a. Suppose we want to add some punch to a partially filled drink dispenser of pu

Question

a. Suppose we want to add some punch to a partially filled drink dispenser of punch. We know that a 60 ounce botle of punch will increase the height of the punch in the dispenser by 1.8 inches. Let h represent the varying height of the punch in the dispenser (in inches) and let represent the varying volume of punch in the dispenser (in ounces). i. Express the change in eight of punch in the dispenser in inces,ah, in terms of the change in the volume of punch in the dis en er in s an Use to enter For example, type dx+5 for Az + 5) Preview i Express the change in the volume of punch in the dispenser in ounces, interns of fthe change in the height ofpunch in the dispenser in inches, . Use d toenter Preview b. Suppose we are fertilizing our lawn and didn't buy enough fertilizer. We want to describe the relationship between how many more square feet of lawn we have to cover and how many more pounds of fertilizer to purchase. We know that a 14 pound bag of fertilizer covers 6000 square feet. Let w represent the weight of fertilizer we purchase (in pounds) and let represent the number of square feet of lawn we have to cover. i Express the change in the number of pounds of fertilizer purchased in terms of the change in the number of square feet of lawn we have to cover, using d" to enter Preview i Express the change in the number of square feet of lawn we have to cover in terms of the change in the number of pounds of fertilizer purchased, using d to enter As Preview

Explanation / Answer

60 oz increases ht by 1.8 inches

We know that when dx = 60, dh = 1.8
So, dh = 1.8/60 * dv
dh = 0.03*dv --> ANS

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We know that
dh = 0.03*dv
So,
dv = dh/0.03
So,

dv = 100*dh/3 --> ANS

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b)
14 pd bag covers 600sq ft

So, we have
dw = 14/600 * ds

So, dw = 7*ds/300

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ds = 300*dw/7
by rearranging

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