It is proven that the other nth roots of z can be found by multiplying the initial one by the nth roots of unity.
A complex number satisfying the equation [tex]z^{n-1} = 0[/tex] is known as the nth root of unity. There are about n nth roots of a unit, according to the fundamental theorem of algebra. We know that,[tex]1=e^{2\pi i}[/tex]. Then, the nth root is written as [tex]\omega=e^{2\pi i/n}[/tex].
The integer of powers of this root between 0 and n-1 provides the other nth roots. Then, the roots are [tex]1, \omega, \omega^2 ,\cdots \cdots, \omega^{(n-1)}[/tex]. Now, factorize the equation [tex]z^{(n-1)} = 0[/tex] we get the required identity as, [tex]z^{(n-1)} = (z- 1)(z^{(n-1)}+ z^{(n-2)} + \cdots \cdots+ z + 1) = 0[/tex].
This indicates that the equation [tex]1+\omega+ \omega^2+\cdots \cdots+ \omega^{(n-1)}[/tex] is true for all nth roots of unity other than 1.
Roots of unity also have the great quality of being periodic, which results from the fact that n = 1. It is equal to a power of that power mod n if the power is bigger than n.
When ω is a third root of unity, [tex]\omega^5 + \omega^4 + 1 = \omega^2 + \omega + 1 = 0[/tex].
To know more about complex numbers:
https://brainly.com/question/20566728
#SPJ4
a = 47.4 rounded to 1 DP
b = 0.19 rounded to 2 DP
Find the minimum of a - b
Answer:
47.21
Step-by-step explanation:
Subistitute:-47.4-0.19
Calculate the sum or difference:-47.21
If angle A=−170∘, what is the radian measure of A? Enter an exact fraction that contains the π symbol.
The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π
How to convert degrees to radians?When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Thus, since we want to find the radian measure of 170 degrees, it means that;
If 180° = π radians,
then; 170° = (170 * π)/180
= ¹⁷/₁₈π
Read more about degree to radians at; https://brainly.com/question/2032409
#SPJ1
I NEED HELP ASAP, I PROMISE WHOEVER IS CORRECT IS GOING TO GET BRAINLIST!
The numbers that correctly complete the two-way table are 100,70, 170, 80, 130, 210, 180,200, and 380 as shown in the attached chart.
How to calculate the number of sweatshirts per color and style?Total of sweatshirts= 380
Total with no hood= 210
Green sweatshirts= 180
Purple sweatshirts with no hood= 70
Based on this information we can conclude:
There are 170 sweatshirts with no hood (380-210= 170)There are 200 purple sweatshirts (380 - 180 = 200)There are 130 purple sweatshirts (200-70 = 130)There are 100 green sweatshirts with hood (170-70= 100)There are 80 green sweatshirts with hood (180-100 = 80)Learn more about two-way tables in https://brainly.com/question/29766382
#SPJQ
2. Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00. Carnuba's Car
Rental charges $.15 per mile and has a service of twenty dollars. At how many miles will the
charge for each company be the same?
The charge of each company will be the same at 40 miles.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let us suppose the miles travelled as x.
Given that:
Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:
C = 0.10(x) + 40
Carnuba's Car rental charges $.15 per mile and has a service of $20.
D = 0.15(x) + 20
The charge of both the companies would be equal when C = D:
0.10(x) + 40 = 0.15(x) + 20
40 -20 = 0.15x = 0.10x
20 = 0.5x
x = 20/ 0.5
x = 40
Hence, the charge of each company will be the same at 40 miles.
