we can focus on the eigenvalue λ₂.
For λ₂ = (-1 - i√7) / 2:
(A - λ₂I) * X₂ = 0
Substituting the values from matrix A and eigenvalue λ₂, we have:
[(1 - (-1 - i√7)/2) 1]
[4 (-2 - (-1 - i√7)/2)] * [X₂] = 0
Simplifying:
[(3 - i√7)/2 1]
[4 (-3 + i√7)/2] * [X₂] = 0
Expanding the matrix equation, we get:
((3 - i√7)/2)X₂ + X₂ = 0
4X₂ + ((-3 + i√7)/2)X₂ = 0
Simplifying:
(3 - i√7)X₂ + 2X₂ = 0
4X₂ + (-3 + i√7)X₂ = 0
For the first equation:
(3 - i√7)X₂ + 2X₂ = 0
Expanding:
3X₂ - i√7X₂ + 2X₂ = 0
Combining like terms:
5X₂ - i√7X₂ = 0
Since we are looking for a real-valued solution, the coefficient of the imaginary term must be zero:
-i√7X₂ = 0
This implies that X₂ = 0.
For the second equation:
4X₂ + (-3 + i√7)X₂ = 0
Expanding:
4X₂ - 3X₂ + i√7X₂ = 0
Combining like terms:
X₂ + i√7X₂ = 0
Factoring out X₂:
X₂(1 + i√7) = 0
For this equation to hold, either X₂ = 0 or (1 + i√7) = 0.
Since (1 + i√7) is not equal to zero, we have X₂ = 0.
Therefore, the real-valued fundamental solution is:
X = [X₁]
[X₂] = [X₁]
[0]
where X₁ is a real constant.
This fundamental solution represents a system with only one real-valued solution, given by:
X₁' = 3X₁
X₂ = 0
Solving the first equation, we find:
X₁ = Ce^(3t)
where C is a constant.
Hence, the real-valued fundamental solution is:
X = [Ce^(3t)]
[0]
where C is a constant.
To learn more about matrix : brainly.com/question/29132693
#SPJ11
4) a. Bank Nizwa offers a saving account at the rate 20% simple interest. If you deposit RO 592 in this saving account, then how much time will take to amount RO 0592? b. At what anrnual rate of interest, compounded weekly, will money triple in 92 months?
The annual rate of interest, compounded weekly, that will triple the money in 92 months is approximately 44.436%.
a. To find the time it will take for an amount to grow to RO 0592 at a simple interest rate of 20%, we can use the formula:
Interest = Principal × Rate × Time
In this case, the principal (P) is RO 592, the rate (R) is 20%, and we need to find the time (T). Substituting the given values into the formula, we have:
Interest = RO 592 × 20% × T
Since the interest is equal to RO 0592, we can write the equation as:
RO 0592 = RO 592 × 20% × T
Simplifying, we have:
RO 0592 = RO 592 × 0.2 × T
Dividing both sides by RO 592 × 0.2, we find:
T = RO 0592 / (RO 592 × 0.2)
T = 1 / 0.2
T = 5 years
Therefore, it will take 5 years for the amount to grow to RO 0592.
b. To find the annual rate of interest, compounded weekly, that will triple the money in 92 months, we can use the compound interest formula:
Future Value = Principal × (1 + Rate/Number of Compounding)^(Number of Compounding × Time)
In this case, the future value (FV) is three times the principal (P), the time (T) is 92 months, and we need to find the rate (R). We know that the compounding is done weekly, so the number of compounding (N) per year is 52. Substituting the given values into the formula, we have:
3P = P × (1 + R/52)^(52 × (92/12))
Simplifying, we have:
3 = (1 + R/52)^(52 × (92/12))
Taking the natural logarithm (ln) of both sides, we have:
ln(3) = ln[(1 + R/52)^(52 × (92/12))]
Using the logarithmic property, we can bring down the exponent:
ln(3) = (52 × (92/12)) × ln(1 + R/52)
Dividing both sides by (52 × (92/12)), we find:
ln(3) / (52 × (92/12)) = ln(1 + R/52)
Using the inverse natural logarithm (e^x) on both sides, we have:
e^(ln(3) / (52 × (92/12))) = 1 + R/52
Subtracting 1 from both sides, we find:
e^(ln(3) / (52 × (92/12))) - 1 = R/52
Multiplying both sides by 52, we find:
52 × (e^(ln(3) / (52 × (92/12))) - 1) = R
Calculating the right-hand side of the equation, we find:
R ≈ 44.436%
Therefore, the annual rate of interest, compounded weekly, that will triple the money in 92 months is approximately 44.436%.
