Remember that for a function of the form

, a parabola, the focus will be:

.
We know that the vertex of the parabola is (0,0), and the sun is the focus of the parabola; we also know that the focus is in the positive y-axis and when the comet is as its vertex, the distance between them is 60'000.000 km; therefore the focus of our parabola is (0, 60'000.000).
Now that we know the focus, we can find

using the focus of the parabola:




Now, the only thing left is replacing the value of

in our equation

:

We can conclude that the equation that represents the path of the comet is
To solve the problem you must apply the corresponding formulas for calculate the area of each figure. Therefore, you have:
1-A cube where the length of each edge is 4 inches: <span>96 square inches
</span><span> A=6a^2=96 inches^2
2- A triangular prism where the area of each base is about 20 square inches, the length of each side of the base is 6 inches, and the height of the prism is 2 inches: </span><span>76 square inches.</span><span>
3- A square pyramid with a base length and slant height of 5 inches: 75</span><span> square inches.
</span><span>A=2(5)(5)+5^2=75 inches^2
4- A rectangular prism with a length of 5 inches, a width of 4 inches, and a height of 3 inches:</span>94 square inches .
A=2(4x5+3x5+3x4)=94 inches^2
Answer:

Step-by-step explanation:
We have been given that
and
. We are asked to find the expression that represents length of PS.
We know that
.
Upon substituting our given values in above equation, we will get:




Therefore, the expression
represents length of PS.
Here you go. Answer is in the Image.
1) width = x
length = x + 8
perimeter = 2 (length + width)
196 = 2 * (x+8+x)
196 = 2* (2x+8)
196 = 4x + 16
180 = 4x
x = 45 (thats width)
2) length would be 45+8=53
3) area = length times width = 45 * 53 = 2385 square feet