Learn more about equation here:
https://brainly.com/question/29657992
#SPJ1
the figure at the right is a regular octagon with the sign length s. Write two algebaric
The expression of the side length is 6y - 5
How to determine the expression of the side lengthThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Perimeter = 48y - 40
Number of sides = 8
The side length s can be calculated as
s =(48y - 40)/8
Evaluate the quotient
s = 6y - 5
Hence, the side length expression is 6y - 5
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
use theorem 2.1.13 to prove that if $f$ and $g$ are continuous functions with open domains $u f$ and $u g$, and if $g(u g)\subseteq u f$, then $f \circ g$ is continuous on $u g$
Since function f andg are continuous and u g subseteq u f, Theorem 2.1.13 states that f circ g is continuous on u g.
In accordance with Theorem 2.1.13, if two functions,f andg, are continuous on open domains [tex]$u f$[/tex]and [tex]$u g$[/tex] respectively, and $g(u g)subseteq u f, then $ circ g is continuous on u g. This is the case since the domain of f, which is u g is a subset of the domain of f, which is u g, and the composition of continuous functions is continuous. The composition of these two functions will be continuous onu g because both of these functions are continuous and u g subseteq u f.
Learn more about function here
https://brainly.com/question/29633660
#SPJ4
HELP ME ASAP! i need help rn
Answer: yes
Step-by-step explanation:
It's right angled if and only if A^2 + B^2 = C^2
- a^2 = (11-3^2 + 11-5^2) = (64 + 36) = 100
- b^2 = (6-3^2 + 1-5^2) = (9 + 16) = 25
a^2 + b^2 = 125 = sqrt(125)^2
i need help 10 divided by 75.10
quotient.
After divide, the value of quotient is 0.133.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
⇒ 10 divided by 75.10.
Now, We get;
⇒ 10 divided by 75.10
⇒ 10 ÷ 75.10
⇒ 0.133
Thus, The value of quotient after divide = 0.133
Learn more about the divide visit:
brainly.com/question/28119824
#SPJ1
Debbie shipped 2 packagesone weighed 2 pounds10 ounces the other weighed 4 pounds and12 ounces what is the total weight of The 2 packages
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
what is unitary method ?The unit tactic is a strategy for addressing issues that entails first figuring out the value of a particular unit, then increasing that value to figure out the needed value. Simply put, the unit method is employed to obtain a minimum unit value from a multiple that is supplied. For example, 40 pens may cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its homologue and reciprocal are equal in terms of mathematics, algebra, linear algebra, applied mathematics, or mathematics for matrices or operators.
given
1 pound = 16 ounces
for 2 packages
2 pounds 10 ounces + 4 pounds 12 ounces
6 pounds and 22 ounces
= 7 pounds 10 pounces
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
Please help! Systems of equation/matrix problem
5. TELEVISION During t
ring the summer, Manuel watches television M hours per day, Monday through Friday. Harry watches television H hours per day, Friday and Saturday. Ellen watches television E hours per day, Friday through
Sunday. Altogether, they watch television 37 hours each week. On Fridays, they watch a total of 11 hours of television.
If the number of hours Ellen spends watching television on any given day is twice the number of hours that Manuel
spends watching television on any given day, how many hours of television does each of them watch each day?
Answer:
see attached
Step-by-step explanation:
Patricia is making homemade snacks. Each snack requires 2.25 cups of almonds. Patricia buys 6 cans of almonds that each contain eight 1/3 cup servings. What is the maximum number of snack bags that Patricia can make with the almonds?
Answer: 7
Step-by-step explanation:
Patricia has 6 cans of almonds that each contain eight 1/3 cup servings, meaning that Patricia has a total of
6 cans x 8 servings x 1/3 cup = 16 cups of almonds
If she needs 2.25 cups of almonds, that would be equal to
16/2.25 = around 7.1
since you can't have a fraction of a snack bag, Patricia just has 7 snack bags.
which of the following is an integral element that defines sport and therefore distinguishes it from play and dramatic spectacle?
One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.
In sports, there are typically opponents or teams competing against each other to achieve a goal or win a match.
This competitive aspect is not present in play or dramatic spectacles, where the focus is typically on individual or group performance rather than competition against others.
