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3 years ago

-3÷(-2/5) simplify the expression

Mathematics

1 answer:

Vika [28.1K]3 years ago

8 0

Answer:

7.5 is the answer you are looking for

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30.72 rounded to the nearest tenth

lisabon 2012 [21]

30.72 rounded to the nearest tenth is 30.7

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Help!!! This is a little confusing

madam [21]

Answer:

60 people

Step-by-step explanation: Multiply 20 by 3 and you will get 60, which is the total combonation of people.

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3 years ago

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Find the missing values

Naddik [55]

I FOUND THEM THEY ARE HIDING IN THE CLOUDS.

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3 years ago

The lines shown below are parallel. If the green line has a slope of -3/7 what is the slope of the red line?

anastassius [24]

When any lines are parallel that means they have the same slope so the slope of the red line would also have a slope of -3/7

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3 years ago

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.

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3 years ago