PreCalculus 1

I have graphed the equations onto my calculator but I don't know how to answer the questions. Can someone explain this to me?

2. Coco, the wonder cat, is watching a spider on a wall that is 18 feet wide and 12 feet tall. The spider moves along for 10 seconds along a path describe by the parametric equations

x(t)=.3(t-2.5)^2+2 and y(t)=1.5 sin t+6

if the lower left corner is taken as the origin. Coco can reach 3 feet up and can move freely from side to side (Set your calculator to Radian mode¡Xnot degree mode¡Xfor this problem).

a. What is the closest that Coco can come to the catching the spider. When does this happen? Given answers to the nearest tenth. Explain your reasoning and how you arrived at this answer.

b. How close does the spider get to the origin? Show/explain how you arrived at this answer.

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  1. (a) since Coco can be anywhere on the line y=3, you want the closest that the spider can get to that line. Since sin(t) has a minimum value of -1, y(t) has a minimum of 4.5, so Coco can never get closer than 1.5 ft to the spider.

    (b) The spider's distance is

    z^2 = x^2+y^2
    = (.3(t-2.5)^2+2)^2 + (1.5 sin t+6)^2

    z has a minimum value of about 5.5 ft

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  2. daniel

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