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fiasKO [112]
4 years ago
12

How many metres would the blue lines be?

Mathematics
1 answer:
TiliK225 [7]4 years ago
8 0
22.86 metres
The two goal lines are 4.0 metres (13.1) from the end boards, and the blue lines are 22.86 metres (75.0 ft) from the end boards
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The diameter of a circle is 4 cm. Find its area to the nearest tenth.
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The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute. Complete this sentence: Th
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a. Calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x bet
miskamm [114]

Answer:

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is \dfrac{4}{3}\pi r^3

    a = -r , b = r , f(x)=\sqrt{r^2-x^2} and V=\dfrac{4}{3}\pi r^3

Solution A)

The given curve, y=3+3e^{-5x} rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

V=\int_a^b\pi R^2dx  

where, a = 2, b= 4 , R=y=3+3e^{-5x} and dx is thickness of disk.

V=\int_2^4\pi (3+3e^{-5x})^2dx

V=9\pi\int_2^4(1+e^{-10x}+2e^{-5x})dx

V=9\pi(x-\dfrac{1}{10}e^{-10x}-\dfrac{2}{5}e^{-5x})|_2^4)

V=9\pi(4-\dfrac{1}{10}e^{-40}-\dfrac{2}{5}e^{-20}-2+\dfrac{1}{10}e^{-20}-\dfrac{2}{5}e^{-10}))

V=9\pi (2-0)

V=18\pi

Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

x^2+y^2=r^2

y=\sqrt{r^2-x^2}

The solid form is sphere of radius r.

Using disk method, to find volume of solid

V=\int_a^b\pi R^2dx  

where, a = -r, b = r , R=y=\sqrt{r^2-x^2} and dx is thickness of disk.

V=\int_{-r}^r\pi (r^2-x^2)dx

V=\pi(r^2x-\dfrac{x^3}{3})|_{-r}^r

V=\pi(2r^3-\dfrac{2r^3}{3})

V=\dfrac{4}{3}\pi r^3

Hence, the volume of sphere is \dfrac{4}{3}\pi r^3

4 0
4 years ago
What is the measure of x?
Simora [160]

Answer:

<h2>x = 36°</h2>

Step-by-step explanation:

We know: the sum of the angles in any quadrilateral is 360°.

Therefore we have the equation:

108 + 108 + 2x + 2x = 360         <em>cobine like terms</em>

(108 + 108) + (2x + 2x) = 360

216 + 4x = 360           <em>subtract 216 from both sides</em>

4x = 144         <em>divide both sides by 4</em>

x = 36

7 0
3 years ago
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