If the base b of a triangle is increasing at a rate of 3 necess per minute while its height h is decreasing at rate of 3 inches per minute which of the following must be true about the area A of the triangle? A is decreasing only when b>h A is decreasing only when b>h A is always decreasing
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mathcalculuscalculus questions and answersif the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area a of the triangle? o a. a is always increasing ob. a is always decreasing oc. a is decreasing only when b<h. od. a is decreasing only when b> h. o e. a remains
Question: If The Base B Of A Triangle Is Increasing At A Rate Of 3 Inches Per Minute While Its Height H Is Decreasing At A Rate Of 3 Inches Per Minute, Which Of The Following Must Be True About The Area A Of The Triangle? O A. A Is Always Increasing OB. A Is Always Decreasing OC. A Is Decreasing Only When B<H. OD. A Is Decreasing Only When B> H. O E. A Remains
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If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inLet f be a function that is differentiable on the open interval (1, 10). If f(2)=-5, and f(5) = 5, and f(9)
= -5, which of th
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Transcribed image text: If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle? O A. A is always increasing OB. A is always decreasing OC. A is decreasing only when b<h. OD. A is decreasing only when b> h. O E. A remains constant. Let f be a function that is differentiable on the open interval (1, 10). If f(2)=-5, and f(5) = 5, and f(9) = -5, which of the following must be true? I. f has at least 2 zeros II. The graph off has at least one horizontal tangent. III. For some c, 2<c<5, f(0) = 3 O A. I and II only B. None C. I and III only D. I, II and III E. I only
Given : The base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at rate of 3 inches per minute
To Find : which of the following must be true about the area A of the triangle?
A is decreasing only when b>h
A is decreasing only when b<h
A is always decreasing
A is always increasing
A is constant
Solution:
Area of a triangle = (1/2) * base * height
base = b inches
height = h inches
Area = (1/2) bh
b = b + 3t where t is time in minutes
h = h - 3t
A (t) = (1/2) (b + 3t) (h - 3t)
= (1/2)bh + (1/2) ( h - b)3t - 9t²
= A - (3/2)(b - h)t - 9t²
= A - ( (3/2)(b - h)t + 9t² )
Area is decreasing if
(3/2)(b - h)t + 9t² > 0
=> (b - h)t + 6t² > 0
=> (b - h) + 6t > 0
=> b + 6t > h
A is decreasing only when b > h