F(x)=2x+1 and g(x)=x-3

It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.

vova2212 [387]

Answer:

300%

Step-by-step explanation:

Given

$y\ \alpha\ \frac{1}{x^2}$

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

$y\ = \ \frac{k}{x^2}$

Where k is the constant of proportionality

When x decreased by 50%

$Y = \frac{k}{(x - 0.5x)^2}$

$Y = \frac{k}{(0.5x)^2}$

$Y = \frac{k}{0.25x^2}$

Expand

$Y = \frac{1}{0.25} * \frac{k}{x^2}$

Substitute $\frac{k}{x^2}$ for y

$Y = \frac{1}{0.25} * y$

$Y = 4 * y$

$Y = 4 y$

The percentage change is then calculated as:

$\%Change = \frac{Y - y}{y} * 100\%$

$\%Change = \frac{4y - y}{y} * 100\%$

$\%Change = \frac{3y}{y} * 100\%$

$\%Change = 3 * 100\%$

$\%Change = 300\%$

The percentage in y is 300%

7 0

3 years ago

Select the correct word to describe the function. the equation y = startfraction 5 x cubed over 8 endfraction represents functio

balandron [24]

The functions and their descriptions are:

Polynomial: $y = \frac{5x^3}{8}$ and $y = 5x^3 + 8$
Logarithm: $y = 6 + 0.25\ln(x)$
Exponential $y = \frac{18}{1 + 6e^{-0.25x}}$

<h3>How to describe the functions?</h3>

The functions are given as:

$y = \frac{5x^3}{8}$

$y = 6 + 0.25\ln(x)$

$y = \frac{18}{1 + 6e^{-0.25x}}$

$y = 5x^3 + 8$

The functions would be described based on the type of function they represent.

Functions that use the "ln" keyword are logarithmic functions, while functions that use the "e" keyword are exponential functions.

Read more about functions at:

brainly.com/question/4025726

#SPJ1

7 0

2 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the linear equations with their x-

jolli1 [7]

Answer:

Part 1) $x-2y=2$ ----> (2,0) and (0,-1)

Part 2) $-3x+3y=7$ ----> (-7/3,0) and (0,7/3)

Part 3) $7x-y=21$ ----> (3,0) and (0,-21)

Part 4) $3x-5y=-20$ ----> (-20/3,0) and (0,4)

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

The x-intercept is the value of x when the value of y is equal to zero

Part 1) we have

$x-2y=2$

1) Find the x-intercept

For y=0

$x-2(0)=2\\x=2$

the x-intercept is (2,0)

2) Find the y-intercept

For x=0

$0-2y=2\\y=-1$

the y-intercept is (0,-1)

Part 2) we have

$-3x+3y=7$

1) Find the x-intercept

For y=0

$-3x+3(0)=7\\x=-\frac{7}{3}$

the x-intercept is (-7/3,0)

2) Find the y-intercept

For x=0

$-3(0)+3y=7\\y=\frac{7}{3}$

the y-intercept is (0,7/3)

Part 3) we have

$7x-y=21$

1) Find the x-intercept

For y=0

$7x-(0)=21\\x=3$

the x-intercept is (3,0)

2) Find the y-intercept

For x=0

$7(0)-y=21\\y=-21$

the y-intercept is (0,-21)

Part 4) we have

$3x-5y=-20$

1) Find the x-intercept

For y=0

$3x-5(0)=-20\\x=-\frac{20}{3}$

the x-intercept is (-20/3,0)

2) Find the y-intercept

For x=0

$3(0)-5y=-20\\y=4$

the y-intercept is (0,4)

8 0

4 years ago

I need a lot of help, can someone pls help me?

Anastaziya [24]

Answer: yes, just tell me the problem

Step-by-step explanation:

3 0

3 years ago

Rodolfo earns $30.00 in 5 days. Max earns $10.00 more than Rodolfo in 5 days. How much is the Max salary in 8 days?

sertanlavr [38]

Answer: Mac made $64
Rodolfo earns $30 in 5, 30 divided by 5 equals 6. Max made $10 more so 40 divided by 5 equals 8. Since we are trying to find how much Max made in 8 days we multiply 8 by 8 and get 64.

5 0

3 years ago