Sports are defined as physical activities that involve a set of rules and are typically competitive in nature. They are typically organized and played by people in order to achieve a goal or win a match. Examples of sports include football, basketball, soccer, tennis, baseball, and golf.
Sports are also a form of recreation, entertainment, and physical activity. They can be played individually or in teams. They help to improve physical fitness, and mental health and also promote teamwork and social interaction.
Therefore, One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.
To know more about sports refer to:
brainly.com/question/30024802
#SPJ4
Jupiter has a radius of 44 ,423 miles. As the planet rotates on its axis, a point on its equator travels at 669,883 miles per day.
(a) Find the angular speed of a point on its equator in radians per day.
(b) Find the number of rotations the planet makes per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
Hey there!
Answers;
(a) 15 radians/day(b) Number of rotations = 2| Explanation |
For part (a):
[tex]v=669,883[/tex] [tex]miles/day[/tex]
[tex]r=44,423[/tex] [tex]miles[/tex]
[tex](a)V=rw[/tex]
[tex]w=\frac{v}{r}[/tex] [tex]=\frac{669883}{44423}[/tex][tex]=15.0796[/tex] [tex]radians/day[/tex]
[tex]15[/tex] [tex]radians/day[/tex]
For part (b):
[tex]Circumference=2\pi r[/tex]
[tex]2*3.14*44423[/tex]
[tex]278976*44[/tex]
Number of rotations = [tex]\frac{669883}{278976*44}[/tex] = [tex]2*40[/tex] ⊥ ≈ [tex]2[/tex]
Hence:
(a) [tex]15[/tex] [tex]radiations/day[/tex]
(b) Number of rotations = [tex]2[/tex]
___________________________________________
Hope this helps! If you mark Brainliest, TYSM! :D
solve for an unknown quantity in a two-variable linear equation, given one of the values. determine a two-variable linear equation that represents a scenario, identifying constraints on the variables in terms of the context.
A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.
If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.
2x+5y = 19
The x intercept is when y=0,
then, 2x+ (5×0) = 20
2x = 20, x=10
y intercept is when x=0, then
2×0 + 5y = 20
5y = 20, y= 20/5 =4
So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.
If one the values are given , we can substitute it in the equation to calculate the other variable.
In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.
2x + (3×2) = 12
2x = 12-6
2x = 6
x =3
So when y=2 then x=3.
Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.
So, we can solve a two variable linear equation through different ways.
For more information regarding two variable linear equations, kindly refer
https://brainly.com/question/24085666
#SPJ4
determine if one of the given vectors is in the span of the other vectors. (hint: check to see if the vectors are linearly dependent, and then appeal to this theorem.) u=[1,7,8,3] v=[-1,3,5,3]
w=[4,8,6,0]
a. None of the vectors is in the span of the other vector.
b. One of the vectors is in the span of the other vector
Out of the given vectors is in the span of the other vectors, b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.
If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.
To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent. We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.
To know more about vectors refer to the link brainly.com/question/13322477
#SPJ4
Can anyone help??
Which line is parallel to y=-4x+11 and goes through (2,1)? Hint: use point slope form
A)y-1=-4x(x-2)
B)y-1=-1/4(x-2)
C)y-1=4(x-2)
D)y-2=-4(x-1)
(I’m trying to do test corrections :c )
A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).
What is the point-slope form?Mathematically, the point-slope form of a line is modeled by this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the given linear equation y = -4x + 11, the slope is given by:
y = -4x + 11
m₁ = -4
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ (m represents the slope.)
At point (2, 1), an equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -4(x - 2)
Read more on slope of parallel lines here: brainly.com/question/28427398
#SPJ1
According to the United States Department of Health and Human Services, the mean height for Americans is 1.757m for men and 1.618 m for women3. The standard deviation is 0.074m for men and m for women.
1)
What -score corresponds to a man who is 1.853m tall?
A man who is 1.853m tall would have a z-score of 1.297.
