Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis: y=x6, y=1 about y=6.

Answer:

16. f(y-2) = 2(y-2)²-5

= 2(y²-4y+4)-5

= 2y²-8y+8-5

= 2y²-8y+3

17. f(a+h)-f(a) = 2(a+h)²-5-(2a²-5)

= 2(a²+2ah+h²)-5-2a²+5

= 2a²+4ah+h²-2a²

= h²+4ah

Assuming the car's speed [tex]\frac{630}{14}=45\mathrm{mph}[/tex] does not change, the car will travel [tex]45\cdot42=\boxed{1890}[/tex] miles.

Hope this helps :)

Answer:

πr

Step-by-step explanation:

radius = r/2

so circumference = 2π(r/2)

= 2πr/2

= πr

Answer:

The answer is B which is C=2πr

Step-by-step explanation:

i just did it

Explanation:

Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by

[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]

Integrating this expression, we get

[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]

or

[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]

[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]

[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]

[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]

Answer:I just need points

Step-by-step explanation:

Hey

Answer:

Step-by-step explanation:

Answer:

1a 300

b 180

c 330

d 1470

e 180

f 7344

Step-by-step explanation:

Answer: 7 / 50

Step-by-step explanation:

Given

0.14

Convert to 100-denominator fraction

= 14 ÷ 100

= 14/100

Divide both numerator and denominator by 2

=(14 ÷ 2) / (100 ÷ 2)

=7 / 50

Hope this helps!! :)

Please let me know if you have any questions

Answer:

24 years

Step-by-step explanation:

total ratio =8

older student=40 years

3/8*40 ÷ 5/8=24

Answer:

8x-21

----------------------

(2x-7)(2x+7)

Step-by-step explanation:

7                       4

-----------   + ------------

4x^2 -49    2x+7

Factor  ( notice that it is the difference of squares)

7                       4

-----------   + ------------

(2x)^2 - 7^2    2x+7

7                       4

-----------       + ------------

(2x-7)(2x+7)    2x+7

Get a common denominator

7                       4(2x-7)

-----------       + ------------

(2x-7)(2x+7)    (2x-7)(2x+7)

Combine

7 +4(2x-7)

----------------------

(2x-7)(2x+7)  

7 +8x-28

----------------------

(2x-7)(2x+7)  

8x-21

----------------------

(2x-7)(2x+7)  

Answer:

(8x - 21) / (2x + 7)(2x - 7)

Step-by-step explanation:

7 / (4x^2 - 49)+ 4 / (2x + 7)

= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)

LCM = (2x + 7)(2x - 7)   so we have

(7 + 4(2x - 7) / (2x + 7)(2x - 7)

=   (8x - 21) / (2x + 7)(2x - 7).

Answer:

Answer:

606.6 and 233.3 respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*9=7560 and (x-y)*9=3360. Solving it, we get x=606.6 and y=233.3

Answer:

45°

Step-by-step explanation:

[tex] \sin \: m\angle F = \frac{EG}{FG} \\ \\ \sin \: m\angle F = \frac{2 \sqrt{11} }{2 \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{\sqrt{11} }{ \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{1}{ \sqrt{2} } \\ \\ \sin \: m\angle F = \sin \: 45 \degree \\ \\ \huge \boxed{ \purple{m\angle F = 45 \degree }}[/tex]

Answer:

False

Step-by-step explanation:

To find the inverse of a function, switch the variables and solve for y.

The inverse of f(n)=-(n+1)^3:

[tex]y=-(n+1)^3[/tex]

[tex]n=-(y+1)^3[/tex]

[tex]\sqrt[3]{n} =-(y+1)[/tex]

[tex]\sqrt[3]{n} =-y-1[/tex]

[tex]\sqrt[3]{n} +1=-y[/tex][tex]-(\sqrt[3]{n} +1)=y[/tex]

[tex]-\sqrt[3]{n} -1=y[/tex]

Answer:

False

Step-by-step explanation:

Answer:

Does the answer help you?

Answer:

If we put x=17/4

f(4×17/4-15)=8×17/4-27

f(2x=34-27

f(x)=7.

Hope i helped you.

9514 1404 393

Answer:

  (x, y) = (4, -4)

Step-by-step explanation:

A graphing calculator makes graphing very easy. The attachment shows the solution to be (x, y) = (4, -4).

__

The equations are in slope-intercept form, so it is convenient to start from the y-intercept and use the slope (rise/run) to find additional points on the line.

