WS22-Related Rates_131_ak_april8

A a pyramid has a height h and a square base with

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Unformatted text preview: pyramid is = ℎ. (A) A pyramid has a height h and a square base with side x. If the height remains fixed and the side of the base is decreasing by 0.002 meters per year, what rate is the volume decreasing when the height is 120 meters and the base length is 150 meters? →=? =? = ℎ= 120 = 40 → 150 ℎ = 120 = −0.002 =0 Volume is decreasing 24 = 80 ∗ = 80 150 −0.002 = −24 / per year when the base length is 150 meters. (B) A pyramid has a height h and a square base with side x. If the height decreases at a rate of 0.0005 meters per year and the side of the base is decreasing by 0.002 meters per year, what rate is the volume decreasing when the height is 120 meters and the base length is 150 meters? . →=? =? = ℎ All three variables are functions of time. → 150 ℎ = 120 = −0.002 = −0.0005 Volume is decreasing 27.75 = 2∗ = ∗ℎ+ ∗ 2 150 −0.002 120 + 150 = −27.75 / per year when base length is 150 meters. −0.0005 12 C h . C is the circumference of the tree in meters at 12π ground level, and h is the height of the tree in meters. Both C and h are functions of time t (years). (Think of C and h as implicit functions of t.) 5. The volume of a tree is given by V = (A) Find a formula for = 2 ℎ∗ dV . What does this represent? dt + ∗ (B) Suppose the circumference grows at a rate of 0.2 meters/year and the height grows at a rate of 4 meters/year. How fast is the volume of the tree growin...
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This note was uploaded on 04/11/2013 for the course MATH 124 taught by Professor Wood during the Spring '13 term at ASU.

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