A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 6-x^2
What are the dimensions of such a rectangle with the greatest possible area?
Width =

Height =

Height: 4 units

Width 2√/2

Explanation:

Start by sketching y = 6 - ². Then draw a rectangle beneath it. You will notice that the width is 2x and the height is 6 ². Area is given by length - times width, so the area function will be A=2x (6 - x²) = 12x - 2x³.

Now you differentiate to find the maximum.

A' = 12 - 6x²

Find critical numbers by setting A' to 0.

x = ± √/2

The derivative is negative at x = 2 and positive at x = 1, which justifies that the rectangle with width of √2 has maximal area.

The height will be y (√2) = 6 – (√2)²) = 4

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation:

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there 2 different things