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hoa [83]
3 years ago
8

Find the slope and y-intercept of 2x - 9y equals 8

Mathematics
1 answer:
MrRa [10]3 years ago
8 0

The slope of this equation would be 2/9 and the y-intercept would be -8/9.

In order to find this, we have to solve the equation for y.

2x - 9y = 8 -----> subtract 2x from both sides

-9y = -2x = 8 -----> divide by -9

y = 2/9x - 8/9

Now we know that the slope is the number attached to x and the y-intercept is the constant at the end.

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A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station. Find the ra
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Answer:

The rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

Step-by-step explanation:

Given information:

A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.

z=1

\frac{dx}{dt}=430

We need to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

y=2

According to Pythagoras

hypotenuse^2=base^2+perpendicular^2

y^2=x^2+1^2

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Put z=1 and y=2, to find the value of x.

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Taking square root both sides.

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Differentiate equation (1) with respect to t.

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

Divide both sides by 2.

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

Put x=\sqrt{3}, y=2, \frac{dx}{dt}=430 in the above equation.

2\frac{dy}{dt}=\sqrt{3}(430)

Divide both sides by 2.

\frac{dy}{dt}=\frac{\sqrt{3}(430)}{2}

\frac{dy}{dt}=372.390923627

\frac{dy}{dt}\approx 372

Therefore the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

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This will give you your multiplier so you can then get your answer but you have to turn it into a decimal.

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