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3 years ago

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I had this question that said What is 3 common multiples of 2 and 6 can someone answer please I can’t find anything online eithe

r

1 answer:

JulijaS [17]3 years ago

5 0

Answer:6,12,18

Step-by-step explanation:

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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

Hi, What is the lowest positive integer greater than 1, which when divided by 5 or 8 leaves a remainder of 1

ludmilkaskok [199]

Very interesting question!

Let's try to get something that would work for just 5 for now.
Any of these numbers would leave a remainder of 1 when divided by just 5:
6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, ...
Notice that they all look like 5*(something) + 1. Basically, they are all multiples of 5 plus 1.

Let's see what would work for just 8:
9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, ...

Are there any matches... AHA! It's 81. This is the lowest positive integer greater than 1 that follows the rule for both 5 and 8.

3 0

4 years ago

Four deep-sea divers reported the depths they went below sea level on their last dive. Which depth is the farthest from sea leve

Andreas93 [3]

Answer: C. -82

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find the geometric mean of 4 and 12.

vagabundo [1.1K]

Answer:

The Geometric Mean of 4 and 12 is 6.9

Step-by-step explanation:

4 0

3 years ago

How do i write: N+5 then divide by 4= 17 as an equation

Alex17521 [72]

Answer: N+5 ÷ 4 = 17

(Hope this helps!)

5 0

3 years ago