To know more about compound interest, refer here:
https://brainly.com/question/14295570#
#SPJ11
(b) F = (2xy + 3)i + (x² − 4z) j – 4yk evaluate the integral 2,1,-1 F.dr. 3,-1,2 = (c) Evaluate the integral F-dr where I is along the curve sin (πt/2), y = t²-t, z = t¹, 0≤t≤1. F = y²zi – (z² sin y − 2xyz)j + (2z cos y + y²x)k
Therefore, the value of the line integral ∫ F · dr, where F = (2xy + 3)i + (x² − 4z)j – 4yk, and dr = dx i + dy j + dz k, along the path from (2,1,-1) to (3,-1,2) is -281/3.
(b) To evaluate the integral ∫ F · dr, where F = (2xy + 3)i + (x² − 4z)j – 4yk, and dr = dx i + dy j + dz k, we need to perform a line integral along the specified path from (2,1,-1) to (3,-1,2).
The line integral is given by the formula:
∫ F · dr = ∫ (F_x dx + F_y dy + F_z dz)
Considering the given path, we parameterize it as r(t) = (x(t), y(t), z(t)), where:
x(t) = 2 + (3 - 2) t
= 2 + t
y(t) = 1 + (-1 - 1) t
= 1 - 2t
z(t) = -1 + (2 - (-1)) t
= -1 + 3t
We differentiate the parameterization with respect to t to find the differentials:
dx = dt
dy = -2dt
dz = 3dt
Now we substitute the parameterized values into the integral:
∫ F · dr = ∫ [(2xy + 3)dx + (x² - 4z)dy - 4ydz]
= ∫ [(2(2+t)(1-2t) + 3)dt + ((2+t)² - 4(-1+3t))(-2dt) - 4(1-2t)(3dt)]
Simplifying the integrand:
∫ F · dr = ∫ [(4 + 4t - 8t² + 3)dt + (4 + 4t + t² + 4 + 12t)(-2dt) - (4 - 8t)(3dt)]
= ∫ [(7 - 8t² + 4t)dt - (12 + 8t + t²)dt + (12t - 24t²)dt]
= ∫ [(7 - 8t² + 4t - 12 - 8t - t² + 12t - 24t²)dt]
= ∫ (-9 - 33t² + 8t)dt
Integrating term by term:
∫ F · dr = [-9t - 11t³/3 + 4t²/2] + C
Now we evaluate the integral at the limits of t = 2 to t = 3:
∫ F · dr = [-9(3) - 11(3)³/3 + 4(3)²/2] - [-9(2) - 11(2)³/3 + 4(2)²/2]
= [-27 - 99 + 18] - [-18 - 88/3 + 8]
= -108 - (-43/3)
= -108 + 43/3
= -324/3 + 43/3
= -281/3
To know more about line integral,
https://brainly.com/question/9812754
#SPJ11
g(x)=3x^7-2x^6+5x^5=x^4+9x^3-60x+2x-3, x(-2)
use synthetic division
Given the polynomial function is g(x) = 3x⁷ - 2x⁶ + 5x⁵ + x⁴ + 9x³ - 60x² + 2x - 3, and the given value is x = -2. We have to use synthetic division to find out the quotient of g(x) by (x + 2).
Before using the synthetic division method, we have to put the coefficient of each power of x in the order of descending powers of x.To do so, we have to rearrange the polynomial as: g(x) = 3x⁷ - 2x⁶ + 5x⁵ + x⁴ + 9x³ - 60x² + 2x - 3 = 3x⁷ - 2x⁶ + 5x⁵ + x⁴ + 9x³ + 0x² + 2x - 3.
We can now use synthetic division to evaluate g(x)/(x + 2).The following steps show how to divide using synthetic division:As shown in the above image, the remainder is 1 and the quotient is 3x⁶ - 8x⁵ + 21x⁴ - 43x³ + 85x² - 170x + 341. Therefore, the quotient of g(x) by (x + 2) is 3x⁶ - 8x⁵ + 21x⁴ - 43x³ + 85x² - 170x + 341.
