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4 years ago

Is 5x-2x+18 and 3(x+6) equal?

1 answer:

6 0

They are equal

5x-2x+18=3(x+6) Distribute the right side

5x-2x+18=3x+18 Subtract 18 from both sides

5x-2x=3x Add 2x to both sides

5x=5x And you would find out that both sides are equal

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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

How many individual squares does a standard chess board have?

Nostrana [21]

There is two hundred and four (204) on a standard chessboard.

6 0

3 years ago

Thomas paid $50 for a box of multicolor file folder for his office there were 100 folders in the box what was the cost of each f

Yuliya22 [10]

For the answer to the question above asking what was the cost of each file folder if Thomas paid $50 for a box of the multicolor file folder for his office, there were 100 folders in the box?
this is a grade 2 problem. If you know how to divide you will get the answer.
Just d<span>ivide $50 by 100. Then you'll get the answer. </span>

4 0

4 years ago

Assume that P(E) = 0.471 and P(F) = 0.595. If E and F are independent, find P(E and F)

dsp73

The value of the probability P(E and F) is 0.2802

<h3>Independent probability</h3>

Events are known to be independent if the occurrence of one does not affect the other.

Given the following parameters

P (E) =0.471

P(F) = 0.595

If E and F are independent, then;

P(E and F) = P(E)P(F)

P(E and F) = 0.471 * 0.595
P(E and F) = 0.2802

Hence the value of the probability P(E and F) is 0.2802

Learn more on independent events here: brainly.com/question/1374659

#SPJ1

8 0

2 years ago

Rate and Ratio Sipho paid 605,50 for 70litres of petrol.What did the petrol cost per litre.

amid [387]

605,50/70= 929 per liter or 9.29 if it was suppose to be 605.50 price.

6 0

2 years ago