(1 point) A rectangle is inscribed with its base on the xx-axis and its upper corners on the parabola y=11−x2y=11−x2. What are the dimensions of such a rectangle with the greatest possible area?

the rectangle has dimensions of length= 2√(11/3) and height=22/3

Step-by-step explanation:

since the parabola

y= 11-x²

is symmetric with respect to the y-axis ( meaning that y(x)=y(-x) );

area of rectangle with base from -x to x and height y = 2 *area of rectangle with base from 0 to x and height y

A=2*x*y

replacing y

A=2*x*( 11-x²) = 22*x - 2*x³

the maximum value can be found when the derivative of the area with respect to x is 0 , thus

dA/dx= 22 - 6*x² = 0

22 - 6*x² = 0

x max = √(22/6)

y max = 11-xmax² =  11-[√(22/6)]²= 11 - 22/6 = 44/6

then the rectangle with maximum area has dimensions of

length = 2*x max= 2√(22/6) and height=y max=44/6

answer: 177/8

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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