To know more about polynomial function visit:
https://brainly.com/question/11298461
#SPJ11
Why is [3, ∞) the range of the function?
The range of the graph is [3, ∞), because it has a minimum value at y = 3
Calculating the range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The above graph is an absolute value graph
The rule of a graph is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain = All real values
Range = [3, ∞), because it has a minimum value at y = 3
Read more about range at
brainly.com/question/27910766
#SPJ1
2. A vat contains 15 black marbles, 10 white marbles, 20 red marbles, and 25 purple marbles. What is the probability that you will reach in and draw out a red or a white marble? ubles, B = 15
To find the probability of drawing a red or a white marble from the vat, follow these steps:
1. Determine the total number of marbles in the vat.
There are 15 black, 10 white, 20 red, and 25 purple marbles, which totals to:
15 + 10 + 20 + 25 = 70 marbles
2. Calculate the probability of drawing a red marble.
There are 20 red marbles and 70 marbles in total, so the probability of drawing a red marble is:
P(red) = 20/70
3. Calculate the probability of drawing a white marble.
There are 10 white marbles and 70 marbles in total, so the probability of drawing a white marble is:
P(white) = 10/70
4. Calculate the probability of drawing a red or a white marble.
Since these are mutually exclusive events, you can add the probabilities together to get the overall probability:
P(red or white) = P(red) + P(white) = (20/70) + (10/70)
5. Simplify the probability:
P(red or white) = 30/70 = 3/7
So, the probability of drawing a red or a white marble from the vat is 3/7.
To know more about probability visit:
https://brainly.com/question/31828911
#SPJ11
Human Blood Types Human blood is grouped into four types. The percentages of Americans with each type are listed below. 435 40 % 12% 5% Choose one American at random. Find the probability that this person a. Has type O blood b. Has type A or B c. Does not have type O or A
The probability of choosing an American having Type O blood is [tex]0.40[/tex], the probability of choosing an American with Type A or Type B blood is [tex]0.17[/tex], and the probability of choosing an American with neither Type O nor Type A blood is [tex]0.48[/tex].
Human blood types are classified into four major types: A, B, AB, and O. A person's blood type is determined by the presence of specific antigens (proteins) on the surface of red blood cells. The percentage of Americans with each blood type is listed in the problem as 40% Type O, 12% Type A, 5% Type B, and 43% Type AB or other types. To find the probability of selecting a person with a certain blood type from the US population, the percentage of people with that blood type is divided by 100.
a. The probability that a randomly chosen American has Type O blood is 0.40 (40%).
b. The probability that a randomly chosen American has Type A or Type B blood is 0.12 + 0.05 = 0.17 (12% + 5%).
c. The probability that a randomly chosen American does not have Type O or Type A blood is [tex]1 - (0.40 + 0.12) = 0.48[/tex].
Learn more about probability here:
https://brainly.com/question/31828911
#SPJ11
i need help
(Show your work.) P9 Use the Laplace transform method to solve the differential equation y" + 3y'-4y= 15et y(0) = 7, y'(0) = 5 (10)
Using Laplace Transform method, the solution of the differential equation y'' + 3y' - 4y = 15et, y(0) = 7, y'(0) = 5 is: `y(t) = (e^(-4t))(19 - 3t) + (5e^t) + (3/2)*t + 2`.
Taking the Laplace transform of both sides of the differential equation, we have`L(y'' + 3y' - 4y) = L(15et)`
Using the linearity of Laplace transform, we getL(y'') + 3L(y') - 4L(y) = L(15et)By property 3 of Laplace transform, we haveL(y'') = s^2Y(s) - sy(0) - y'(0) = s^2Y(s) - 7s - 5L(y') = sY(s) - y(0) = sY(s) - 7L(y) = Y(s)
SummaryThe Laplace Transform method was used to solve the differential equation y'' + 3y' - 4y = 15et, y(0) = 7, y'(0) = 5. The final solution was y(t) = (e^(-4t))(19 - 3t) + (5e^t) + (3/2)*t + 2.
Learn more about Laplace Transform click here:
https://brainly.com/question/29583725
#SPJ11