Can someone help pls the question in the pic (geometry)

Mathematics

2 answers:

Eddi Din [679]3 years ago

8 0

Reflecting over the y-axis

Aleonysh [2.5K]3 years ago

5 0

Answer:

Reflection over y axis, and translate right 1

Step-by-step explanation:

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Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

3 years ago

Which equation is an identity?

zloy xaker [14]

3w + 8 - w = 4w - 2(w - 4)
is an identity
3w-w + 8 = 4w - 2w + 8
2w + 8 = 2w + 8
2w - 2w = 8 - 8
0 = 0
zero equal to zero implies that any value of w satisfies the statement 3w + 8 - w = 4w - 2(w - 4) hence it is an identity.

3 0

4 years ago

Read 2 more answers

Ill make you brainliest answer!!

galina1969 [7]

I think using a computer software would be the best answer because it is then fair

3 0

3 years ago

Read 2 more answers

I also need help with this one

icang [17]

It is c.

explanation:

20+130+h =180

when you solve you get h=50

130+g = 180

g= 50

50+60+f = 180

f=70