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Tresset [83]
3 years ago
14

Use a net to find the surface area of the cylinder use 3.14 for pi

Mathematics
1 answer:
telo118 [61]3 years ago
7 0

Answer:

3.14

Step-by-step explanation:

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Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate​ axes, the curve
Salsk061 [2.6K]

Answer:

\large \boxed{2\pi(15 - \ln16)}

Step-by-step explanation:

A 90° portion of your volume is shown below.

Let's use the shell method and decompose the solid of revolution into cylindrical shells.

The volume of each cylindrical shell is

dV = 2πrh dx

where  

r = ln16 - x

h = eˣ

So

dV = 2π(ln16 - x)eˣdx  

\begin{array}{rcl}V& =& 2\pi \int_{0}^{\ln16}(\ln16 - x)e^{x}dx\\\\&=&2\pi \int_{0}^{\ln16}(\ln 16)e^{x}dx -2\pi \int_{0}^{\ln16} xe^{x}dx\\\\&=& 2\pi \ln16 \int_{0}^{\ln16}e^{x}dx - 2\pi\int_{0}^{\ln16}xe^{x}dx\\\\\end{array}

Let's integrate the two terms separately.

\begin{array}{rcl}A &=& 2\pi \ln16 \int_{0}^{\ln16}e^{x}dx\\\\&=& 2\pi\ln16[e^{x}]_{0}^{\ln16}\\\\&=& 2\pi\ln16(16 - 1)\\&= &\mathbf{30\pi\ln1}\\\\B &=&2\pi\int_{0}^{\ln16}xe^{x}dx\\\end{array}

Use the integration by parts formula

\int u dv  = uv - \int v du

\begin{array}{rcl}uv - \int v du &=&\\B &=& 2\pi[xe^{x}]_{0}^{\ln16} - 2\pi \int_{0}^{\ln16} e^{x}dx\\\\&=&2\pi[xe^{x}]_{0}^{\ln16}-2\pi [e^{x}]_{0 }^{\ln16}\\\\&= &2\pi(16\ln16- 0) -2\pi(16 - 1)\\&=& \mathbf{32\pi \ln16 -30\pi}\\A - B &= &30\pi\ln16 - 32\pi \ln16 +30\pi\\&=& 30\pi - 2\pi \ln16\\&=&\mathbf{2\pi(15 - \ln16)}\end{array}\\\text{The volume of the solid is $\large \boxed{\mathbf{2\pi(15 - \ln16)}}$}

7 0
3 years ago
20 POINTS!! EASY QUESTION! WILL MARK BRAINLIEST!! READ THE INFO! THEN FILL IN THE BLANKS!
LUCKY_DIMON [66]

To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.


New Steps: $7.50/1.5 hours = $5 per hour


Stepping High: $6.50/1.25 hours = $5.20 per hour

8 0
2 years ago
Read 2 more answers
Write .0296 in word form
TEA [102]

two hundred ninety-six ten thousandths

4 0
2 years ago
Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates
natali 33 [55]

The rule for a rotation by 180° about the origin is (x,y) -->(−x,−y)

So A(-3, 2) to A'(3, -2)

Answer:

A'(3, -2)

4 0
2 years ago
What is x, the distance between points A and A'? 2. 4 units 4. 8 units 13. 6 units 14. 4 units.
adelina 88 [10]

The distance between points A (3, -5) and A' (2, -3) is 2.4 units.

Given that,

The points A (3, -5) and A' (2, -3).

We have to determine,

The distance between point A and A'.

According  to the question,

The distance between two points is determined by using the distance formula.

\rm Distance \ formula = \sqrt{(x_2-x_2) ^2+ (y_2-y_2)^2

Then,

The distance between points A (3, -5) and A' (2, -3) is,

\rm Distance  = \sqrt{(2-3) ^2+ ((-3)-(-5))^2}\\\\ Distance  = \sqrt{(-1) ^2+ (2)^2}\\\\ Distance  = \sqrt{1+4}\\\\Distance = \sqrt{5}\\\\Distance = 2.4 \ units

Hence, The distance between points A (3, -5) and A' (2, -3) is 2.4 units.

For more details refer to the link given below.

brainly.com/question/8069952

6 0
1 year ago
Read 2 more answers
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