SHOW STEPS AND SIMPLIFY! 30 POINTS!!!

The original price of a pair of headphones is $39.99 before tax. When David bought the headphones they rang up for $31.99 before

aleksley [76]

Answer:

To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.

Step-by-step explanation:

8 0

3 years ago

Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving

harina [27]

Answer:

The volume of the solid is 714.887 units³

Step-by-step explanation:

* Lets talk about the shell method

- The shell method is to finding the volume by decomposing

a solid of revolution into cylindrical shells

- Consider a region in the plane that is divided into thin vertical

rectangle

- If each vertical rectangle is revolved about the y-axis, we

obtain a cylindrical shell, with the top and bottom removed.

- The resulting volume of the cylindrical shell is the surface area

of the cylinder times the thickness of the cylinder

- The formula for the volume will be: V = $\int\limits^a_b {2\pi xf(x)} \, dx$ ,

where 2πx · f(x) is the surface area of the cylinder shell and

dx is its thickness

* Lets solve the problem

∵ y = $x^{\frac{5}{2}}$

∵ The plane region is revolving about the y-axis

∵ y = 32 and x = 0

- Lets find the volume by the shell method

- The definite integral are x = 0 and the value of x when y = 32

- Lets find the value of x when y = 0

∵ $y = x^{\frac{5}{2}}$

∵ y = 32

∴ $32=x^{\frac{5}{2}}$

- We will use this rule to find x, if $x^{\frac{a}{b}}=c, then=== x=c^{\frac{b}{a}}$ , where c

is a constant

∴ $x=(32)^{\frac{2}{5}}=4$

∴ The definite integral are x = 0 , x = 4

- Now we will use the rule

∵ $V = \int\limits^a_b {2\pi}xf(x) \, dx$

∵ y = f(x) = x^(5/2) , a = 4 , b = 0

∴ $V=2\pi \int\limits^4_0 {x}.x^{\frac{5}{2}}\, dx$

- simplify x(x^5/2) by adding their power

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{7}{2}}} \, dx$

- The rule of integration of $x^{n} is ==== \frac{x^{n+1}}{(n+1)}$

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{9}{2}}} \, dx=2\pi[\frac{x^{\frac{9}{2}}}{\frac{9}{2}}]$ from x = 0 to x = 4

∴ $V=2\pi[\frac{2}{9}x^{\frac{9}{2}}]$ from x = 0 to x = 4

- Substitute x = 4 and x = 0

∴ $V=2\pi[\frac{2}{9}(4)^{\frac{9}{2}}-\frac{2}{9}(0)^{\frac{9}{2}}}]=2\pi[\frac{1024}{9}-0]$

∴ $V=\frac{2048}{9}\pi=714.887$

* The volume of the solid is 714.887 units³

5 0

3 years ago

I need help with this question please and thank you

marissa [1.9K]

Answer:

y = -1x + 3 or f(x) = -1x + 3

Step-by-step explanation:

Rise/run = 3/-3 = -1

Crosses the y-axis at 3

y = -1x + 3 or f(x) = -1x + 3

8 0

4 years ago

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Find the distance between parallel lines whose equations are y = x - 6 and y = x + 8.

Sidana [21]

Answer:

14

Step-by-step explanation:

Distance between y2 = x + 8 and y1 = x - 6

y2 - y1 = (x + 8) - (x - 6) = 14

8 0

3 years ago

The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x

Anna11 [10]

We're looking for the two values being subtracted here. One of these values is easy to find:

g(1) = ∫f(t)dt = 0
since taking the integral over an interval of length 0 is 0.

The other value we find by taking a Left Riemann Sum, which means that we divide the interval [1,15] into the intervals listed above and find the area of rectangles over those regions:

Each integral breaks down like so:

(3-1)*f(1)=4

(6-3)*f(3)=9

(10-6)*f(6)=16

(15-10)*f(10)=10.

So, the sum of all these integrals is 39, which means g(15)=39.

Then, g(15)-g(1)=39-0=39.

I hope my answer has come to your help. God bless and have a nice day ahead!

3 0

3 years ago

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