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2 years ago

A circle has a radius of 10. An arc in this circle

Mathematics

1 answer:

emmasim [6.3K]2 years ago

4 0

Answer: The answer is 20 pi over 5

Step-by-step explanation:

You start by finding the circumference which you would get 20 pi by doing 2 times pi times your radius which is 10 then you find the fraction of the circle using the central angle which is 1/5 then you multiply 1/5 by 20 pi which you would put over 1 which then gives you 20 pi over 5

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A group of students was discussing the meaning of this statement. They were arguing back and forward about whether the converse

Savatey [412]

Answer:

The statement is missing. The statement is -- "A ray can be part of a line."

The answer is : The converse is not true, so Jahmiah is correct.

Step-by-step explanation:

A conditional statement is represented by showing p → q. It means if p is correct or true, then q is also correct or true.

And the converse of p → q can be shown as q → p.

But we know that the converse of a statement is not always true, it may be true and may not be true.

In the context, the statement is " a ray can be a part of a line." And so the converse would be "A line can be a part of the ray".

So by definition we know that a line is continuous line having no end points, it extends in one direction. While a ray starts from a point and extends to infinity in one direction.

Thus ray is part of line but line is not a part of the ray. So the converse of the statement is not correct.

Hence, Jahmiah is correct.

6 0

2 years ago

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

2 years ago

Which box plot represents a set of data that has the least mean absolute deviation?

Y_Kistochka [10]

Answer

b is the correct answer on ed and e2020

Step-by-step explanation:

tell me if you agree.

8 0

2 years ago

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On the first play, the football team lost 6 yards. On the second play, the team lost 5yards. What was their total change in yard

WINSTONCH [101]

The total change in yards the team lost was 11

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2 years ago

The inverse of Fx) is a function.<br> FOD<br> A. True<br> B. False

anastassius [24]

Not all functions have inverse functions. Those that do are called invertible. For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y.

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2 years ago