What is the simplified form of the following expression? 6m² + 7.2n - 4n+2m2-n

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

3 0

Answer:

6m² + 2.2n + 4m

Step-by-step explanation:

this the answer

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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

<img src="https://tex.z-dn.net/?f=the%20%5C%3A%20angle%20%5C%3A%20of%20%5C%3A%20measure%20%5C%3A%20%20%5Cfrac%7B31%5Cpi%7D%7B6%7

Yakvenalex [24]

Answer:

3rd quadrant

Step-by-step explanation:

First we just convert the angle from radians to degrees
$\frac{31\pi radians }{6}*\frac{180degrees}{\pi radians} =\frac{31*180}{6} degrees=930degrees$
Now that's too big, all this means is if we start rotating from the positive y-axis in a circle we will cross the starting point 2 times, 2 full circles;
$930degrees-360degrees=570degrees\\570degrees-360degrees=210degrees$
Now in which quadrant it 210 degrees?
0 degrees to 90 degrees is 1st quadrant
90 degrees to 180 degrees is 2nd quadrant
180 degrees to 270 degrees is 3rd quadrant
270 degrees to 360 degrees is 4th quadrant
So our answer is the 3rd quadrant.