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3 years ago

Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64cm^2

1 answer:

6 0

Let x =lenght, y = width, and z =height
The volume of the box is equal to V = xyz 
Subject to the surface area 
S = 2xy + 2xz + 2yz = 64 
= 2(xy + xz + yz) 
= 2[xy + x(64/xy) + y(64/xy)] 
S(x,y)= 2(xy + 64/y + 64/x) 
Then 
Mx(x, y) = y = 64/x^2 
My(x, y) = x = 64/y^2 
y^2 = 64/x 
(64/x^2)^2 = 64 
4096/x^4 = 64/x 
x^3 = 4096/64 
x^3 = 64 
x = 4 
y = 64/x^2 
y = 4 
z= 64/yx 
z= 64/16 
z = 4 

Therefor the dimensions are cube 4.

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suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio

djyliett [7]

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3$

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

$\mu = \mu_X - \mu_Y = 45 - 35 = 0$

$\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{25} = 5$

We want to find P(X > 0), that is, 1 subtracted by the pvalue of Z when X = 0. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0 - 10}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

4 0

3 years ago

HALP MEH! MY HOMEWORK IS SOOOO CONFUSING

frutty [35]

Answer:

Step-by-step explanation:

7 0

2 years ago

Twenty-six , 2 tens 6 ones , 25, 20+6 which one is the odd one out?

Aneli [31]

Answer:

Step-by-step explanation:

twenty-six=26

2 tens 6 ones= 26

25=25

20+6=26

25 is the odd one out.

8 0

3 years ago

It cost $109 per night to rent a motel room in Hampton. There is a one time $30 nonrefundable deposit required how much will it

bekas [8.4K]

Answer:

793

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The graph of F(x) can be stretched vertically and flipped over the x axis to produce the graph of G(x) if F(x)=x^2 which of the

ladessa [460]

Answer:

g(x) = -5x²

(option B)

Step-by-step explanation:

we know that our original graph, f(x) = x² is a parabola.

So, we can consider what happens when we adjust the function/equation of a parabola.

when we "vertically stretch" a parabola, we are increasing the value of x.

think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.

Let's say our x = 5

if f(x)=x²

f(5) = 25

> y value / steepness is 25

f(x) = 3x²

f(5) = 75

> y value / steepness is 75

So, we are looking for an equation with an increase in x present.

When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative

suppose that x = 1

if y = x² ; y = 1² = 1

if y = -(x²) ; y = -(1²) ; y = -1

So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)

This means that we are looking for a function with a negative x value.

So, we are looking for a negative x-value that is multiplied by a number >1

The graph that fits our requirements is g(x) = -5x²

hope this helps!!

6 0

1 year ago