\(\csc(\arccos u ) \\~\\ =\frac{1}{\sin(\arccos u)} \\~\\ =\sqrt{ (\frac{1}{\sin(\arccos u)})^2 } \\~\\ =\sqrt{ \frac{1}{\sin^2(\arccos u)} } \\~\\\)

And... sin²θ = 1 - cos²θ

\(=\sqrt{ \frac{1}{1-\cos^2(\arccos u)} } \\~\\ =\sqrt{ \frac{1}{1-\cos(\arccos u)\cos(\arccos u)} } \\~\\ =\sqrt{ \frac{1}{1-uu} } \\~\\ =\frac{1}{\sqrt{1-u^2}} \\~\\\)

a car with a tire diameter of 20 inches will make  about   (5280 * 12) / (20 pi)  = 1008 revolutions per mile
 
A car with a tire diameter of 25 inches will make  about     (5280 * 12) / (25 pi)  =  807 revolutions per mile
 

10 = (1/2) * 5 * height
10 = 5/2 * height
 
Multiply both sides of the equation by 2/5.
10 * 2/5 = height
4 = height

1. The state that follows birth, and precedes death; the state of being alive and living.
2. heading A period of time.
3. heading Personal existence.

Math is the best thing on Earth!

Does the prism look something like this?

Part A:

In the purple writing, I found the height of the triangle using the Pythagorean theorem.

I think this is what the question is calling the "height of the box".

height of the box = 15 cm

Part B:

The amount of cardboard needed for the sides will be the lateral area of this prism.

lateral area = perimeter of triangle * height of prism

lateral area = (16 + 17 + 17) * 20

lateral area = 50 * 20

lateral area = 1,000    cm²

area of circle = π * (radius)2
 
radius = diameter / 2
radius = 28 yd / 2
radius = 14 yd
 
area of circle = π * (14 yd)2
area of circle = 196π    yd2
area of circle ≈ 196(3.14)  yd2   ≈   615  yd2

I don't know

D. coefficient

Surface area  =  pi * radius * slant height  +  pi * 8^2  = 

pi * ( 8)  * sqrt (8^2  + 24^2) + pi * 8^2  = 837 m^2

574 pi  =   pi * 29 * slant height       divide through by  29 pi

574/ 29  = 19.79 cm  = 19.8 cm  (rounded )

I think it is D                              and you're welcome

I'm not trying to be mean, but 0/0 isn't 0; it's undefined.

Math is for everyone to use their brain

this is what i've gotten so far. i've only firgured out most of part b

Part B: first, i drew out the actual shape, but just flat. then i labeled all of the sides w/ their measurments. next, i found the area for each individual shape.
TRIANGLES: (17 * 16) / 2 = 136
RECTANGLES: 20 * 16 = 320
 

We have the form

Ax^2 + Bx + C  =  6x^2 + 12x + ( - 18 )

The x coordinate of the vertex  =   -B / [ 2A]  =   -12 / [ 2 (6) ]  =  -12 / 12   = -1

And the y coordinate  =   6(-1)^2 + 12((-1)  + (-18)    =   6 - 12  - 18   =   -24

So....the vertex  is   ( -1, 24 )

Also....you can say

a = (1/2)bh          , where a is area, b is base, and h is height

Divide both sides of this equation by b

a/b = (1/2)h

Multiply both sides of this equation by 2.

2a/b = h

Now you can just plug in what you know for "a" and "b" and and solve for h 

Thank You

y = mx + b

In this form, we know that b is the y-intercept..... b = 7

y = mx + 7

We know that this line passes through the point (-9, 0) , so we can plug this point in and solve for m.

0 = m(-9) + 7

-7 = -9m

7/9 = m

Now we know b = 7 and m = 7/9 , so the equation of this line in slope-intercept form is

y = (7/9)x + 7

thank you SO much. nothing else was giving me a straight answer, so this was my last resort. thanks alot

Euler's formula says that

Faces + Vertices − Edges = 2

So

Faces + 13 - 28  = 2

Faces - 15  = 2       add  15 to both sides

Faces  =   17

area = (1/2) * base * height

For example....if we know that    base = 5    and   area = 10 sq units,    then

10 = (1/2) * 5 * height

10 = 5/2 * height

Multiply both sides of the equation by 2/5 .

10 * 2/5 = height

4 = height

Jessie bought a shirt for $6 . it was originally $8, what % discount did she recieve?

$8 - $6 = $2 the amount of the discount on the shirt.

$2 / $8 =0.25 x 100= 25% discount that Jessie received on the shirt.

You can also do it this way:

1 - ($6 / $8) = 1 - 0.75 = 0.25 x 100 = 25%. Choose the method you understand the best.