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loris [4]
3 years ago
10

A rectangular box has a base that is 4 times as long as it is wide. The sum of the height and the girth of the box is 200 feet.

(a) Express the volume V of the box as a function of its width w. Determine the domain of V (w).
Mathematics
1 answer:
enyata [817]3 years ago
6 0

Answer: V(W) = (1/3)*(*W^2*800ft - 8W^3) and the domain is 0 < W < 100ft.

Step-by-step explanation:

The dimensions of the box are:

L = length

W = width

H = heigth.

We know that:

L = 4*W

And the girth of a box is equal to: G = 2*W + 2*H

then we have:

2*W + 2*H + H = 200ft

2W + 3*H = 200ft

Then we have two equations:

L = 4*W

2W + 3*H = 200ft

We want to find the volume of the box, which is V = W*L*H

and we want in on terms of W.

Then, first we can replace L by 4*W (for the first equation)

and:

2*W + 3*H = 200ft

3*H = 200ft - 2*W

H = (200ft - 2*W)/3.

then the volume is:

V(W) = W*(4*W)*(200ft - 2*W)/3

V(W) = (1/3)*(*W^2*800ft - 8W^3)

The domain of this is the set of W such that the volume is positive, then we must have that:

W^2*800ft > 8W^3

To find the maximum W we can see the equality (the minimum extreme is 0 < W, because the width can only be a positive number)

W^2*800ft = 8W^3

800ft = 8*W

100ft = W.

This means that if W is equal or larger than 100ft, the equation gives a negative volume.

Then the domain is 0 < W < 100ft.

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3 years ago
Cecilia is making cookies for her friends. The recipe, which makes 48 cookies, calls for 4 cups of flour and 1 1/3 cups of sugar
Vsevolod [243]

Answer:

2. Cecilia uses 3 cups of flour for 36 cookies

4. Cecilia is making 3/4 of the original recipe

Step-by-step explanation:

Recipe for 48 cookies

Flour = 4 cups

Sugar = 1 1/3 cups

Recipe for 36 cookies

48 cookies : 36 cookies

= 4 : 3

Flour used in 36 cookies = x cups

Flour used in 48 cookies = 4 cups

4 cups : x cups

4 : 3 = 4 : x

4/3 = 4/x

4*x = 3*4

4x = 12

x = 12/4

x = 3 cups

Sugar = 1 1/3 cups

Sugar used in 36 cookies = y cups

Sugar used in 48 cookies = 1 1/3 cups

4 : 3 = 1 1/3 : y

4/3 = 4/3 ÷ y

4/3 = 4/3 × 1/y

4/3 = 4/3y

4*3y = 3*3

12y = 9

y = 9/12

= 3/4

y = 3/4

The true statement are:

2. Cecilia uses 3 cups of flour for 36 cookies

4. Cecilia is making 3/4 of the original recipe

8 0
3 years ago
Which option is an even function?
Grace [21]

The correct answer is option D. Which is the even function is f (x) = x⁴.

<h3>What is an even function?</h3>

The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).

let us check the given four options:-

A f(x) = √x ;  f(-x) = √-x  here f(x) ≠ f(-x)

B f(x) = x ;  f(-x) = -x    here f(x) ≠ f(-x)

C f(x)  = x³ + 1 ; f(-x) = -x³ + 1  here f(x) ≠ f(-x)

D f(x)  = x⁴  ;  f(-x) = (-x)⁴ = x⁴  here f(x) = f(-x)

We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).

Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.

To know more about even functions follow

brainly.com/question/2284364

#SPJ1

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Answer:

Step-by-step explanation:

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8x -17 = -26x

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Step-by-step explanation:

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