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2 years ago

F(x) = 5/(7x-8) What is the inverse of this function?

2 answers:

3 0

$f(x)=\dfrac{5}{7x-8}\\\\y=\dfrac{5}{7x-8}\iff\dfrac{1}{y}=\dfrac{7x-8}{5}\ \ \ |multiply\ both\ sides\ by\ 5\\\\\dfrac{5}{y}=7x-8\ \ \ |add\ 8\ to\ both\ sides\\\\7x=\dfrac{5}{y}+8\\\\7x=\dfrac{5}{y}+\dfrac{8y}{y}\\\\7x=\dfrac{5+8y}{y}\ \ \ \ |divide\ both\ sides\ by\ 7\\\\x=\dfrac{5+8y}{7y}\\\\Answer:\boxed{f^{-1}(x)=\dfrac{5+8x}{7x}\ other\ form\ f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}$

zzz [600]2 years ago

3 0

$f(x)=\dfrac{5}{7x-8}\\
y=\dfrac{5}{7x-8}\\
7x-8=\dfrac{5}{y}\\
7x=\dfrac{5}{y}+8\\
x=\dfrac{5}{7y}+\dfrac{8}{7}\\
\boxed{f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}
$

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The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.

Natalija [7]

Answer:

$A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524$

Step-by-step explanation:

Use the Washer Method $A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx$ where $R(x)$ is the outer radius and $r(x)$ is the inner radius.

If we sketch out the graph, we see that $y=1$ intersects points $(1,1)$ and $(3,1)$ , which will be our bounds of integration.

Here, our outer radius will be $R(x)=(-1-1)=-2$ and our inner radius will be $r(x)=-1-\frac{1}{x}$ .

Thus, we can compute the integral and find the volume:

$A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2} \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\$

$A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524$

In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!

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1 year ago

When cut into 10 equal slices, each slice is 1/10 of the pizza. Express how much of the pizza 7 of these slices would be in deci

Elena L [17]

1 pizza =1/10

7 pizza=7/10

=0.7 answer

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3 years ago

The diameter of holes for a cable harness is known to have a normal distribution with σ = 0.01 inches. A random sample of size 1

Rama09 [41]

Answer: (1.4964, 1.5126)

Step-by-step explanation:

We know that the confidence interval for population mean is given by :-

$\overline{x}\ \pm z*\dfrac{\sigma}{\sqrt{n}}$

, where ${\sigma$ = population standard deviation.

n= sample size

$\overline{x}$ = Sample mean

As per given , we have

σ = 0.01 inches

n= 10

$\overline{x}=1.5045$

Also, the critical value for 99% confidence interval = $z*=2.576$ [From x-value table.]

[Significance level =1-0.99=0.01 and $z_{\alpha/2}\ at\ \alpha=0.01$ is 2.576.]

Then, the 99% two-sided confidence interval on the mean hole diameter will be :-

$1.5045\ \pm (2.576)\dfrac{0.01}{\sqrt{10}}\\\\\approx1.5045\pm(2.576)(0.00316)=1.5045\pm0.00814016=(1.5045-0.00814016,\ 1.5045+0.00814016)\\\\=(1.49635984,\ 1.51264016)\approx(1.4964,\ 1.5126)$

Hence, the required confidence interval = (1.4964, 1.5126)

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3 years ago

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RoseWind [281]

Answer:

Y = 3/4x - 2

Step-by-step explanation:

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b = -5 - (3/4)(-4)

b = -5 + 3 = -2

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