-- After dog ate 1/2 of the collection, there were 29 remaining.
-- Just before dog came along, there were (2 x 29) = 58 cards.
-- That was after Dan added 5 new ones.
-- Before he added the 5 new ones, there were (58 - 5) = 53 cards.
-- When this story began, Dan had <em>53 cards</em>.
Answer:
Radius= 8.99 mm (9 mm)
Step-by-step explanation:
We use the formula for the volume of a cone which is
1/3 pi ×(radius)^2 *height
932.58 = (pi) × (11) ×(r^2/3)
Radius^2 = (932.58×3) / (11pi)
= 80.96m
Radius= 8.99mm
Answer:

Step-by-step explanation:
We want to find the inverse of
![y = \sqrt[3]{ \frac{x}{3} + 1}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7Bx%7D%7B3%7D%20%2B%201%7D%20)
We interchange x and y to get:
![x= \sqrt[3]{ \frac{y}{3} + 1}](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7By%7D%7B3%7D%20%2B%201%7D%20)
We solve for y;

Multiply through by 3

Subtract 1 from both sides:

Therefore the inverse is

The area for the perimeter of a rectangle is:
<em>P = 2l + 2w</em>
In this problem, we are given that
P = 155 and
l = 45.5. To solve for area, we must find w. To do this, plug in the given info and isolate the w like so:

Now we know
w = 32. Knowing all the necessary info, we can use the area formula, <em>A=lw</em>, to solve for A.

The area is
1,456 sq ft. Hope this helps!