there exists an integer that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers ∃x∈ℤ: x > 5 ∧ x² < 40
1. Start by writing down the equation: x² < 40
2. Take the square root of both sides of the equation to isolate the variable x: √x² < √40
3. Simplify both sides of the equation: x < √40
4. Check that the result makes sense: x < 6.3
5. Take the integer part of the result: x < 6
6. Since the requirement is that x is greater than 5, the answer is x = 6.
We start by writing the equation x² < 40 and then take the square root of both sides to get x < √40. We check that the result is reasonable and then take the integer part of the result to get x < 6. Since the requirement is that x is greater than 5, the answer is x = 6. To confirm, we can calculate that x² = 36 which is smaller than 40, and indeed, 6 is greater than 5. Therefore, the integer that is greater than 5 and whose square is smaller than 40 is 6. This can be expressed mathematically as ∃x∈ℤ: x > 5 ∧ x² < 40 which translates to: There exists an integer x such that x is greater than 5 and the square of x is smaller than 40.
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#20 i need help with this question
Answer:
Step-by-step explanation:
tha answer is 69
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 52 minutes of calls is $14.06 and the monthly cost for 78 minutes is $17.18. What is the monthly cost for 73 minutes of calls?
Answer:
16.58
Step-by-step explanation:
as you can see from the graph, there's a monthly fixed cost on Y axis. so you need to figure out 1: how much per minute. and 2. the monthly fixed fee. you've got 2 scenarios = 2 equations, for 2 variables. so you can solve both.
assume: x=per min rate; m = monthly fixed cost.
1. 14.06 =52x+m
2. 17.18 =78x+m
use equation 2 minus equation 1 & you get
3.12 = 26 x. so x = 0.12
plug this into equation 1: 14.06 =52*0.12 +m so m=7.82
now for 73 mins the cost = 73*0.12 +7.82 =16.58
scenario 3-6 a researcher wishes to study how the average weight y (in kilograms) of children changes during the first year of life. he plots these averages versus the age x (in months) and decides to fit a least-squares regression line to the data with x as the explanatory variable and y as the response variable. he computes the following quantities. r
The slope of the least-squares line is: 0.30
The correct answer is an option (A)
We have following information:
correlation between X and Y (r) = 0.9
mean of the values of X ([tex]\bar{X}[/tex]) = 6.5
mean of the values of Y ([tex]\bar{Y}[/tex]) = 6.6
the standard deviation of the values of X ([tex]S_{X}[/tex]) = 3.6
the standard deviation of the values of Y ([tex]S_{Y}[/tex]) = 1.2
We know that the slope of a least squares regression can be calculated by the formula,
slope m = r [tex]\frac{S_\bar{Y}}{S_\bar{X}}[/tex],
where, r is the correlation coefficient
Let us assume that for given scenario, m represents the slope of of the least-squares line.
Using above formula,
⇒ m = r [tex]\frac{S_\bar{Y}}{S_\bar{X}}[/tex]
⇒ m = 0.9 × [tex]\frac{1.2}{3.6}[/tex]
⇒ m = 0.9 × 0.333
⇒ m = 0.2997
⇒ m ≈ 0.3
Thus, the slope is 0.30
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The complete question is:
A researcher wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least- squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities.
r = correlation between X and Y = 0.9
X = mean of the values of X = 6.5
Y = mean of the values of Y = 6.6
S_(X) = standard deviation of the values of X = 3.6
S_(Y) = standard deviation of the values of Y = 1.2
The slope of the least-squares line is: ?
A. 0.30 B. 0.88 C. 1.01 D. 2.70 E. 3.00
Claire is 5 feet tall and casts a 96 inch shadow. How tall is her friend Steve if his shadow is 1.5 inches shorter than hers?
