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2 years ago

find the surface area a planet if its circumference is about 18,000 miles long. Round to the nearest thousand square miles

Mathematics

1 answer:

Furkat [3]2 years ago

7 0

The surface area of the planet is 103,184,713.4 miles².

<h3>What is the surface area?</h3>

A planet has the shape of a sphere.

The first step is to determine the radius of the planet from the circumference.

Radius = circumference / (π x 2)

18,000 / (3.14 x 2) = 2,866.24 miles

Surface area of a sphere = 4πr²

4 x 3.14 x ( 2,866.24²) = 103,184,713.4 miles²

To learn more about the surface area of a sphere, please check: brainly.com/question/27267844

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F(20) = 1000 * (1.09)n

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Answer:

= 21800

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Step-by-step explanation:

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2 years ago

Camille had a very fun birthday party with lots of friends and family attending. The party lasted for 3 hours. She and her frien

Elena-2011 [213]

Camille spent 22 minutes and 30 seconds opening presents.

Since Camille had a very fun birthday party with lots of friends and family attending, and the party lasted for 3 hours, and she and her friends played games for 3/8 of the time, ate pizza and cake for 50% of the time , and spent the remainder of the time opening presents, to determine the amount of time spent opening presents the following calculation must be performed, posing the following linear equation:

Total time - time spent on other activities = time spent opening presents

3 - (3 x 3/8) - (3 x 0.5) = X
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22.5 = X

Therefore, Camille spent 22 minutes and 30 seconds opening presents.

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3 years ago

An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards example 2g each. compute the probability that

stiks02 [169]

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3 years ago

I have 4 papers sizes 8.5 inches by 11 inches how many square feet are the 4 papers?

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3 years ago

Find the critical numbers of the function f(x) = x6(x − 2)5.x = (smallest value)x = x = (largest value)(b) What does the Second

Marrrta [24]

Answer:

$a) x=0, x=\frac{12}{11}, x=2 \:$ b) The 2nd Derivative test shows us the change of sign and concavity at some point. c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

Step-by-step explanation:

a) To find the critical numbers, or critical points of:

$f(x)=x^{6}(x-2)^{5}$

1) The procedure is to calculate the 1st derivative of this function. Notice that in this case, we'll apply the <em>Product Rule</em> since there is a product of two functions.

$f(x)=x^{6}(x-2)^{5}\Rightarrow f'(x)=(f*g)'(x)\\=f'g+fg'\Rightarrow (fg)'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4} \Rightarrow 6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}=0\\f'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}$

2) After that, set this an equation then find the values for x.

$x^{5}(x-2)^{4}[6(x-2)+5x]=0\Rightarrow x^{5}(x-2)^{4}[11x-12]=0\Rightarrow x_{1}=0\\(x-2)^{4}=0\Rightarrow \sqrt[4]{(x-2)}=\sqrt[4]{0}\Rightarrow x-2=0\Rightarrow x_{2}=2\\(11x-12)=0\Rightarrow x_{3}=\frac{12}{11}$

$x=0\:(smallest\:value)\:x_{3}=\frac{12}{11}\:x=2 (largest value)$

b) The Second Derivative Test helps us to check the sign of given critical numbers.

Rewriting f'(x) factorizing:

$f'(x)=(11x-12)(x-2)^4x^{5}$

Applying product Rule to find the 2nd Derivative, similarly to 1st derivative:

$f''(x)>0 \Rightarrow Concavity\: Up\\\\f''(x)$

$f''(x)=11\left(x-2\right)^4x^5+4\left(x-2\right)^3x^5\left(11x-12\right)+5\left(x-2\right)^4x^4\left(11x-12\right)\\f''(x)=10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)$

1) Setting this to zero, as an equation:

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\\\$

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\(x-2)^{3}=0 \Rightarrow x_1=2\\x^{4}=0 \therefore x_2=0\\11x^{2}-24x+12=0 \Rightarrow x_3=\frac{12+2\sqrt{3}}{11}\:,x_4=\frac{12-2\sqrt{3}}{11}\cong 0.78$