All Answers 358090 Answers

The radius of the pentagon can be found as :

4/sin 54°

And the area of the base  =

5 (1/2) [4/sin(54°)]^2 * sin(72°) =  40 sin (72°) /[sin(54°)]^2

So.....the volume is

Base * Height  =

 40 sin (72°) /[sin(54°)]^2 *  16   ≈  929.97 cubic cenimeters = 930 cubic centimeters

 You are definitely not the first person to make a careless mistake PB, we all do it!!! 

But 200 kilometers by 100 kilometers is still pretty humongous...that is about 124 miles by 62 miles.

I can still answer the question anyway, though.

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perimeter = length + length + width + width

perimeter = 200 + 200 + 100 + 100

perimeter = 600 kilometers

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area = length × width

area = 200 × 100

area = 20,000 square kilometers

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You can just replace the word "kilometers" with whatever units you have. 

UGHHHHHH. I MEANT 200 kilometers and 100 kilometers. Someone change my username to DumbestPersonOf2017!

volume of a prism = area of base * height

Here is a top-down view of the base.

As you can see, it can be split into 5 triangles.

The area of each triangle = (1/2)(2)(4 tan 36º)(4) = 16 tan 36º

So...

the area of the base = 5 * 16 tan 36º = 80 tan 36º

And so..

the volume of the prism = 80 tan 36º * 16 = 1,280 tan 36º ≈ 929.974 cubic cm

Hey! I got one...just came up with it right now. 

Question: Which side of an ice cube is the coolest?

Answer: Trick question..there's only one side—the west side 

Let's put these into standard form, first

x^2 + y^2 -2x + 4y + 1 = 0 

x^2 - 2x + y^2 + 2x =  -1       complete the square on x and y

x^2 - 2x + 1 + y^2 + 2x + 4  =  -1 + 1 + 4     factor

(x - 1)^2 + ( y + 2)^2  =  4

This is a circle centered at (1, -2) with a radius of 2

x^2 + y^2 -2x + 4y - 11 = 0

x^2 - 2x + y^2+ 4y = 11

x^2 - 2x + 1 + y^2 + 4y + 4  = 11 + 1 + 4

(x - 1)^2  + (y + 2)^2  = 16

This is  a circle with the same center and a radius of 4

The area between the concentric circles =

pi [ 4^2 - 2^2]   = pi [16 - 4 ]  =  12pi units^2  ≈  37.7 units^2

It's 77284 for sure.

77284....? I'm not sure.

The resistance, R (in ohms) of a wire varies directly with the length, L (in cm) of the wire, and inversely with the cross-sectional area, A (in cm^2). A 500 cm piece of wire with a radius of 0.2cm has a resistance of 0.025 ohm. Find an equation that relates these variables in the form of  \(R=\frac{\Box \cdot \pi \dot\ L}{\Box}\)

\(R=\rho\times \frac{L}{A}\)

\(R[\Omega]=\rho[\frac{\Omega \cdot mm^2}{m}]\times \frac{L[m]}{\pi\cdot r^2[mm^2]}\)

example

\(R=0,025\Omega\)

\(r=2 mm\)

\(L=0.5 m\)

\(\rho=\frac{A\cdot R}{L}=\frac{r^2\pi\cdot R}{L}=\frac{2^2mm^2\cdot \pi \cdot 0.025\Omega}{0.5m}\color{blue}=0.62832\frac{\Omega \cdot mm^2}{m}\)    [ stainless steel ]

  !

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inverse tan is the same as atan. 

you can just type in 

atan(number goes here)  if you want

Note  that the series can be  written as

3⁰, 3¹, 3², 3³.......  =

3⁴ⁿ, 3^{4n + 1},  3^{4n + 2},^, 3^{4n + 3}........  for n = 0, 1, 2, 3 ..........

And the last digit has the repeating pattern

1, 3, 9, 7 ...........

So....the 99th term  is   3⁹⁸  =   3^{4(24) + 2}  which will end in 9

You can either push SHIFT and click on tan or type atan into the box 7UR7L3M4N☢🐢☣

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The outside....? 

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