Answer:
4.725 ft
Step-by-step explanation:
well if i see this right the shadow for claire is 1.60x the person's hight
PLEASE HELP ME IT’S URGENT
The images of the points after the transformation are (6, 1), (3, 6), (5, 2) and (-8, -4)
How to determine the coordinates of the point?r(x-axis) o T(2, -3) (4, 2)
This implies that we reflect the point (4, 2) across the x-axis and then translate it by (x + 2, y - 3)
Mathematically, this is represented as
Image = (x + 2, 3 - y)
Substitute the known values in the above equation, so, we have the following representation
Image = (4 + 2, 3 - 2)
Evaluate
Image = (6, 1)
T(2, -5) o R 90 CCW (4, 2)
This implies that we translate the point (4, 2) by (x + 2, y - 5) and then rotate it by 90 degrees counterclockwise
Mathematically, this is represented as
Image = (5 - y, x + 2)
Substitute the known values in the above equation, so, we have the following representation
Image = (5 - 2, 4 + 2)
Evaluate
Image = (3, 6)
T(1, 4) o r(y-axis) (4, 2)
This implies that we translate the point (4, 2) by (x + 1, y + 4) and then reflect it across the y-axis
Mathematically, this is represented as
Image = (x + 1, 4 - y)
Substitute the known values in the above equation, so, we have the following representation
Image = (4 + 1, 4 - 2)
Evaluate
Image = (5, 2)
r(y-axis) o T(1, 4) (4, 2)
This implies that we reflect the point (4, 2) across the y-axis and then translate it by (x + 4, y + 2)
Mathematically, this is represented as
Image = (-x - 4, y + 2)
Substitute the known values in the above equation, so, we have the following representation
Image = (- 4 - 4, 2 + 2)
Evaluate
Image = (-8, 4)
Hence, the image is (-8, -4)
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Solve the system by elimination 8x+3y=4 2x+y=2 what is the solution
The solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4
How to evaluate for the solutions of the equations by eliminationwe shall write the equations as:
8x + 3y = 4...(1)
2x + y = 2...(2)
multiply equation (2) by 3 to get equation (3)
3(2x + y) = 3 × 2
6x + 3y = 6...(3)
subtract equation (1) from (3) to eliminate y
6x + 3y - 8x - 3y = 6 - 4
-2x = 2
divide through by -2
x = -1
put the value -1 for x in equation (2) to get y
2(-1) + y = 2
-2 + y = 2
y = 2 + 2 {add 2 to both sides}
y = 4
Therefore, the solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4.
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–35 –
–20 = N please need k to
Answer: - 15 = N
Step-by-step explanation:
2 negatives make a positive so it would be -35 + 20 = -15 Have a nice day ;)
consider the following input-output table. p q r s 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 the output column, s, was created from the student id 21444368 using the algorithm: if id digit n (left-to-right) is an even integer, place a 0 in s, row n (top-down) if id digit n (left-to-right) is an odd integer, place a 1 in s, row n (top-down) create a similar table, but with s reflecting the result of the algorithm applied to your student id (do this on scratch paper). on the quiz essay: record your student id, id
The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S.
Student ID: 81725225
P Q R S
1 1 1 0
1 1 0 1
1 0 1 1
0 1 0 0
0 0 1 1
0 1 1 0
0 0 0 1
Student ID: 81725225
P: The first digit of my student ID is 8 so it is an even integer, therefore I place a 0 in row 1 of column P.
Q: The second digit of my student ID is 1 so it is an odd integer, therefore I place a 1 in row 2 of column Q.
R: The third digit of my student ID is 7 so it is an odd integer, therefore I place a 1 in row 3 of column R.
S: The fourth digit of my student ID is 2 so it is an even integer, therefore I place a 0 in row 4 of column S.
The resulting table is:
P Q R S
1 1 1 0
1 1 0 1
1 0 1 1
0 1 0 0
0 0 1 1
0 1 1 0
0 0 0 1
The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S. The same algorithm was applied to my student ID 81725225, resulting in the table shown above.
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carrie is flying on two different airlines with a heavy bag both airlines have the same weight limit by charge different fees the first airline charges $25 checked bag fee plus an additional four dollars for every pound that the bag is over the weight limit with the second airline and the price is three dollars per pound over the weight limit and addition to a $28 fee for checking the bag Carrie ended up paying the exact amount and baggage fees at the two airlines how many pounds over the limit was Carrie’s bag how much did she have to pay in fees for each airline
Answer: Let x be the weight of the bag over the limit in pounds.
We know that both airlines have the same weight limit and Carrie paid the same baggage fee at each airline, so we can set up the following equation:
25 + 4x = 28 + 3x
Solving for x:
x = 25
So, Carrie's bag was 25 pounds over the weight limit.
To find the fee for each airline, we can substitute x into the equations for the fees:
Fee for the first airline: 25 + 4(25) = $125
Fee for the second airline: 28 + 3(25) = $103
Therefore, Carrie paid $125 in fees for the first airline and $103 in fees for the second airline.
Step-by-step explanation:
which has the lowest price per unit.
$23.35 per 6.5 lbs.
$31.60 per 8 lbs.
Tim+is+attempting+to+bike+a+12+mike+race+he+knows+at+every+third+of+the+race+he+will+need+to+take+a+break+to+stretch+his+leg+how+many+miles+wo
Answer:
he takes a stretch every 4 miles
Step-by-step explanation: 12/3 = 4
Select the figure with an angle of 300°
on a circle in standard position.
