Given y varies inversely as x, and y = 5 when x = 9. *Write the inverse function

Given:

The given function is:

[tex]\dfrac{(x^3+1)(x-2)}{x^2}[/tex]

To find:

The differentiation of the given function.

Solution:

Consider the given function,

[tex]y=\dfrac{(x^3+1)(x-2)}{x^2}[/tex]

It can be written as:

[tex]y=\dfrac{(x^3)(x)+(x^3)(-2)+(1)(x)+(1)(-2)}{x^2}[/tex]

[tex]y=\dfrac{x^4-2x^3+x-2}{x^2}[/tex]

[tex]y=\dfrac{x^4}{x^2}-\dfrac{2x^3}{x^2}+\dfrac{x}{x^2}-\dfrac{2}{x^2}[/tex]

[tex]y=x^2-2x+\dfrac{1}{x}-\dfrac{2}{x^2}[/tex]

Differentiate with respect to x.

[tex]y'=\dfrac{d}{dx}(x^2)-\dfrac{d}{dx}(2x)+\dfrac{d}{dx}(x^{-1})-\dfrac{d}{dx}\2(x^{-2})[/tex]

[tex]y'=2x-2(1)+(-x^{-2})-2(-2x^{-3})[/tex]

[tex]y'=2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}[/tex]  

Therefore, the differentiation of the given function is [tex]2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}[/tex].

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Explanation:

We're told that "The black trapezoid is a dilation of the green trapezoid". This means the black trapezoid is the image, while the green one is the preimage. In other words, the green is the "before" and the black is the "after". The mapping is [tex]\text{green} \to \text{black}[/tex] because of the ordering [tex]\text{preimage} \to \text{image}[/tex]

Since the green figure (preimage) is larger than the black figure (image), the scale factor must be some value k such that 0 < k < 1. That narrows the answer choices between A and B.

Focus on the green trapezoid. The bottom left corner is at (-10,0). The bottom right corner is at (5,0). The distance between these two points is 15 units.

Using the same idea, the distance along the bottom edge of the black trapezoid is 3 units. We can count out the spaces along the bottom, or we can note the two bottom corners are at (-2,0) and (1,0).

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So far we found:

These two edges correspond to one another. We divide the values to get the scale factor. We divide the image length over its corresponding preimage length.

scale factor = (image length)/(preimage length)

scale factor = 3/15

scale factor = 1/5

Answer:

35.................

Answer:

The volume would be 86.63 feet squared

Hope this helps!

Mark me brainliest if I'm right :)

Answer:

5q = 4p + 2

Step-by-step explanation:

4p = 5q - 2

4p + 2 = 5q - 2 + 2

5q = 4p + 2

Answer:

R=(180-100)/2=40.

Step-by-step explanation:

Answer. Answer: (1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40.

Answer:

D. y+5 = -2(x+4)

Step-by-step explanation:

[tex] \large \boxed{y - y_1 = m(x - x_1)}[/tex]

The equation above is point-slope form where x1 and y1 both are the point that the graph passes through ane m is slope as usual.

We are given the point (-4,-5) and slope of -2. We substitute these values in.

[tex] \large{y - ( - 5) = - 2(x - ( - 4))} \\ \large{y + 5 = - 2(x + 4)}[/tex]

Answer:

1/2

Step-by-step explanation:

Point A is (2, 3)

Point B is (6, 5)

To get the slope of a line, first select any two points on that line.

Then, take the difference of the y values, and divide it by the difference of the x values. This is also known as the change in y over the change in x, or rise over run.

[tex]\frac{3-5}{2-6} =\frac{-2}{-4} =\frac{1}{2}[/tex]

1/2 is the slope.

Step-by-step explanation:

we have

5x+4=2x+9

5x-2x=9+4

3x=13

x=13/3

Answer:

x = 13/3

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ 2x + 9 = 5x - 4

Then the value of x will be,

→ 2x + 9 = 5x - 4

→ 2x - 5x = -4 - 9

→ -3x = -13

→ x = (-13)/(-3)

→ [ x = 13/3 ]

Hence, the value of x is 13/3.

Answer:

To find your answer you would subtract $6.50 and $2.85 from $14.85

you would get $5.50 so that is how much she spent on a round trip ticket to the zoo.

Step-by-step explanation:

Answer:

30 students: $346.5

1 student: $11.55

Step-by-step explanation:

It would cost a total of $57.75 every 5 student so just multiply by 6 to get your amount for 30 students. Then divide by 30 to get the amount per student.

Answer:

Road shimmer

Wiggling the vision

Heat heat waves

I'm swimming in a mirror

Road shimmer

Wiggling the vision

Heat heat waves

I'm swimming in a

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out

Can't make you happier now

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out

Can't make you happier now

Usually I put

Something on TV

So we never think

About you and me

But today I see

Our reflections

Clearly in Hollywood

Laying on the screen

You just need a better life than this

You need something I can never give

Fake water all across the road

It's gone now the night has come but

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out…

Answer:490

Step-by-step explanation:

Answer:

what number

Step-by-step explanation:

Answer:

turtles are vulnerable. so A is your correct answer

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

30-5x-10

-5x+30-10

-5x+40

-5x= -40

divide both sides by -5

-5x/-5= -40/-5

x=8

Answer:

(-1, -2) or x=-1 y=-2

Step-by-step explanation:

3x+y=-4      (1)

3x-4y=6      (2)

i used the first equation to subtract the second this cancels out the x

and you are left with:

5y=-10

y=-2

plug this back in:

2x+(-2)=-4

2x-2=-4

add 2 to both sides:

2x=-2

x=-1

Answer:

[tex]x = \frac{1}{4} [/tex]

[tex]y = \frac{2}{4} [/tex]

Answer:

56

Step-by-step explanation:

The simplest way to do this is to divide 3 by 21 to get 7.  This means that it takes $7 to buy one T-shirt.  If you multiple 8 X 7, you get 56.  This mean that the correct answer is A. $56.00

Hope it helped and have a great day :)

Answer:

Below.

Step-by-step explanation:

325/18

= 18.055...   minutes

= 18 minutes to nearest minute.

Answer:

x<-1

Step-by-step explanation:

I think and hope it helps

Thats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya LungsThats Metal In Ya Lungs

Answer:

√13

Step-by-step explanation:

Distance formula

√(4-2)²+(5-2)² = 2²+3² = √4+9 = √13

Answer: Y= 7, X= 6

Step-by-step explanation:

Answer:

0=2

There are no solutions

Step-by-step explanation:

Answer:

2x – 5x + 16 = – 3(x – 6)

-3x + 16 = - 3x + 18

-3x + 3x + 16 = 18

16 = 18

Thus, This is a False Equation

-TheUnknownScientist