Ask a New Question

Question

What is the largest rectangle that can be inscribed in the first quadrant of the ellipse 9x^2+16y^2=144?
15 years ago

Answers

Reiny
base along x-axis, height along y-axis, bottom left vertex at (0,0).
let the top right vertex be (x,y)
from equation
y = (1/4)√(144 - 9x^2)

Area = xy
= x(1/4)√(144 - 9x^2)
differentiate using the product rule, set the derivative equal to zero and solve for x
I got x = 4√3/3 for a max area of 384√3/3

but check my arithmetic.
15 years ago

Related Questions

What is the largest sum you can get when you add two 2-digit numbers? Explain. Find the rectangle of largest area that can be inscribed in a semicircle of radius R, assuming that... Determine the largest rectangle that can be inscribed inside the cavities of the two curves: y = –... What is the largest possible integer that can be chosen as one of five distinct positive integers wh... Rectangle ABCD ~ Rectangle EFGH. which similarity postulate or theorem lets you conclude that triang... Find the rectangle of largest area that can be inscribed inside the region bounded by y = 1 − x^2 an... The largest value of $x$ that satisfies $\sqrt{x+1}=x-2$ can be written as $\dfrac{a+\sqrt{b}}{c}$ w... Which of these is the largest living carbon sink? Insects Ocean Forest Soil Which rectangle has the largest area? * 15inx12in 30inx 25in 20inx5in 12 inx 12 in What is the largest value of x that would make the following list of a points not a function. (__,1...
Ask a New Question
Archives Contact Us Privacy Policy Terms of Use