What is the z-score?Generally, To find the z-score for a man who is 1.853m tall, we need to use the formula for a z-score:
= (x - mean) / standard deviation.
In this case, the mean height for men is 1.757m and the standard deviation is 0.074m, so the z-score for a man who is 1.853m tall would be:
(1.853 - 1.757) / 0.074 = 1.297297297
Read more about z-score
https://brainly.com/question/15016913
#SPJ1
In 2015, as part of its 10th high school reunion, the class of 2005 held a reception at the high school. In an informal survey, the principal of the high school asked 50 of the attendees about their income. The principal computed the mean income of the 50 attendees to be $148,535. In an article published by the local newspaper, the principal was quoted as stating, "The members of our class of 2005 enjoyed resounding success. Last year, they had a mean income of $148,535!"
Part A: What is a statistical advantage of using the median of the reported incomes, rather than the mean, as the estimate of the typical income? (4 points)
Part B: The principal felt the individuals who attended the reception may be different from the class as a whole. A more detailed survey of the class was planned to determine a better estimate of income. The staff developed two methods based on the available funds to carry out the survey.
Method 1: Send out an e-mail to all 2,476 members of the class and ask them to complete an online form. The staff estimates that at least 500 members will respond.
Method 2: Select a simple random sample of members of the class and contact the selected members directly by phone. Follow up to ensure all responses are obtained. Because method 2 requires more time than method 1, the staff estimates only 100 members of the class can be contacted using method 2.
Which of the two methods would you select for estimating the average yearly income of all 2,476 members of the class of 2005? Explain your reasoning by comparing the two methods and by describing the effect of each method on the estimate.
Method 2 is the best option for estimating the average yearly income of the class of 2005.
What type of sampling technique is used?I would select Method 2 for estimating the average yearly income of all 2,476 members of the class of 2005. Method 2 involves selecting a simple random sample of members of the class and contacting them directly by phone. This method guarantees that the sample will be representative of the entire population and thus provides the best estimate of the average income of the class. By randomly selecting the sample, we can be sure that the sample will be unbiased and the results will be more reliable. Method 1, on the other hand, involves sending an e-mail to all 2,476 members of the class and asking them to complete an online form. Although this method is easier and less time-consuming, it does not guarantee a representative sample. If only 500 people respond, it is possible that the sample will not be representative of the entire population and thus, the results will not be accurate. Overall, It will ensure that the sample is representative of the entire population and that the results are unbiased and reliable.To learn more about the sampling theory refer to:
https://brainly.com/question/28016369
#SPJ1
Find the line passing through the point of intersection of the lines xâ3y+1=0,2x+5y=9
and
(i) parallel to yâ2x=0
(ii) perpendicular to 2x+yâ5
the equation of the required line is 3xâ2y+1=3x1â2y1+1.
(i) We are given the parallel line of the given equation, that is yâ2x=0.
So, the equation of the required line will be yâ2x=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get
y1â2x1=c
or, c=y1â2x1
Hence, the equation of the required line is yâ2x=y1â2x1.
(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.
So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get
3x1â2y1+1=c
or, c=3x1â2y1+1
Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
6= 1/v+2
Solve for V
simplify your answer as much as possible
Answer:
your question is 6=1/v+2
Step-by-step explanation:
6-2=1/v
4v=1
v=1/4
State if the three numbers can be the measures of the sides of a triangle. 7, 10, 10
Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.
Can be the measures of the sides of a triangle?Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:
A + B > C
A + C > B
C + B > A
As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.
if we use:
A = 7
B = 10
C = 10
Then we get:
7 + 10 > 10 ---> 17 > 10
7 + 10 > 10 ---> 17 > 10
10 + 10 > 7 ---> 20 > 7
All the ienqualities are true, thus, these can be the measures of the sides of a triangle.
Learn more about triangles at:
https://brainly.com/question/2217700
#SPJ1
Area:
10
Area:
?
