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3 years ago

Hellllllllllllllllp points if you answeer correctly

Mathematics

1 answer:

sp2606 [1]3 years ago

4 0

Answer:

the answer will be [-3/4,1/2]

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

Please help! 15 points!! brainliest if right

Stels [109]

Answer:

a)7x-3x

b)4+28y

Step-by-step explanation:

first one follow bidmas

2nd one just do 4 times 1 =4 and 7y times 4 equals 28y

7 0

3 years ago

Why is it important to know the relationships between categorical variables?

Naily [24]

Answer: it is important to know the relationships between both to make sure you will use the correct way to use each and to explain a problem.

Step-by-step explanation:

A pie chart or bar graph might be used to display the distribution of a categorical variable while a boxplot or histogram might be used to picture the distribution of a measurement variable.

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3 years ago

Part I

klemol [59]

It depends on the shape it may be rotation

6 0

3 years ago

Ashton had 28 1/2feet of wrapping paper. He uses 3/8

sammy [17]

Answer:

Step-by-step explanation.

here is a trick

try turning both fractions into a decimal and then divide then. It will be much easier.

4 0

2 years ago