(a)
An angle in standard position with terminal side at five-sixths of a full revolution counterclockwise.
(b)
An angle in standard position with terminal side at one-twelfth of a full revolution counterclockwise.
(c)
An angle in standard position with terminal side at one-third of a full revolution counterclockwise.
(d)
An angle in standard position with terminal side at two-thirds of a full revolution counterclockwise.
Note that the figure with an angle of 300° on a circle in standard position is: "An angle in standard position with the terminal side at two-thirds of a full revolution counterclockwise." (Option D)
What is an Angle in Standard Position?A standard position angle is one measured counterclockwise from the positive x-axis in a coordinate plane.
This signifies that the angle's starting side is on the positive x-axis, while the angle's terminal side is in the first or fourth quadrant. The angle's vertex is placed at the origin.
Angles are commonly measured in degrees or radians, with a full rotation being comparable to 360 degrees or 2 radians. Angles may now be readily graphed and compared to one another in a coordinate plane.
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4 2/3 - 3/4 answer? Please help me anwser this
Answer: 3 11/12
Step-by-step explanation:
Rewrite the equation with the parts seperated:
4 + 2/3 − 3/4
Find the LCD of 2/3 and 3/4
(Which is 12)
Keep going
8/12−9/12= −1/12
Finally, subtract 4 − 1/12 to get 3 11/12
Hope this helps!
4. For a process quality characteristics, the specification limits are 0.4037 +/- 0.0013 (that is from 0.4024 to 0.4050). The following data gives the data for 14 measurement data sets, each data set is a subgroup of 5 measurement. The value is recorded in the units of 0.0001 (that is, the specification limit will be considered 24 to 50) Based on the following data, compute Cp,Cpk,Pp and Ppk.(Use MINITAB is ok) and determine if the capability of the process. Subgroup Subgroup # 1 2 3 4 5 # 1 2 3 4 5 . 1 36 35 34 33 32 34 28 35 34 38 . 2 31 31 34 32 30 36 35 37 34 33 . 3 30 30 32 30 32 30 37 33 34 35 . 4 32 33 33 32 35 38 31 33 33 33 . 5 32 34 37 37 35 33 30 34 33 35
If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.
To calculate Cp, Cpk, Pp, and Ppk using MINITAB, you would need to input the data into the software and run the appropriate statistical analysis.
Cp and Cpk are measures of a process's capability, they are calculated as follows:
Cp = (USL - LSL) / (6*σ)Cpk = min(Cpu, Cpl)Where,
USL and LSL are the upper and lower specification limitsσ is the standard deviation of the process.Pp and Ppk are similar to Cp and Cpk, but they are calculated using the range of the data instead of the standard deviation.
Pp = (USL - LSL) / (4*R)Ppk = min(Ppu, Ppl)Where R is the range of the data.
If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.
It is worth noting that Capability analysis can only be performed on stable and in-control processes. If the process is not in control, analyzing process capability is not meaningful.
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Sophie is a dog that loves to play catch. Unfortunately, she isn't very good, and the probability that she catches a ball is only 0.2. Let x be the number of tosses required until Sophie catches a ball. (a) Does x have a binomial or a geometric distribution? (b) What is the probability that it will take exactly two tosses for Sophie to catch a ball? P(exactly two tosses) (c) What is the probability that more than three tosses will be required? P(more than three tosses)
X has a geometric distribution because it is the number of trials (tosses) required until a success (catching the ball) occurs.
b) The probability that it will take exactly two tosses for Sophie to catch a ball is P(x=2) = (0.2)(0.8)^1 = 0.16. This is calculated by multiplying the probability of success (0.2) by the probability of failure (0.8) raised to the power of the number of trials (2-1=1)
c) To find the probability that more than three tosses will be required, we need to find the probability that Sophie does not catch the ball on the first three tosses and then catch it on the fourth toss.
This can be found by summing the probabilities of Sophie not catching the ball on the first three tosses (0.8^3 = 0.512) and Sophie catching the ball on the fourth toss (0.8^3*0.2 = 0.1024). The probability that more than three tosses will be required is P(x>3) = 1 - P(x≤3) = 1 - (0.512 + 0.1024) = 0.3856.
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A company is expanding its team at a rate of 10% per year. 17 a) Calculate how many members of staff there will be after 1 year if there are initially 200 members of staff.