Area:
40
Answer: THE CORRECT ANSWER IS 30
Step-by-step explanation:
suppose that sum a n and sum b n are series with positive terms. prove that if lim n -> infty a n/b n does not exist, and sum b n diverges, then sum a n also diverges
The comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.
Suppose that [tex]$\sum_{n=1}^{\infty} a_{n}$ and $\sum_{n=1}^{\infty} b_{n}$[/tex] are series with positive terms. We assume that does not exist and that [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex]diverges.
To prove that [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] also diverges, we will use the comparison test. Since [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex] diverges, we can find a number M such that [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges. Since [tex]$\lim_{n\rightarrow \infty} \frac{a_{n}}{b_{n}}$[/tex] does not exist, we can find a number N such that for all [tex]$n \geq N$, $\frac{a_{n}}{b_{n}} > 1$[/tex].
Now, for any [tex]$n \geq \max \{M,N\}$[/tex], we have [tex]$\frac{a_{n}}{b_{n}} > 1$[/tex]. Thus, [tex]$a_{n} > b_{n}$[/tex]. By the comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.If the ratio of two series with positive terms,[tex]$\sum_{n=1}^{\infty}a_n$[/tex] and [tex]$\sum_{n=1}^{\infty}b_n$[/tex], does not converge to a limit as n approaches infinity and [tex]$\sum_{n=1}^{\infty}b_n$[/tex] diverges, then [tex]$\sum_{n=1}^{\infty}a_n$[/tex] must also diverge.
Learn more about comparison test here:
https://brainly.com/question/29971306
#SPJ4
The top selling brand of vape machines sold 10000 units at $89 per unit in 2018. what is their market share if the vape machine market had sales of $1.4M?
The market share of the vape machine market had sales of $1.4M is given as 63.57%.
How to solve for the market share of the vape machineTo calculate the brand's market share, you would need to divide the brand's sales by the total sales of the market and then multiply by 100 to get the percentage.
In this case, the brand's sales are 10000 units x $89/unit = $890,000.
So the market share would be:
$890,000 / $1,400,000 x 100 = 63.57%.
Read more on market share here: https://brainly.com/question/25309906
#SPJ1
A marble statue of height h1metres is mounted on a pedestal. The angles of elevation of the top and bottom of the statue from a point h2metres above the ground level are αandβrespectively. Show that the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.
So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.
To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.
From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.
We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.
Let's call the height of the pedestal as "h3"
So we can write the following equations:
h1/((h3+h1)-h2)= tan(α)
h1/((h3)-h2)= tan(β)
By solving the above equations we can get the value of h3 which is the height of the pedestal.
((h1−h2)tanβ+h2tanα)/tanα−tanβ
This is the final equation which gives the height of the pedestal.
To learn more about angles of elevation
Visit; brainly.com/question/21137209
#SPJ4
X^2 - y^2
—————-
3x - Зу
Step-by-step explanation:
x² - y² = (x + y)(x - y)
3x - 3y = 3(x - y)
(x + y)(x - y) / (3(x - y)) = (x + y)/3
Answer:
x^2 - y^2
_______
3x - 3y
(x+y) (x-y)
_______ { (x-y) (x-y) cancels out}
3(x-y)
(x+y)
____
3
Hope this will help you...!!!!
two expressions that are equivalent to 3f
The two expressions are written as :
3f + 2f + 4s 5f + 4sHow to solve for the expressions that are equivalent to 3f+4s+2f3f+4s+2f this expression that we have here is a mathematical expression that we can combine by making use of the commutative addition.
We would have the first expression when we write the equation as:
3f+4s+2f = 3f + 2f + 4s
We would have the second expression when we write the equation as
5f + 4s
This is the solution of the expression.
Read more on mathematical expressions here: https://brainly.com/question/723406
#SPJ1
two expressions that are equivalent to 3f+4s+2f ?
