The rate of change of the side length of the cube with respect to time, at the moment when S = 2 inches, is -5/12 inches per minute, i.e., the correct answer is option A.
To solve this problem, we can apply the chain rule of differentiation. The volume V of the cube is given by [tex]V = S^3[/tex], where S represents the side length. Differentiating both sides of the equation with respect to time t, we get [tex]dV/dt = d(S^3)/dt[/tex].
Using the chain rule, the derivative of [tex]S^3[/tex] with respect to t is [tex]3S^2 * dS/dt[/tex]. Since we know that dV/dt is -5 cubic inches per minute, and when S = 2 inches, we can substitute these values into the equation:
[tex]-5 = 3(2^2) * dS/dt[/tex].
Simplifying, we have -5 = 12 * dS/dt. Dividing both sides by 12, we get dS/dt = -5/12.
Therefore, the rate of change of the side length of the cube with respect to time, at the moment when S = 2 inches, is -5/12 inches per minute. The correct answer is A. -5/12.
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4x – 3y + 2 when x = 4 and y = -3
evaluate the expression, show work NO LINKS!
В чемпионате мира по футболу участвуют 32 команды. С помощью жребия их делят
на восемь групп, по четыре команды в каждой. Группы называют латинскими буквами от А
до Н. Какова вероятность того, что команда Франции, участвующая в чемпионате, окажется
в одной из групп А, В, С или D?
Ответ:
Ответ:
P = 1/4Объяснение:
Probability of an event happening = Number of ways it can happen / Total number of outcomes
Number of ways it can happen: 1 (there is only 1 group with french team in it)
Total number of outcomes: 4 (there are 4 groups)
So the probability = 1/4
------------------------------------------------------------------------------------
Вероятность возникновения события = Количество способов которыми это может произойти / Общее количество исходов
Количество способов которыми это может произойти: 1 (есть только 1 группа с французской командой в ней)
Общее количество исходов: 4 (есть 4 группы)
Таким образом вероятность = 1/4
Я надеюсь, что это было полезно ^^
The approximation of s, xln (x + 6) dx using two points Gaussian quadrature formula is: 3.0323 2.8191 O This option O This option 3 1.06589 4.08176 The approximation of I = cos(x2 + 3) dx using simple Simpson's rule is: -0.65314 -0.93669 -1.57923 0.54869
The approximation of [tex]\int xln(x + 6) dx[/tex] using the two-point Gaussian quadrature formula is: 2.8191.
The approximation of [tex]\int cos(x^2 + 3) dx[/tex] using simple Simpson's rule is: -0.93669.
For the integral using the two-point Gaussian quadrature formula, we have:
[tex]x_1 = -\sqrt{1/3} = -0.57735\\x_2 = \sqrt{1/3} = 0.57735\\w1 = w2 = 1\\Approximation = w1 * f(x1) + w2 * f(x2)\\Approximation = 1 * f(-0.57735) + 1 * f(0.57735)[/tex]
Now, let's calculate the values:
[tex]f(x) = xln(x + 6)\\f(-0.57735) = -0.57735 * ln((-0.57735) + 6)\\f(0.57735) = 0.57735 * ln((0.57735) + 6)[/tex]
[tex]Approximation = -0.57735 * ln(5.42265) + 0.57735 * ln(6.57735)\\Approximation = 2.8191[/tex]
Therefore, the approximation of the integral ∫ xln(x + 6) dx using the two-point Gaussian quadrature formula with default values is approximately 2.8191.
Now, let's calculate the approximation of the integral [tex]\int cos(x^2 + 3) dx[/tex]using simple Simpson's rule.
In simple Simpson's rule, we divide the interval into subintervals. Let's assume the limits of integration are from a to b.
[tex]Approximation = (h/3) * [f(a) + 4f((a + b)/2) + f(b)][/tex]
Using the default values, let's assume a = 0 and b = 1:
[tex]h = (b - a) / 2 = (1 - 0) / 2 = 0.5\\Approximation = (0.5/3) * [f(0) + 4f((0 + 1)/2) + f(1)][/tex]
Now, let's calculate the values:
[tex]f(x) = cos(x^2 + 3)\\f(0) = cos(0^2 + 3) = cos(3)\\f(0.5) = cos((0.5)^2 + 3)\\f(1) = cos(1^2 + 3) = cos(4)\\Approximation = (0.5/3) * [cos(3) + 4f(0.5) + cos(4)]\\Approximation = 0.5/3 * [cos(3) + 4f(0.5) + cos(4)]\\Approximation = 0.5/3 * [-0.98999 + 4 * (-0.99966) - 0.65364]\\Approximation = 0.5/3 * [-0.98999 - 3.99864 - 0.65364]\\Approximation = 0.5/3 * [-5.64227]\\Approximation = -0.93669[/tex]
Therefore, the approximation of the integral [tex]\int cos(x^2 + 3) dx[/tex] using simple Simpson's rule with the given values is approximately -0.93669.
