SOLUTION: use the formular for the area of a rectangle and the pythagorean Theorem to solve: A small television has a picture with a diagonal measure of 10 inches and a viewing area of 48 s

Question 4061: use the formular for the area of a rectangle and the pythagorean Theorem to solve: A small television has a picture with a diagonal measure of 10 inches and a viewing area of 48 square inches. find the length and width. the width is y and the length is w. I know x times y = 48 square inches. y = 48 divided by x and I must be not setting up the equation. thought it was 2x + 2y = something????? x is 8 and y is 6 but I need step by step please.
Another question is this that I cannot work through.
A planet's orbit follows a path described by 16x^2 + 4y^2 =64. A comet follows the parabolic path y=x^2 - 4. Where might the comet intersect the orbiting planet?
Hope you can help me ASAP

Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
please submit one problem at a time.
A planet's orbit follows a path described by 16x^2 + 4y^2 =64. A comet follows the parabolic path y=x^2 - 4. Where might the comet intersect the orbiting planet?
That's a nice one.
That they intersect means that there is a moment of time when their x and y positions, respectively, are the same. If they are both in the point (x, y), that means that

Let's use the second formula for y and substitute it into the first equation:

Use z for x^2:

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

This is an equation! Solutions: z=4,z=0.
Graphical form: Equation was fully solved.
Text form: 16z+4*(z-4)^2=64 simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( 16z+4*(z-4)^2=64 )
If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved these terms to the left highlight_green%28+-64+%29

It becomes .

Look at .
Equation highlight_red%28+16%2Az%2B4%2A%28z-4%29%5E2-64=0+%29

is a quadratic equation: 4*z^2-16*z =0, and has solutions 4,0
It becomes .
Result:
This is an equation! Solutions: z=4,z=0.

Universal Simplifier and Solver

Done!

Solutions z=4, z=0 mean:
x^2=4, x^2 = 0, or
x=-4, 0, 4.
Use formula to calculate values of y, for every value of x.
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