State the critical values for a one-sample t test given the following conditions:
1. Two-tailed test, a = .05, n = 12
2. One-tailed test, lower-tail critical, a = .01, df = 15
3. Two-tailed test, a = .01, df = 26
4. One-tailed test, upper-tail critical, a = .05, n = 30
Use the values listed in the table; do not round. Be sure to include the appropriate signs in your answers:
• if positive --> + and the value
. if negative --> - and the value
if both --> +/- and the value
(Privitera, 2019, p. 250, #14)
The critical values for a one-sample t test given the following conditions are +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.
What is value?Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.
1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729
To know more about value click-
https://brainly.com/question/843074
#SPJ1
If a rock is thrown upward on the planet Mars with a velocity 16 m/s, its height in meters t seconds later is given by y = 16t − 1.86t2. (Round your answers to two decimal places.)
(a)Find the average velocity (in m/s) over the given time intervals:
A. [1,2]
B. [1,1.5]
C. [1,1.1]
D. [1,1.01]
E. [1,1.001]
The average velocity (in m/s) over the given time intervals is [1,2]
Part A.
Keep in mind that the formula for average velocity is
(Y2 - Y1)/V avg = displacement/time interval (t2 - t1)
Given that the rock's position at time t is determined by:
y = 16t - 1.86*t^2
Part 1
for the time period [1, 2]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*2 - 1.86*22 = 24.56 m when t2 = 2 sec.
So
average Velocity = (24.56 - 14.14)/(2 - 1) (2 - 1) = 10.42 m/s V avg
Part 2.
for the time period [1, 2]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.5 - 1.86*1.52 = 19.815 m when t2 = 1.5 sec.
So,
average Velocity = (19.815 - 14.14)/(1.5 - 1) (1.5 - 1) = 11.35 m/s V avg
Part 3.
During the period [1, 1] .1]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.1 - 1.86*1.12 = 15.3494 m when t2 = 1.1 sec.
So,
average Velocity = (15.3494 - 14.14)/(1.1 - 1) (1.1 - 1)
average Velocity = 12.094 m/s and equals 12.09 m/s (In two decimal places)
Part 4.
During the period [1, 1] .01]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.01 - 1.86*1.012 = 14.262614 m when t2 = 1.01 sec.
So,
average Velocity = (14.262614 - 14.14)/(1.01 - 1) (1.01 - 1)
12.26 m/s and V avg = 12.2614 m/s (In two decimal places)
Part 5.
During the period [1, 1] .001]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.001 - 1.86*1.0012 = 14.15227814 m when t2 = 1.001 sec.
So,
average Velocity = (14.15227814 - 14.14)/(1.001 - 1) (1.001 - 1)
12.28 m/s V avg = 12.27814 m/s (In two decimal places)
Part B.
Rock's immediate velocity will be determined by:
d[16t - 1.86t2]/dt = V= dy/dt
Velocity = 16*1 - 2*1.86*t
time = 1 second,
Velocity = 16 - 2*1.86*1
average velocity at time t is equal to V = 12.28 m/s.
For more such questions on velocity, Refer:
https://brainly.com/question/25749514
#SPJ4
What is the measure of n?
28
m
7
n = [?]
Give your answer in simplest form.
The measure of the side length n is equal to 14 for the right triangle.
How to evaluate the length of n in the right triangleConsidering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;
cosθ = m/35
for the smaller right triangle with adjacent 7 and hypotenuse m
cosθ = 7/m
m/35 = 7/m
m² = 245 {cross multiplication}
m = √245 = 7√5 {take square root of both sides}
(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}
245 = 49 + n²
n² = 245 - 49 {collect like terms}
n² = 196
n = √196 {take square root of both sides}
n = 14
Therefore, the measure of the side length n is equal to 14 for the right triangle
Know more about triangle here:https://brainly.com/question/2217700
#SPJ1