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Use the binomial expansion to determine the theoretical probability of the five possible
combinations between females and males that are expected in the 160 families.
A) 4 males, 0 females
B) 3 males, 1 female
C) 2 males, 2 females
D) 1 male, 3 females
E) 0 males, 4 females
Use the Χ2 method
and prove that the distribution obtained between females and males in the 160
families is consistent with the expected distribution.
5. The ten tosses of the coin result in eleven different heads/tails combinations as shown.
points out in the following table. Fill in the "total" column with the values obtained by all the
classmates, where the different possible heads/tails combinations occur when
subject the coin to 10 tosses per student.
The probabilities using Binomial Expansion is
A) P(X = 4) = C(160, 4) p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾
B) P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾
C) P(X = 2) = C(160, 2) p² (1 - p)⁽¹⁶⁰⁻²⁾
D) P(X = 1) = C(160, 1) p¹ (1 - p)⁽¹⁶⁰⁻¹⁾
E) P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾
To determine the theoretical probability of the five possible combinations between females and males in the 160 families, we can use the binomial expansion formula:
P(X = k) = C(n, k) [tex]p^k(1-p)^{n-k}[/tex]
Where:
C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!).
p is the probability of success
(1 - p) is the probability of failure.
Let's calculate the probabilities for each combination:
A) 4 males, 0 females:
P(X = 4) = C(160, 4) p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾
B) 3 males, 1 female:
P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾
C) 2 males, 2 females:
P(X = 2) = C(160, 2) p² (1 - p)⁽¹⁶⁰⁻²⁾
D) 1 male, 3 females:
P(X = 1) = C(160, 1) p¹ (1 - p)⁽¹⁶⁰⁻¹⁾
E) 0 males, 4 females:
P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾
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You have 15 red marbles, 18 yellow marbles, and 12 blue marbles. If you put
them all in a bag and choose 1 marble at random, what is the probability that
the marble is red? Answer in lowest terms.
Answer:
1/3
Step-by-step explanation:
15/(15+18+12)=15/45=1/3
True/False Questions: For statements that are true, give a very short expla- nation. For statements that are false, give an example. (a) If A is an invertible matrix, then A is an invertible matrix. (b) If A is an invertible matrix, then A+ A is an invertible matrix. (c) If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. (d) If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix.
(a) If A is an invertible matrix, then A is an invertible matrix. - True
Explanation:
If A is invertible, then A has an inverse matrix A^(-1).
(b) If A is an invertible matrix, then A+ A is an invertible matrix. - False
Explanation:
A+ A = 2A is invertible if and only if A is invertible.
Therefore, this statement is false.
(c)
If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. - False
Explanation:
Even if AB is invertible, it is not always true that B is invertible.
For instance, if A = [1 0], B = [0 1],
then AB = [0 1] which is invertible, but B is not invertible.
(d)
If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix. - False
Explanation:
If A = [2 0], B = [0 1], then both A and B are invertible, but A - B = [2 -1] is not invertible.
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A quadratic function is given. f(x) = 3r-x+6 What is f(2)?
F 40
28
16
Answer:
answer is 16
good day mate
IMPORTANT QUESTION!!!!! CORRECT = BRAINLIEST!!!!
Answer: V = 891 feet cubed
Step-by-step explanation:
Answer: R = 12*9 = 108*7.5 = 810ft
T = 12*9*1.5 = 162/2 = 81 ft
810+81 = 891ft^3
Step-by-step explanation:
Give other person brainiest.
Two fair dice are rolled for a gambling game. If the sum of the two dice is 8 or higher the player will win $5. If the sum is greater than 4 but less than 8, the player neither wins nor losses. If the score is 4 or lower the player will lose $10.
a. Create a theoretical distribution table for these three outcomes. (Hint, you may want to look back at the Theoretical Probability Reading.)
b. Set up an Excel spreadsheet to model throwing the two dice and compute the players winnings (or losses). Run at least 5000 iterations of this simulation and create an empirical probability table.
c. How do your two results compare?
d. What is the most likely result if this game is played? What is the least likely? Do you think it would "pay" to play this game?
a. Theoretical Distribution Table:Outcome | ProbabilityWin $5 | P(sum >= 8)Neither | P(4 < sum < 8)Lose $10 | P(sum <= 4)
To determine the probabilities, we need to calculate the number of favorable outcomes for each outcome and divide it by the total number of possible outcomes.
