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yuradex [85]
2 years ago
12

Find the volume of the cone. Round your answer to the nearest tenth.

Mathematics
1 answer:
oee [108]2 years ago
4 0

Answer:

15205.3  

Step-by-step explanation: H=30  R²=484  3.14=π  →= rounded up to tenth  V = Volume

<em><u>formula (no numbers): H x R² x π ÷</u></em><u> </u>\frac{1}{3}<u> (or 3) </u><em><u>= V</u></em>

<u><em>how i got the answer :  30 x 484 x 3.14 ÷ 3 = 15205.31  → 15205.3</em></u>

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<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%20%5Cinfty%20%20%5Cfrac%7B%20%5Csqrt%5B%20%20%5Cscriptsize%5Cphi%
Rasek [7]

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx

Replace x \to x^{\frac1\phi} = x^{\phi-1} :

I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx

Split the integral at x = 1. For the integral over [1, ∞), substitute x \to \frac1x :

\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx

The integrals involving tan⁻¹ disappear, and we're left with

I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}

8 0
2 years ago
In the figure, lines m and n are parallel. What is the value of y? a.42 b.48 c.132 d.138
Ierofanga [76]
C
the angle under y is 48 and line n adds up to 180
3 0
3 years ago
Read 2 more answers
The cost to manufacture x number of chairs can be represented by the function C(x)=36x. In this context, what does the statement
ss7ja [257]

Answer:

<em>The cost to manufacture 63 chairs, and that cost is 2268.</em>

Step-by-step explanation:

<u>Mathematical Models</u>

The cost to manufacture x chairs is given as the math model:

C(x)=36x

For example, to manufacture 10 chairs, we write:

C(10)=36*10=360

According to the explained above, the statement C(63)=2268 means we are calculating the cost to manufacture 63 chairs, and that cost is 2268.

4 0
2 years ago
Stays rope is 4 feet shorter than 3 times the length of Travis rope.stacys rope is 23 feet long.write an equation and solve it
oksian1 [2.3K]
T = 3s - 4
T = 3(23) - 4
T = 69 - 4
T = 65
3 0
3 years ago
Identify the property or rule shown by each equation. 9 divided 1 =9 and 33 times 1 =33
kicyunya [14]

identity property=something times one
5 0
3 years ago
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