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creativ13 [48]
2 years ago
5

A triangle's base is increasing at the rate of 3 inches/sec, its height at 2 inches/sec. At what rate is the area of the rectang

le increasing when base is 10 inches and height is 14 inches
Mathematics
1 answer:
Triss [41]2 years ago
3 0

Answer:

dA/dt = 31  in²/ sec

Step-by-step explanation:

The area of the triangle is:

A(t)  = (1/2)*b*h     where  b is the base and h the height

Differentiation on both sides of the equation we obtain

dA/dt  =  (1/2)* db/dt * h + (1/2)* dh/dt * b   (1)

db/dt  = 3 in/sec

dh/dt =  2 n/sec

b =  10 in

h = 14 in

By substitution in (1)

dA/dt =  0,5* 3*14 +  0,5* 2*10

dA/dt =  21 in² /sec + 10 in²/sc

dA/dt = 31  in²/ sec

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