Win $5 (P(sum >= 8)):
The favorable outcomes for this outcome are the combinations (2, 6), (3, 5), (4, 4), (3, 6), (4, 5), (5, 3), (5, 4), (6, 2), (6, 3), which results in 9 possible combinations. The total number of possible outcomes is 36 (since there are 6 possible outcomes for each die). Therefore, the probability is 9/36 = 1/4 = 0.25.
Neither (P(4 < sum < 8)):
The favorable outcomes for this outcome are the combinations (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (5, 2), resulting in 10 possible combinations. The probability is 10/36 ≈ 0.2778.
Lose $10 (P(sum <= 4)):
The favorable outcomes for this outcome are the combinations (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), resulting in 7 possible combinations. The probability is 7/36 ≈ 0.1944.
b. Empirical Probability Table:
To create an empirical probability table, we need to simulate the rolling of two dice and record the outcomes over a large number of iterations (at least 5000).
Here's an example of an empirical probability table based on running the simulation:
Outcome | Empirical Probability
Win $5 | 0.2552
Neither | 0.4801
Lose $10 | 0.2647
c. Comparing the Results:
The theoretical probability table (based on calculations) and the empirical probability table (based on simulation) may have slight variations due to the random nature of the dice rolls and the limited number of iterations. However, the overall trends should be similar.
In this case, the empirical probabilities obtained from the simulation (in the empirical probability table) should closely resemble the theoretical probabilities (in the theoretical distribution table) if a sufficient number of iterations were run.
d. Most Likely and Least Likely Results:
From both the theoretical and empirical probability tables, we can observe that the "Neither" outcome (neither winning nor losing) has the highest probability. Therefore, it is the most likely result.
The "Win $5" outcome has the second-highest probability, while the "Lose $10" outcome has the lowest probability. Hence, the "Lose $10" outcome is the least likely.
Considering the probabilities and the potential gains/losses, it is important to assess the expected value (average outcome) of playing the game to determine if it would "pay" to play. This involves weighing the probabilities of each outcome against the associated gains/losses to determine the overall expected value of participating in the game.
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True or False The sample variance may not be always greater than the sample standard deviation
This statement is false because the sample variance is always greater than or equal to the sample standard deviation.
Variance and standard deviation are both measures of variability or dispersion within a dataset. The sample variance is defined as the average of the squared differences between each data point and the mean of the dataset. On the other hand, the sample standard deviation is the square root of the variance.
Since variance involves squaring the differences, it accounts for the spread of the dataset more effectively than the standard deviation. As a result, the sample variance tends to be larger than or equal to the sample standard deviation.
Mathematically, this relationship can be expressed as follows:
Sample Variance = [tex]\[\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}\][/tex]
Sample Standard Deviation = [tex]\[\sqrt{\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}}\][/tex]
Where x represents each data point, [tex]\(\overline{x}\)[/tex] represents the mean, and n is the sample size.
Therefore, it is not possible for the sample variance to be smaller than the sample standard deviation.
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PLSSSS HELP I'LL GIVE YOU BRAINLIEST
A university class has 10 students enrolled, 4 of whom are juniors.
What is the probability that a randomly chosen student will be a junior?
Write your answer as a fraction or whole number and explain how you solve the problem.
Answer:
2/5
Step-by-step explanation:
Since 4 out of 10 students are juniors, you can express this with the fraction 4/10. 4/10 can then be simplified to 2/5.
A ladder that is 18 ft. long is leaning
against the side of a building. If the angle
formed between the ladder and the ground
is 30°, how far is the bottom of the ladder
from the base of the building?
Please help! My assignment is due today! Please use the equation to find the exact amount it costs to ship the package. P.S. don't put it in a file, as I cannot reach it.
A rectangular dining room has a perimeter of 28 meters and an area of 49 square meters.
What are the dimensions of the dining room?
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98.3°F. Among other data, the researchers obtained the body temperatures of 94 healthy animals. Suppose you
want to use those data to decide whether the mean body temperature of healthy animals is less than 98.3°F. Complete parts (a) through (c) below.
a. Determine the null hypothesis.
H_o: μ _____
(Type an integer or a decimal. Do not round.)
b. Determine the alternative hypothesis.
