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Zigmanuir [339]
2 years ago
11

The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 sq

uare feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x. What is the constant of variation? What is the equation representing the direct variation?
Mathematics
2 answers:
Mariana [72]2 years ago
5 0

Answer:

the correct answer is;

A.1/9

A.y=(1/9)x

lara [203]2 years ago
3 0

Answer:

Part 1) The constant of variation is k=1/9

part 2) The equation is y=\frac{1}{9}x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

Let

x -----> the number of square feet

y ----->  the number of square yards

Three square yards are equivalent to 27 square feet

so

we have the point (27,3)

Part 1) What is the constant of variation?

The constant of variation or proportionality is equal to

k=y/x

substitute the values

k=3/27

Simplify

k=1/9

Part 2) What is the equation representing the direct variation?

we know that

y=kx

substitute the value of k

y=\frac{1}{9}x

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Read 2 more answers
The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its la
cluponka [151]

Answer:

x = 31 hundred dolars   and      

y = 91/2 = 45.5 hundred dolars

Step-by-step explanation:

Given

R(x) = (40−8x+5y)*x + (50+9x−7y)*y

C(x) = (40−8x+5y)*10 + (50+9x−7y)*29

We can use the equation

P(x) = R(x) - C(x)

where

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R(x) is the revenue

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In order to maximize the telephone company's profit, we apply

P'(x) = R(x)' - C(x)' = 0

⇒ R(x)' = ((40−8x+5y)*x + (50+9x−7y)*y)' = (40x-8x²+14xy+50y-7y²)'

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The first-order partial derivatives of these functions are

Px(x,y) = -16x-141+14y

Py(x,y) = -14y+203+14x

Setting these equal to zero and solving we obtain:

-16x+14y-141 = 0

14x-14y+203=0

we get the solution

x = 31     and       y = 91/2 = 45.5

Finally, the company should produce  3100  units of the first system, and  4550 units of the second system.

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