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sergiy2304 [10]

2 years ago

5

Donald needs to stamp 145 pieces of mail. He has finished 97 pieces. How many more does he have to do? A. 58 B. 48 C. 42 D.

52

2 answers:

Sloan [31]2 years ago

8 0

He has 48 left to do.

inn [45]2 years ago

5 0

B 48 forty eight 145- 97 makes your answer

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Debra can run 20.5 miles in 2.5 hours how many miles per hour can she run math problems

pashok25 [27]

She can run 20.5/2.5 equaling 8.2mph

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3 years ago

Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

3 years ago

Math (88 points by the way)<br>I put transformation on the very first blank line by the way.

Temka [501]

This Question is actually for 44 points not 80 :(

7 0

3 years ago

Read 2 more answers

Plz help I need help

crimeas [40]

Answer:

The answer is 30.66, mark me as brainliest

4 0

2 years ago

If the cos of angle x is 8 over 17 and the triangle was dilated to be two times as big as the original, what would be the value

Viktor [21]

Answer:

the answer is 8/17

Step-by-step explanation:

i got it right on the quiz

6 0

2 years ago