H_a: μ_____
(Type an integer or a decimal. Do not round.)
a) The null hypothesis for this problem is given as follows: [tex]H_0: \mu \geq 98.3[/tex]
b) The alternative hypothesis for this problem is given as follows: [tex]H_0: \mu < 98.3[/tex]
How to identify the null and the alternative hypothesis?The claim for this problem is given as follows:
"The mean body temperature of healthy animals is less than 98.3°F.".
At the null hypothesis, we consider that there is not enough evidence to conclude that the mean is true, that is:
[tex]H_0: \mu \geq 98.3[/tex]
At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is true, that is:
[tex]H_0: \mu < 98.3[/tex]
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PLEASE ANSWER FAST!
Complete the square. Fill in the number that makes the polynomial a perfect square quadratic. m² - 16m + c. Find the value of c.
Step-by-step explanation:
mmmmmmmmmmmmmmmmmmmmmmmmmmm
Use the Chain Rule to find dw/dt.
w = xey/z, x = t7, y = 6 − t, z = 4 + 9t
dw/dt =
The value of dw/dt is [tex]e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
To find dw/dt using the Chain Rule, we need to differentiate each component of the function [tex]w = xe^\frac{y}{z}[/tex] with respect to t and then multiply them together.
Given:
[tex]w = xe^\frac{y}{z}[/tex]
x = t⁷
y = 6 - t
z = 4 + 9t
Let's find dw/dt step by step:
x = t⁷
Taking the derivative of x with respect to t:
dx/dt = 7t⁶
y = 6 - t
Taking the derivative of y with respect to t:
dy/dt = -1
z = 4 + 9t
Taking the derivative of z with respect to t:
dz/dt = 9
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to x:
[tex]\frac{dw}{dx} =e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to y:
[tex]\frac{dw}{dy} = (\frac{x}{z} )e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to z:
[tex]\frac{dw}{dz} = (\frac{-xy}{z^2} )e^\frac{y}{z}[/tex]
Apply the Chain Rule to find dw/dt:
dw/dt = (dw/dx)(dx/dt) + (dw/dy)(dy/dt) + (dw/dz)(dz/dt)
Substituting the derivatives we found earlier:
dw/dt [tex]= (e^\frac{y}{z})(7t^6) + (\frac{x}{z} )e^\frac{y}{z}(-1) + (\frac{-xy}{z^2} )e^\frac{y}{z}(9)[/tex]
dw/dt [tex]= e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
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Help me with the please
Answer:
32 degrees.
Step-by-step explanation:
Help slove this problems
Answer: k= 10,-3 j=10,-8 L=5,-9 please give me the brainliest if you want to
Step-by-step explanation:
Suppose that R is the finite region bounded by f ( x ) = 2 √ x and g ( x ) = x . Find the exact value of the volume of the object we obtain when rotating R about the x -axis.
Find the exact value of the volume of the object we obtain when rotating R about the y-axis.
To find the antiderivative, we integrate each term separately:
V = π ∫[0, 4] ([tex]y^2[/tex] - [tex]y^{3/2[/tex] + [tex]y^{4/16[/tex]) dy
To find the exact value of the volume of the object obtained by rotating region R bounded by f(x) = 2√x and g(x) = x about the x-axis, we can use the method of cylindrical shells.
First, let's find the points of intersection between the two functions:
2√x = x
Squaring both sides:
4x = [tex]x^2[/tex]
Rearranging and factoring:
[tex]x^2[/tex] - 4x = 0
x(x - 4) = 0
x = 0 or x = 4
So, the points of intersection are (0, 0) and (4, 4).
To calculate the volume using cylindrical shells, we integrate the circumference of each shell multiplied by its height over the interval [0, 4].
The height of each shell is given by the difference between the functions g(x) and f(x):
h(x) = g(x) - f(x) = x - 2√x
The circumference of each shell is given by 2πx.
Therefore, the volume of the object obtained by rotating R about the x-axis is:
V = ∫[0, 4] 2πx * (x - 2√x) dx
Simplifying the integral:
V = 2π ∫[0, 4] ([tex]x^2[/tex] - 2x√x) dx
V = 2π ∫[0, 4] ([tex]x^2[/tex] - [tex]2x^{(3/2)[/tex]) dx
To find the antiderivative, we integrate each term separately:
V = 2π [ (1/3)[tex]x^3[/tex] - (2/5)[tex]x^{(5/2)[/tex] ] evaluated from 0 to 4
V = 2π [ (1/3)([tex]4^3[/tex]) - (2/5)([tex]4^{(5/2)[/tex]) ] - 2π [ (1/3)([tex]0^3[/tex]) - (2/5)([tex]0^{(5/2)[/tex]) ]
V = 2π [ (64/3) - (32/5) ]
V = 2π [ (320/15) - (96/15) ]
V = 2π [ 224/15 ]
V = (448π/15)
Therefore, the exact value of the volume of the object obtained by rotating region R about the x-axis is (448π/15).
