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BARSIC [14]
3 years ago
9

Find the volume of a right circular cone that has a height of 11.1 cm and a base with a diameter of 17.2 cm. Round your answer t

o the nearest tenth of a cubic centimeter.
Mathematics
1 answer:
vovangra [49]3 years ago
3 0

Answer:

2577.8\text{ cm}^3

Step-by-step explanation:

GIVEN: A right circular cone that has a height of 11.1 cm and a base with a diameter of 17.2 cm.

TO FIND: Volume of cone.

SOLUTION:

radius of cone =\frac{\text{diameter}}{2}=\frac{17.2}{2}=8.6\text{ cm}

height of cone =11.1\text{ cm}

Volume of cone =\frac{1}{3}\pi r^2h

putting values we get

Volume of cone =\frac{1}{3}\times3.14\times8.6\times8.6\times11.1

                           =2577.8\text{ cm}^3

Hence the volume of cone is 2577.8\text{ cm}^3

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Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home
castortr0y [4]

Answer:

D) 40 miles

Step-by-step explanation:

First we must find the distance between the mall and the house.  The figure formed is a right triangle.  The length of the side from the mall to the house forms the hypotenuse of the triangle.  We can use the Pythagorean theorem to find the length:

a² + b² = c²

The two legs of the triangle, a and b, are 15 and 8:

15² + 8² = c²

225 + 64 = c²

289 = c²

Take the square root of each side:

√289 = √(c²)

17 = c

This makes the total distance

15+8+17= 40 miles

4 0
3 years ago
Read 2 more answers
Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p
Juli2301 [7.4K]
I'm reading this as

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy

with \nabla f=(2xe^{-y},2y-x^2e^{-y}).

The value of the integral will be independent of the path if we can find a function f(x,y) that satisfies the gradient equation above.

You have

\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}

Integrate \dfrac{\partial f}{\partial x} with respect to x. You get

\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx
f=x^2e^{-y}+g(y)

Differentiate with respect to y. You get

\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]
2y-x^2e^{-y}=-x^2e^{-y}+g'(y)
2y=g'(y)

Integrate both sides with respect to y to arrive at

\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy
y^2=g(y)+C
g(y)=y^2+C

So you have

f(x,y)=x^2e^{-y}+y^2+C

The gradient is continuous for all x,y, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy=f(4,1)-f(1,0)=\frac9e
8 0
3 years ago
Andre types 208 words in 4 minutes. Noah types 342 words in 6 minutes. Who types faster?
Vesna [10]

Answer:

Noah types faster

Step-by-step explanation:

Andre's typing speed per minute - 52 words per minute

\frac{208}{4} = 52

Noah's typing speed per minute - 57 words per minute

\frac{342}{6} = 57

3 0
3 years ago
1. *
slavikrds [6]

Answer:

I am not so clear about this question

3 0
3 years ago
Order these numbers for lest to greatest 1/2 ,1.1 ,5/3 ,2, 0 ,0.4, -2 ,5/8
Nat2105 [25]

The least number should always start off with negatives if there are any. In this case there is so we can start with -2 as our least amount. Next are the small fractions. If you're allowed a calculator, I would use that to find what the decimals will look like for each fraction:

\frac{1}{2} =0.5\\ \\ \frac{5}{3} =1.6666666666666666666666666666667\\ \\ \frac{5}{8} =0.625

After -2 the next least number is 0 and the next one is the fraction or decimal closest to the number 0 which is 0.4

The next number would be from the fractions we solved earlier. 0.5 and 0.625 would follow 0.4 and then 1.1 and 1.6667(solved for from fraction).

Here is the list:

-2,0,0.4,\frac{1}{2} ,\frac{5}{8} ,1.1,\frac{5}{3}

Hope this helps!


6 0
3 years ago
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