The first line can be drawn by staring at (0, -2) and moving down 1 grid unit for each 2 to the right.

The second line can be drawn by starting at (0, 2) and moving down 3 grid units for each 2 to the right.

The point of intersection of the lines, (4, -4), is the solution to the system of equations.

Answer:

f(x) can not be equal to g(x)

Step-by-step explanation:

If the result is possible:

f(x) = g(x)

x + 8 = x + 2

x + 8 - (x + 2) = x + 2 - (x + 2)

6 = 0

Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)

Answer:

B. 1/2

Step-by-step explanation:

Slope formula = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

[tex]\frac{(-4)-(-8) }{(6)-(-2)}[/tex]

[tex]\frac{4}{8}[/tex]

[tex]\frac{1}{2}[/tex]

Answer:

The polynomial is:

[tex]p(x) = -x^3 - 2x^2 + 5x + 6[/tex]

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Zeros of −3, −1, and 2

This means that [tex]x_1 = -3, x_2 = -1, x_3 = 2[/tex]. Thus

[tex]p(x) = a(x - x_{1})*(x - x_{2})*(x-x_3)[/tex]

[tex]p(x) = a(x - (-3))*(x - (-1))*(x-2)[/tex]

[tex]p(x) = a(x+3)(x+1)(x-2)[/tex]

[tex]p(x) = a(x^2+4x+3)(x-2)[/tex]

[tex]p(x) = a(x^3+2x^2-5x-6)[/tex]

Passes through the point (1,12).

This means that when [tex]x = 1, p(x) = 12[/tex]. We use this to find a.

[tex]12 = a(1 + 2 - 5 - 6)[/tex]

[tex]-12a = 12[/tex]

[tex]a = -\frac{12}{12}[/tex]

[tex]a = -1[/tex]

Thus

[tex]p(x) = -(x^3+2x^2-5x-6)[/tex]

[tex]p(x) = -x^3 - 2x^2 + 5x + 6[/tex]

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

the number before the x² is regarded as the identity element

Answer:Mark Brainliest please

Answer is 4.86 which is rounded to 5

Step-by-step explanation:

Cos 40 degree = VW/7

0.694 =VW/7

0.694 * 7 =VW

4.858 =VW

VW=4.86 is the answer

Answer:

1/13

Step-by-step explanation:

There are 52 cards in a deck of cards and 13 of them are hears

P(heart) = hearts / total

              = 13/52 = 1/13

Answer:

because the power of variable is -2

Step-by-step explanation:

polynomials are a combination of constant and variable or only variable, being that power of variable is always positive natural no.

7/x^2 denotes 7x^-2

Answer:

53.68

Step-by-step explanation:

tan54 = bc/39

bc = 39tan54

Step-by-step explanation:

Hey there!

From the given figure;

Angle CAB = 54°

Side AC = 39

To find: side BC

Taking Angle CAB as reference angle;

Perpendicular (p) = BC = ?

Base (b) = AC = 39

Hypotenuse (h) = AB

Taking the ratio of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep value;

[tex] \tan(54) = \frac{bc}{39} [/tex]

Simplify it;

1.376381*39 = BC

Therefore, BC = 53.678.

Hope it helps!

Hi there!

[tex]\large\boxed{a + b + c = 6}[/tex]

We can begin by using the point (0, 1).

At the graph's y-intercept, where x = 0, y = 1, so:

1 = a(0)² + b(0) + c

c = 1

We can now utilize the first point given (-3, 10):

10 = a(-3)² + b(-3) + 1

Simplify:

9 = 9a - 3b

Divide all terms by 3:

3 = 3a - b

Rearrange to solve for a variable:

b = 3a - 3

Now, use the other point:

15 = a(2)² + 2(3a - 3) + 1

14 = 4a + 6a - 6

Solve:

20 = 10a

2 = a

Plug this in to solve for b:

b = 3a - 3

b = 3(2) - 3 = 3

Add all solved variables together:

2 + 3 + 1 = 6

Answer:

Step-by-step explanation:

In order to find out how long it takes for the rocket to hit the ground, we only need set that position equation equal to 0 (that's how high something is off the ground when it is sitting ON the ground) and factor to solve for t:

[tex]0=-4.9t^2+112t+395[/tex]

Factor that however you are factoring in class to get

t = -3.1 seconds and t = 25.9 seconds.

Since time can NEVER be negative, it takes the rocket approximately 26 seconds to hit the ground.

Answer:

-6

Step-by-step explanation:

Answer:

[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]