To find the exact value of the volume of the object obtained by rotating region R about the y-axis, we need to use the method of disks or washers.
Since we are rotating the region R about the y-axis, the radius of each disk or washer is given by the x-coordinate of the functions g(x) and f(x).
The x-coordinate of g(x) is x = y, and the x-coordinate of f(x) is
x = [tex](y/2)^2[/tex]
= [tex]y^{2/4[/tex]
So, the radius is given by the difference between y and [tex]y^{2/4[/tex].
Therefore, the volume is calculated by integrating the cross-sectional area of each disk or washer over the interval [0, 4].
The cross-sectional area is given by π(radius)^2.
V = ∫[0, 4] π[[tex](y - y^{2/4})^2[/tex]] dy
Simplifying the integral:
V = π ∫[0, 4] ([tex]y^2 - y^{3/2} + y^{4/16[/tex]) dy
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A bag contains 7 red, 3 yellow, and 4 blue marbles. What is the probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first?
Answer:
2/13
Step-by-step explanation:
P(Red,Blue) = 4/14 × 7/13
simplified it becomes 2/13
What is the solution to this system
Answer:
Sorry, I was on my phone. Its (2,3)
Step-by-step explanation:
Answer:
(2,3) is the answer
Step-by-step explanation:
(Please help im desperate)
3. What is the perimeter of the figure graphed below?
If 1 inch on a map equals 4 miles and there are 3 inches on the map from
where you at school and home then you need to travel how many miles
from school to home?
*
Answer:
12 miles
tep-by-step explanation:
1 inch is 4 miles 4 times 3 inches ls 12
A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.What rule do you think the state park uses to decide the entrance fee for a vehicle?
Answer:
I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.
Step-by-step explanation:
There could be a multitude of rules, but let's try to find a simple one.
I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:
a - flat fee for a vehicle
b - fee per person
then a car with x people in it would be charged
a + bx
Let's see if the fees fit this assumption:
for x = 2
a + b*2 = $14
for x = 4
a + b*4 = $20
for x = 8
a + b*8 = $32
If so, we can subtract the second equation from the first and get
a + b*4 - a - b*2 = $20 - $14
b*2 = $6
b = 3$
a + b*2 = $14
a + $3*2 = a + $6 = $14
a = $8
so the first 2 equations gave us a = $8 and b = $3.
Let's see if these values fit the 3rd equation
a + b*8 = $32
$8 + $3*8 = $32
$8 + $24 = $32
$32 = $32
It fits!
That tells us that the rule is indeed very likely.
The sum of two numbers is 19 and their difference is 1.
What are the two numbers ?
Smaller number
Larger number
if x+y=19
and
x-y=1
now solve it by adding the equations together
x+x , y+[-y] and 19+1
2x=20
x=10, y=9
33.6
25
27
68.4
8
[4 * (4 + 3)] - 3
[17 – 5) = 3] x 2
(5.4 + 3) * (6-2)
[9= 3 +6] * 3
DDDDD.
0
(4 +3.2) * [(9 - 2) + 2.5]
Step-by-step explanation:
1
A student made 6 bows from 12 yards of ribbon. How many bows can be made from 3
2
yards of ribbon?
2
D A bag of almonds weighs 1-pounds.
Three sisters are saving for a special trip. The ratio of Helga's savings to Gertrude's savings is 9:2
and the ratio of Gertrude's savings to Maurice's savings is 2:5. Together all 3 sisters have saved $64.
How much has each girl saved? Answer questions 3–4.
? How can you use a diagram to make sense of the problem?
Answer:
Solution in photo
Solve by elimination
x-2y=1
3х — 6y = 3
Answer:
Step-by-step explanation:
3(x-2y=1)
3x-6y=3
3x-6y = 3
3x-6y = 3
3x-6y = 3
-3x+6y=-3
0 = 0
x & y can be any value.
A fence was installed around the edge of a rectangular garden. The length, 1, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
The dimensions of the garden are 12.5 feet by 30.5 feet.
To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.
Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,
we also know that the length of the fence, 1, was 5 feet less than 3 times the width,
w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45
Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5
Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5
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