The altitude of a triangle is increasing at a rate of 1.500 centimeters/minute while the area of the triangle is increasing at a rate of 2.000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.000 centimeters and the area is 98.000 square centimeters?

The base of the triangle is shrinking at a rate of centimeters per minute.

Step-by-step explanation:

The formula of the area of a triangle is given by the following expression:

Where:

- Area of the triangle, measured in square centimeters.

- Base of the triangle, measured in centimeters.

- Height of the triangle, measured in centimeters.

The base of the triangle is:

If and , the base of the triangle is:

The rate of change of the area of the triangle in time, measured in minutes, is obtained after differentiating by rule of chain and using deriving rules:

The rate of change of the base of the triangle is now cleared:

Given that , , and , the rate of change of the base of the triangle is:

The base of the triangle is shrinking at a rate of centimeters per minute.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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step-by-step explanation: