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laiz [17]
3 years ago
9

You use 240 cubic inches of clay to make a sculpture shaped as a rectangular prism. The width is 4 inches less than the length a

nd the height is 2 inches more than three times the length. What are the dimensions of the sculpture ?
Mathematics
1 answer:
murzikaleks [220]3 years ago
7 0

Answer:

L: 6

W: 2

H: 20

Step-by-step explanation:

First, we need to know the expression to calculate the volume of rectangular prism which is:

V = L * W * H

The only thing we know is that the volume is 240 in³ and that the width is 4in less than length, the height is 2 in more than 3 times length. So, everything is set in function of the length, therefore, we'll call L = x and then solve for x

L = x

W = x - 4

H = 3x + 2

Let's replace the data in the formula of volume:

240 = x * (x - 4) * (3x + 2)

240 = (x² - 4x)(3x + 2)

Solving this we have:

240 = 3x³ - 10x² - 8x

Rearranging the equation:

3x³ - 10x² - 8x - 240 = 0

Now, in order to solve this, we need to factorize the left side:

3x³ - 18x² + 8x² - 48x + 40x - 240 = 0

3x²(x - 6) + 8x(x - 6) + 40(x - 6) = 0

(x - 6)(3x² + 8x + 40) = 0

Now that we have this, we can solve the value of x.

x1 -----> x - 6 = 0 ---> x = 6

x2 ---> (3x² + 8x + 40) = 0

Δ = 8² - 4*3*40 = 64 - 480 = -416

This value of -416 means that it's not possible to get a real number as x (only the imaginary numbers), therefore the value of x should be 6

x = L = 6

With this value we can calculate W and H:

H = 6 - 2 = 4

W = (3*6) + 2 = 20

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Because 1/8 and 2/8 have the same denominator, add them by adding their numerators.

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3 years ago
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VladimirAG [237]
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2 years ago
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Andru [333]

Answer:

y intercept = 5

Step-by-step explanation:

f(x)=5•(1/6)^x

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f(0)=5•(1/6)^0      

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If the question is

f(x)=5•(1/6)x

although I have never seen the question written this way

The y intercept is when x =0

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5 0
2 years ago
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3 years ago
Carlos is 33 years younger than Kristen. 2 years ago, Kristen's age was 2 times Carlos's age. How old is Carlos now?
ale4655 [162]

Answer:

Carlos is 35 years old now

Step-by-step explanation:

Assume that Carlos is x years old now

∵ Carlos is x years old now

∵ Carlos is 33 years younger than Kristen

- Kirsten's age is the sum of x and 33

∴ Kirsten is x + 33 years old now

2 years ago

∵ Carlos's age = x - 2

∵ Kristen's age = x + 33 - 2 = x + 31

∵ Kristen's age was 2 times Carlos's age

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∴ x + 31 = 2(x - 2)

- Simplify the right hand side

∴ x + 31 = 2x - 4

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- Add 4 to both sides

∴ 35 = x

∵ x represents Carlos's age now

∴ Carlos is 35 years old now

6 0
3 years ago
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