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3 years ago

Find the volume of the solid of revolution formed by rotating the bounded region about the x-axis.

Mathematics

1 answer:

lana66690 [7]3 years ago

3 0

Answer:

$40.5 \pi$ cubic units

Step-by-step explanation:

Given is a function exponential as

$f(x) =\sqrt{ (x-4)}$

The region bounded by the above curve, y =0 , x =13 is rotated about x axis.

the intersection point is at x=4

The limits for x are 4 and 13

The volume when rotated through x axis is found by

$\pi\int\limits^b_a {f(x)^2} \, dx$

Here a = 4 and b =13

volume = $\pi\int\limits^13_(4) x-4} \, dx$

= $\pi (\frac{x^2 }{2}-4x )\\= \frac{\pi}{2} (153-72)\\= 40.5 \pi$ .cubic units

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Can anyone walk me through this?

Fiesta28 [93]

Assuming that we are solving in terms of n.

Start by distributing:

2(n + 5)

(2*n) + (5*2)

2n + 10 = -2

Subtract 10 to start toward isolating your variable:

2n = -12

Divide by two to finish solving:

n = -6

6 0

3 years ago

Read 2 more answers

From 19 measurements of a pressure controller, the mean operating pressure is 4.97 kPa with a standard deviation of 0.0461 kPa.

Semenov [28]

Answer:

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =4.97$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.0461 represent the sample standard deviation

n=19 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=19-1=18$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.10$