Step-by-step explanation:
If a company is expanding its team at a rate of 10% per year, and it currently has 200 members of staff, we can calculate the number of staff after 1 year using the formula:
number of staff after 1 year = 200 + (10/100) * 200
number of staff after 1 year = 200 + 20
number of staff after 1 year = 220
So, there will be 220 members of staff after 1 year if there are initially 200 members of staff.
For the rectangular parking area of the shopping
center shown, which one of the following equations
says that the area is 30,000 yd² ?
A. x(4x +300) = 30,000
B. x+(4x +300)=30,00
Equation
(Type A, B, C, or D.)
says that the area is 30,000 yd².
CO
C. 2x + 2(4x + 300) = 30,000
D. x² (4x+300)² = 30,000²
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For the rectangular parking area of the shopping center shown, an equation which says that the area is 30,000 yd² is: A. x(2x + 200) = 30,000.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.From the information provided about the rectangular parking area of the shopping center shown in the image attached below, we have the following dimensions:
Length = x
Width = 2x + 200
Substituting the given points into the area of rectangle formula, we have the following;
30,000 = x × (2x + 200)
30,000 = x(2x + 200) ⇒ (required equation).
30,000 = 2x² + 200x.
2x² + 200x - 30,000 = 0.
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A liter of petrol cost 93 for an equation to find the cost in pound of any number of liter of petrol
The equation for finding cost y for x liters of petrol is y = 93x
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, A liter of petrol cost £93,
Since, the unit rate of the petrol is £93 per liter
If we say let x be the number of liters we need, the total cost will have to pay will be = 93x
And, if total cost is y, then,
y = 93x
Hence, the equation for finding cost y for x liters of petrol is y = 93x
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PLEASE HELP ASAP!!!
Mrs. Lopez needs 40 ounces of sweetened milk to make flans. She has 24 ounces. Which equation shows how many more ounces of sweetened milk Mrs. Lopez needs to make flans?
Answer: As Mrs Lopez required 40 ounce
Step-by-step explanation:
2 x – 3 y = 7
–4 x + y = –5
What is the x -value of the solution to this system of equations?
Answer:
x = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
2x - 3y = 7 → (1)
- 4x + y = - 5 → (2)
multiplying (2) by 3 and adding to (1) will eliminate y
- 12x + 3y = - 15 → (3)
add (1) and (3) term by term to eliminate y
- 10x + 0 = - 8
- 10x = - 8 ( divide both sides by - 10 )
x = [tex]\frac{-8}{-10}[/tex] = [tex]\frac{4}{5}[/tex] (= 0.8 )
Please help me on this
Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (6,0) and (0,-8) . We know that slope can be calculated by ,
[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta [/tex]
[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
[tex]\longrightarrow m =\dfrac{0-(-8)}{6-0}\\[/tex]
[tex]\longrightarrow m =\dfrac{8}{6}\\ [/tex]
[tex]\longrightarrow m =\dfrac{4}{3}\\ [/tex]
[tex]\longrightarrow \underline{\underline{ m = 1.\bar{3}}}[/tex]
And we are done!
9b² – 100
Factor it
What is the solution to this equation: 42 +82=²? (Round answer to the nearest tenth.)
O c= 8.9
O e = 12
Oc=6.3
O c=3.5
The solution to this equation: 42 +82=x² is x = 12.
What is square number?A square number, also known as a perfect square, is an integer that is the square of another integer; in other words, it is the result of multiplying another integer by itself. For instance, 9 is a square number because it equals 32 and can be written as 3 3.
Instead of the product n n, the equivalent exponentiation n2, which is typically pronounced "n squared," is used to represent a number's square. The name of the shape is where the term "square number" originated. The area of a unit square (1 × 1) is the unit of area.
The solution to this equation: 42 +82=x²
x = √(42 +82)
x = √(144)
x = 12
Thus, The solution to this equation: 42 +82=x² is x = 12.
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for each limit in exercise 55-64 use graphs and algebra to approximate the largest delta or the smallest magnitude n taht corresponds to the given value of epsilon or m, according to the appropriate formal limit definition
The largest δ value of the given limit [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000 is calculated. The required δ value is [tex]\delta=\sqrt{1+10^{-3}}-1[/tex].
When no values are defined, a limit is used to assign values to certain functions. It is possible to assess the limits using algebraic techniques. A collection of guidelines for manipulating limits when using other operators is known as the algebra of limits. Given the expression [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000. When x>1, we write this expression as,
[tex]\begin{aligned} \frac{1}{x^2-1}& > 1000\\x^2-1& < 1000^{-1}=10^{-3}\\x^2& < 10^{-3}+1\\x& < \sqrt{1+10^{-3}}\end{aligned}[/tex]
Now, choosing, [tex]\delta=\sqrt{1+10^{-3}}-1[/tex] when we have δ > 0. Therefore, [tex]\sqrt{1+10^{-3}} > 1[/tex]. Then, [tex]x\in(1, 1+\delta)[/tex]. This is given by,
[tex]\begin{array}{ccc}1& < x& < 1+\delta\\1& < x& < \sqrt{1+10^{-3}}\end{array}[/tex]
This implies, [tex]\frac{1}{x^2-1} > 1000=M[/tex].
