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3 years ago

8. Suppose y varies directly as x. If y = -4 when x = 32, find x when ys -0.

Mathematics

1 answer:

Nata [24]3 years ago

4 0

Answer:

$x=0$

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 $y=kx$

in this problem

For x=32, y=-4

Find the value of the constant of proportionality k

$k=y/x$

substitute

$k=-\frac{4}{32}$

simplify

$k=-\frac{1}{8}$

The linear equation is

$y=-\frac{1}{8}x$

Find x when the value of y=0

Remember that

In a proportional relationship the line passes through the origin

If y=0

then

the value of x must be equal to zero

therefore

$x=0$

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3 years ago

A plane flying horizontally at an altitude of 1 mile and a speed of 510 mi/h passes directly over a radar station. Find the rate

sdas [7]

Answer:

442 miles

Step-by-step explanation:

Given

To properly solve this question, I illustrate some given parameters using attached image

From the image, apply Pythagoras theorem

$x^2 + 1^2 = y^2$

Differentiate w.r.t time (t)

$2x\frac{dx}{dt} + 0 = 2y\frac{dy}{dt}$

$2x\frac{dx}{dt} = 2y\frac{dy}{dt}$

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From the question, we have that the plan travels are 510mi/h.

This implies that:

$\frac{dx}{dt} = 510mi/h$

So, we then calculate the value of x when the distance (y) is 2mi i.e.:

$y = 2mi$

Apply Pythagoras theorem

$x^2 + 1^2 = y^2$

$x^2 + 1^2 = 2^2$

$x^2 + 1 = 4$

$x^2 = 4-1$

$x^2 = 3$

$x = \sqrt 3$

So, the expression becomes:

$x\frac{dx}{dt} = y\frac{dy}{dt}$

$\sqrt 3 * 510 = 2* \frac{dy}{dt}$

$\frac{\sqrt 3 * 510}{2} = \frac{dy}{dt}$

$\sqrt 3 * 255 = \frac{dy}{dt}$

$\frac{dy}{dt} = 255\sqrt 3$

$\frac{dy}{dt} = 255 * 1.7321$

$\frac{dy}{dt} = 441.655$

$\frac{dy}{dt} = 442$

Hence, the distance is 442 miles

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3 years ago

3.14 x 10 <img src="https://tex.z-dn.net/?f=3.14%20%5Ctimes%2010%20%3D%20" id="TexFormula1" title="3.14 \times 10 = " alt="3.

fiasKO [112]

When you multiply 10, move the decimal point to the right one place value

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3 years ago

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..........................................answer

blagie [28]

Answer:

2x-5=?

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Step-by-step explanation:

therefore 2x-5=2*3-5
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3 years ago

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Gelneren [198K]

Answer:

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2 years ago

8. Suppose y varies directly as x. If y = -4 when x = 32, find x when ys -0.​

8. Suppose y varies directly as x. If y = -4 when x = 32, find x when ys -0.