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3 years ago

A hotel swimming pool measures 20 m by 9 m. The hotel manager wants to put a 2 m wide deck

Mathematics

1 answer:

Lostsunrise [7]3 years ago

6 0

Answer:

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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

Write words to match the expression<br> 36÷4

romanna [79]

Thirty six divided by four is equal to nine

8 0

3 years ago

Read 2 more answers

Sydney is playing a game on a map with a marked grid. To start, she places a game piece at (1, 4). She moves 3 units east and 2

Anastasy [175]

Answer:

(7, 8)

Step-by-step explanation:

If Sidney places each piece 3 units east and 2 units north of the last one, we can figure out which coordinate comes first by subtracting the position of the second piece (S) by the position of the first piece (F):

$S - F = (4,6) - (1,4) = (3,2)$

We can conclude that coordinates are in the (East, North) format.

Therefore, the location of the third piece (T) is:

$T = S(E,N) +(3,2)= (4,6)+(3,2)\\T = (7,8)$

6 0

3 years ago

Scores on an english test are normally distributed with a mean of 31.5 and a standard deviation of 7.3. find the score that sepa

kobusy [5.1K]

Let X be the score on an english test which is normally distributed with mean of 31.5 and standard deviation of 7.3

μ = 31.5 and σ =7.3

Here we have to find score that separates the top 59% from the bottom 41%

So basically we have to find here x value such that area above it is 59% and below it is 49%

This is same as finding z score such that probability below z score is 0.49 and above probability is 0.59

P(Z < z) = 0.49

Using excel function to find the z score for probability 0.49 we get

z = NORM.S.INV(0.49)

z = -0.025

It means for z score -0.025 area below it is 41% and above it is 59%

Now we will convert this z score into x value using given mean and standard deviation

x = (z* standard deviation) + mean

x = (-0.025 * 7.3) + 31.5

x = 31.6825 ~ 31.68

The score that separates the top 59% from the bottom 41% is 31.68

3 0

3 years ago

3. What is the value of 42 – 2(3 • 5+ 1)?

sp2606 [1]

Answer:

Step-by-step explanation:

6 0

3 years ago

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