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3 years ago

G(x)=-2/5x-2 inverse function with steps please

Mathematics

1 answer:

podryga [215]3 years ago

4 0

Answer:

${g}^{ - 1} (x) = - \frac{5}{2} x - 5$

Step-by-step explanation:

We want to find the inverse of

$g(x) = - \frac{2}{5}x - 2$

Let

$y= - \frac{2}{5}x - 2$

We interchange x and y to get:

$x= - \frac{2}{5}y - 2$

We now solve for y to obtain:

$x + 2=-\frac{2}{5}y$

$5x = - 2y - 10$

Add 10 to both sides to get:

$5x + 10 = - 2y$

Divide through by -2

$y = - \frac{5}{2} x - 5$

Therefore

${g}^{ - 1} (x) = - \frac{5}{2} x - 5$

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Consider two circular swimming pools. Pool A has a radius of 22 feet, and Pool B has a diameter of 13.6 meters. Complete the des

maw [93]

Answers:

13 42 m; B; 0.57 m

Step-by-step explanation:

Data:

Pool A: r = 22 ft

Pool B: D = 13.6 m

Calculations:

1. Radius of Pool A

r = 22 ft × (0.305 m/1 ft) = 6.71 m

2. Diameter of Pool A

D =2r = 2 × 6.71 = 13.42 m

The diameter of Pool A is 13.42 m.

3. Compare pool diameters

The diameter of Pool B is 13.6 m.

So, the diameter of Pool B is greater.

4. Compare circumferences

The formula for the circumference of a circle is

C = 2πr or C = πD

Pool A: C = 2π × 6.71 = 42.16 m

Pool B: r = π × 13.6 = 42.73 m

Pool B - Pool A = 42.73 - 42.16 = 0.57 m

The circumference is greater by 0.57 m.

8 0

3 years ago

Ava wants to ride her bicycle more than 75 miles this week. She has already ridden her bicycle 16 miles. Which inequality could

Whitepunk [10]

Answer:

I think it may be 5m + 16 < 75

Step-by-step explanation:

I don't know if its wrong

6 0

3 years ago

Find the solution to the following system using substitution. y = - 4 + 9 y = 3x - 5

lbvjy [14]

Answer:

1/2, 11/6

Step-by-step explanation:

y=-4+9y

9y-y=4

8y=4

y=1/2

3x-5=1/2

3x=5+1/2=11/2

x=11/6

6 0

2 years ago

Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

Complete function tables part 2 please help its the last one pleasee

Annette [7]

Answer:

e=3 d=2

e=7 d=3

e=11 d=4

e=15 d=5

Step-by-step explanation:

all you have to do is solve for the d by substituting the value of e into the equation.

5 0

2 years ago

G(x)=-2/5x-2 inverse function with steps please​

G(x)=-2/5x-2 inverse function with steps please