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zzz [600]
3 years ago
14

The circumference of the earth is about 40050 km. Which of the following is the closest approximation of the diameter? Use 3.14

for π.
A. 6375 km
B. 9450 km
C. 10025 km
D. 12750 km
Mathematics
1 answer:
prohojiy [21]3 years ago
7 0
D is the answer
40050 divided by 3.14 is 12754.77707
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Paladinen [302]
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Neko [114]

Answer:

v =  \frac{32\pi}{3}

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v=33.52

Step-by-step explanation:

Given

f(x) = 4x - x^2

g(x) = x^2

[a,b] = [0,2]

Required

The volume of the solid formed

Rotating about the x-axis.

Using the washer method to calculate the volume, we have:

\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx

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v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx

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Substitute values for a, b, f(x) and g(x)

v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx

Evaluate the exponents

v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx

Simplify like terms

v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx

Factor out 8

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Integrate

v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0

v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0

Substitute 2 and 0 for x, respectively

v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])

v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])

v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]

v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]

Take LCM

v = 8\pi [ \frac{16*4- 16 * 3}{12}]

v = 8\pi [ \frac{64- 48}{12}]

v = 8\pi * \frac{16}{12}

Simplify

v = 8\pi * \frac{4}{3}

v =  \frac{32\pi}{3}

or

v=\frac{32}{3} * \frac{22}{7}

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PtichkaEL [24]

Answer:

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Step-by-step explanation:

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slope (m) = \frac{24}{3}

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y = mx + b

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16 = b

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y = mx + b

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Substitute y = 112 in the equation

112 = 8x + 16

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Ede4ka [16]
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