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USPshnik [31]
3 years ago
13

The sum of 5 and twice a number.

Mathematics
2 answers:
FromTheMoon [43]3 years ago
8 0

Answer:

5 + 2x

Step-by-step explanation:

Sum means your adding so it would be 5 + any given number which you can call x times by 2. Which is 5 + 2x

snow_lady [41]3 years ago
4 0

Answer:

5+x2

Step-by-step explanation:

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2 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

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3 years ago
The sale price of a pair of sneakers was $33.75. What is the discount % if the original cost is $75?
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Answer:

55%

Step-by-step explanation:

To find the percent discount

Take the original price and subtract the new price

75-33.75 =41.25

Divide this by the original price

41.25/75

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Multiply by 100

55%

This is the percent decrease

5 0
2 years ago
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It looks all good to me! :) gj
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2 years ago
Maths! please help! will give brainliest!
Gwar [14]

Answer:

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Step-by-step explanation:

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