A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 7 − x 2 y=7-x2. what are the dimensions of such a rectangle with the greatest possible area?
Write the meaning of each algebraic expression. Then, evaluate the algebraic expression for the given value. 5x - 4 if x= 3
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Answer:
Step-by-step explanation:
Begin by grouping the x terms and the y terms together and separating the constants out.
Now we'll complete the square on those x and y terms. Take half the linear term of each, square it, and add it to both sides. Our linear x term is 2, half of 2 is 1 and 1 squared is 1, so we add that in. Likewise, half the linear y term (which is 8) is 4, and 4 squared is 16, so we add that in, too. Like this:
Doing this gives us the perfect square binomials for each of the x and y terms, and then gives us the radius on the right:
This is a circle with a center of (1, 4) and a radius of 3.