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3 years ago

Adam Zetts is an aerospace engineer. He earns $78,000 a year

Mathematics

1 answer:

Firlakuza [10]3 years ago

6 0

Answer:

Social Security: $201.50, Medicare: $47.13

Step-by-step explanation:

divide 78,000 by 24(semimonthly) - $78000/24 = $3250(gross semimonthly basis)

multiply 3250 by .062(social security) - 3250 x .062 = $201.50

multiply 3250 by 0.0145(medicare) - 3250 x 0.0145 = $47.13

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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

Anika [276]

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

$hypotenuse^2=base^2+perpendicular^2$

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

$y^2=x^2+1$ .... (1)

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

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

$4=x^2+1$

$4-1=x^2$

$3=x^2$

Taking square root both sides.

$\sqrt{3}=x$

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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3 years ago

How many times larger is 9 × 10^9 than 3 x 10^-4

ratelena [41]

<span> 9 × 10^9
---------------- = 3 x 10^13
</span><span>3 x 10^-4

answer
3 x 10^13 times larger</span>

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