The altitude of a triangle is increasing at a rate of 2.5 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 2 2 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7.5 7.5 centimeters and the area is 96 96 square centimeters

The base of the triangle is decreasing at a rate 8 centimeter per minute.      

Step-by-step explanation:

We are given the following in the question:

Instant height = 7.5 cm

Instant area = 96 square centimeters

Area of triangle =

where b is the base and h is the height of the triangle.

Rate of change of area of triangle =

Putting values, we get,

Thus, the base of the triangle is decreasing at a rate 8 centimeter per minute.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.