HURRY ITS URGENT!!!!

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12 - x2? (4 points)

wolverine [178]

Answer: 16 square units

Step-by-step explanation:

let the vertex in quadrant I be (x,y)

then the vertex in quadratnt II is (-x,y)

base of the rectangle = 2x

height of the rectangle = y

Area = xy

= x(12 - x²)

= -x³ + 12x

d(area)/dx = 3x² - 12 = 0 for a maximum of area

3x² = 12

x² = 4

x = ±2

y = 12-4 = 8

So, the largest area = 2 x 8 = 16 square units

7 0

3 years ago

PLEASE HELPP MEEEEE

pav-90 [236]

The smallest region that can be photographed is
5*7 = 35 square km
so we want to know how long it takes to zoom out to an area of
35 * 5 = 175 square km.

Notice that the length and width increase at the same rate, 2 km/sec, and they start out with a difference of two, so when the width has increased from 5 to x, the length will have increased from 7 to x+2. At the desired coverage area, then,
x(x+2) = 175
x^2 + 2x = 175
x^2 + 2x + 1 = 176 [completing the square]
(x+1)^2 = 176
x+1 = ±4√11
x = -1 ±4√11

Since a negative value for x is meaningless here, x must be
-1 + 4√11 = about 12.27 km
and the time it took to increast to that value was
(12.27 - 5) km / (2 km/sec) = about 3.63 seconds

6 0

3 years ago

Mr. Sarpy went to shoot some hoops on the basketball court. For every shot that he made within the three-point line he earned 2

Lostsunrise [7]

Answer:

x + y = 50 (1) and 2x + 3y = 115 (2); x = 35, y = 15

Step-by-step explanation:

Since x represents the number of 2 point shots and y represents the number of 3 point shots. If the total number of shots is 50, then x + y = 50 (1)

Also, the total 2 point shots is number of 2 point shots × points per shot = 2x and the total 3 point shots is number of 3 point shots × points per shot = 3y. Since the total number of points is 115, then

2x + 3y = 115 (2)

So, the system of equations are

x + y = 50 (1) and 2x + 3y = 115 (2)

We can solve for x and y by substituting x = 50 - y into (2)

So, 2(50 - y) + 3y = 115

100 - 2y + 3y = 115

100 + y = 115

y = 115 - 100

y = 15

So, x = 50 - y

= 50 - 15

= 35