Therefore, the largest δ value will be [tex]\sqrt{1+10^{-3}}-1[/tex].
The complete question is -
For each limit, use graphs and algebra to approximate the largest δ or the smallest magnitude N that corresponds to the given value of ∈ or M, according to the appropriate formal limit definition.
[tex]\lim_{x\to 1^+} \frac{1}{x^2-1}=\infty[/tex], M=1000, find largest δ > 0.
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What is the slope of the following linear graph 2/3 -2/3 3/2 -3/2
The slope of following points (3, 3) and (6,1) is -2/3 .
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
Given points are (3, 3) and (6,1)
we know that slope = y2-y1 / x2-x1
y2-y1 = 1-3
The difference of y -intercept is -2
= -2
x2-x1 = 6-(3)
= 6-3
The difference of x-intercept is 3
= 3
So, slope could be y2-y1 / x2-x1 that is -2/3.
Therefore, The slope of following points (3, 3) and (6,1) is -2/3 .
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Will Mark brainliest
Write an equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation.
(3, - 2) ; y = 2/3x + 4
An equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation is y=2/3 x²+4x
How to find the equation?A mathematical equation is a formula that uses the equals sign ('=') to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation in English is any well-formed formula consisting of two expressions related by an equals sign, while an equation in French is defined as containing one or more variables.
step 1
y=2/3+4
y=2/3 x²+4x
y=m x+ b
step 2
y= y coordinate
m=slope
x=x coordinate
b=y intercept
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14. Calculate the x-intercepts of the equation by factoring:
8x²-16x = 0
Add 4x +1
To
5x+6
Write the following as an algebraic expression. Simply if possible
Answer:
9x + 7
Step-by-step explanation:
Add 4x + 1 to 5x + 6
in an algebraic expression is:
4x + 1 + 5x + 6
To simplify, combine like terms. This means add the x terms together and add the constants (plain number- - the 1 and 6) together.
4x + 1 + 5x + 6
= 4x + 5x + 1 + 6
= 9x + 7
Label The Missing angle measures for this triangle.
The measure of the missing angles are 100° and 30°
What is a triangle?A polygon with three vertices, angles and sides.
Given is a triangle XYW, whose side WZ is extended to the point z,
We know that,
The sum of two opposite interior angles of a triangle is equal to the measure of exterior angle,
∠ 1 + 50° = 150°
∠ 1 = 100°
We know that, sum of the interior angles of a triangle is 180°
∠ 1 + ∠ 2 + 50° = 180°
150°-180° = ∠ 2
∠ 2 = 30°
Hence, the measure of the missing angles are 100° and 30°
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Find the equation for the plane through Po(-4,-3,8) perpendicular to the following line.
x = -4+t, y=-3-3t, z= -4t, -∞
The equation of plane is x - 3y - 4z = 27.
What method can be used to determine the equation of a plane that is perpendicular to a vector?a plane produced by the application of vectors perpendicular to a normal. The implication of this is that, given a vector a, b, c, we may deduce that all planes perpendicular to it have the form ax+by+cz=d and that any surface with this form is a plane perpendicular to a, b, c.
The equation for a plane perpendicular to a given line with direction ratios a, b, and c> and passing through a point is a(x-x1) + b(y-y1) + c(z-z1) = 0. (x1, y1, z1).
The equation of the plane traveling through the points x, y, and z on a plane perpendicular to the line whose parametric equation is provided
Equation of a plane through the point (-4,-3,8) is
a(x - 4) + b(y - 3) + c(z + 8) = 0
Since it is perpendicular to the line :
x = -4+t, y=-3-3t, z= -4t,
t = x + 4 = -y - 3 / 3 = -z/4
therefore coefficients a, b, c must be proportional to 1, - 3 & (-4) respectively.
Therefore, putting the values of a, b & c in eq.(1), we get the required equation of the plane as ;
λ(x - 4) -3 λ(y - 3) - 4λ(z + 8) = 0 (λ is a constant)
⇒ x - 4 - 3y + 9 -4z - 32 = 0
⇒ x - 3y - 4z = 27
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