Finals Prep

[tlwaring]

After completing what I could on a review sheet there are a few word problems I am having trouble setting up. Can you help get me started?

1. An object on Earth is projected upward at an initial velocity of 32 ft/sec. Its height after t seconds is given by h=32t-16tsqr. What is the maximum height the object reaches? Find the number of seconds until the object hits the ground.

2) Glenn can row 7 mph in still water. If it takes him the same time to row 6 miles downstream as it takes to row 4 miles upstream, what is the rate of the current?

3) Natalie can ride her bike 4 mph faster than her husband, Chuck. If Natalie can ride 48 miles in the same time that Chuck can ride 24 miles, what are their speeds?

4) How many gallons of 15% acid and 33% acid should be mixed to get 20 gallons of 21% acid?

5) A ball is thrown upward from ground level. After t seconds, its height in feet is a function defined by f(t) =16tsqr+96t. When will the ball reach 128 feet?

Thanks so much!

 

[stapel]

1) The maximum of a negative quadratic occurs at the vertex of the parabola. Find the vertex. (Either complete the square, or use the formula.)

2) Use the "uniform rate" formula, "d = rt". Recall that the current adds to his speed when he's going downstream, but subtracts when he's going upstream.

. . . . .downstream:
. . . . .distance: 6
. . . . .rate: 7 + w
. . . . .time: 6/(7 + w)

. . . . .upstream:
. . . . .distance: 4
. . . . .rate: 7 - w
. . . . .time: 4/(7 - w)

3) Pick a variable for Chuck's speed; write an expression, in terms of this variable, for Natalie's speed. Note that, if d = rt, then t = d/r. Write expressions for the equal times they rode, in terms of their distances and relative speeds. Set the expressions equal, and solve.

4) Use the standard "mixture" set-up:

. . . . .gallons solution:
. . . . .15%: x
. . . . .33%: 20 - x
. . . . .mix: 20

. . . . .percent acid:
. . . . .15%: 0.15
. . . . .33%: ??
. . . . .mix: ??

. . . . .gallons acid:
. . . . .15%: 0.15(x)
. . . . .33%: ??
. . . . .mix: ??

Complete the table. Add the input amounts, set equal to the output, and solve.

5) Plug in "128" for the height, and solve for the time "t".

Eliz.