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alekssr [168]
3 years ago
12

If the radius of mars is about 13.7% of neptune's radius, what is the radius of neptune?

Mathematics
1 answer:
Marianna [84]3 years ago
6 0
The volumetric mean radius of Mars is about 3389.5 km. We know that it's 13.7% of Neptune's mean radius, so we can write it down as:

3389.5 = 13.7% of x (where x is Neptune's radius)
3389.5 = 13.7% x
3389.5 = 137/1000x                / * 1000 (both sides)
3389500 = 137x                       / ÷ 137 (both sides)
x = 24740.87591240876
x ≈ 24740.88

Answer: The mean radius of Neptune is about 24740.88 km.
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find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu
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The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

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Substitute value of y in the above equation, we get,

\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}

Now, differentiate P with respect to x, and we get,

\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}

Solving the above equation to zero, we get,

\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\begin{aligned}y&=108-36\\y&=72\end{aligned}

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

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