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Mathematics

1 answer:

alexandr402 [8]3 years ago

7 0

Answer:

The answer is E

Step-by-step explanation:

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The net worthw(t) of a company is growing at a rate of′(t) = 2000−121t2dollarsper year, wheretis in years since 1990.(a) If the

stiv31 [10]

Answer:

The worth of the company in 2000 is $56,000.

Step-by-step explanation:

The growth rate of the company is:

$f'(t)=2000-12t^{2}$

To determine the worth of the company in 2000, first compute the change in the net worth during the period 1990 (<em>t</em> = 0) to 2000 (<em>t</em> = 10) as follows:

$\int\limits^{10}_{0} {2000-12t^{2}} \, dt =\int\limits^{10}_{0} {2000} \, dt-12\int\limits^{10}_{0} {t^{2}} \, dt=2000 |t|^{10}_{0}-12|\frac{t^{3}}{3}|^{10}_{0}\\=(2000\times10)-(4\times10^{3})\\=20000-4000\\=16000$

The increase in the company's net worth from 1990 to 2000 is $16,000.

If the company's worth was $40,000 in 1990 then the worth of the company in 2000 is:

Worth in 2000 = Worth in 1990 + Net increase in company's worth

$=40000+16000\\=56000$

Thus, the worth of the company in 2000 is $56,000.

4 0

3 years ago

The formula to find the period of orbit of a satellite around a planet is (T^2) = (4pi^2/ gm) r3 where r is the orbit’s mean rad

Inga [223]

See the attached graphic to see this solved for "r".
You should be very careful about stating the units for each of those variables.
time in seconds
radius in meters
mass in kilograms
G = 6.674 x 10^-11 m^3 / (kilograms * seconds²)
Also, it would be worth your while to go to this web page http://www.1728.org/kepler3a.htm
It has a calculator and other information about Kepler's Third Law.