glittergirl17

hey, i'm really confused with a couple of the blue book math questions, and i need some serious help with solving them . . .

PT1 S6 #17 (this one is a grid in)
In the XY-coordinate plane, the graph of x=y^2 -4 intersects line L at (0,p) and (5,t). What is the greatest possible value of the slope of L?

PT3 S8 #9
A regulation for riding a certain amusment park ride requires that a child be between 30 inches and 50 inches tall. Which of the following inequalities can be used to determine whether or not a child's height h satisfies the regulation for this ride?
(A) |h-10| < 50
(B) |h-20| < 40
(C) |h-30| < 20
(D) |h-40| < 10
(E) |h-45| < 5

i'm trying desperately to up my math score for october and really need some help!

tanman

#17

Plug the x's into the equation to get the y's
p = 0^2-4 = -4
t = 5^2-4 = 21

Then calculate the slope
m (slope) = /\ y / /\ x = (21 - -4) / (5-0) = 25/5 = 5

tanman

#9

If the height range is 30-50, then the child has to be within 10 inches of 40, which is the middle of the range. You need an inequality that says (difference between h to 40) < 10. To find the difference between any number to another number, you subtract them and take the absolute value (because you only want a posiitve difference) to get D: |h-40| < 10

gcf101

#17

tanman, that's a great example of how ETS protects 800 from smart people.

It's another way around:
0 = p^2-4 --> 2 solutions
5 = t^2-4 --> 2 solutions

There are 2*2=4 possible ways to draw line L, and 4 possible values for its slope.
You don't really need to calculate them all to find the greatest. Think graphically.

What could help you to avoid this mistake?
The words "greatest value". It's extremely unlikely that you asked to find it, but you end up with only one choice.

tanman

Whoops.. too early in the morning to be doing SAT problems

Here's a new (hopefully correct) explanation:

0 = p^2-4 => p = 2 or -2 => point A = (0,2) or (0,-2)
5 = t^2-4 => t= 3 or -3 => poing B = (5.3) or (5,-3)

Like gcf101 said, instead of calculating all the slopes, it would probably be easier to plot the four points and look for the pair with the highest (steepest) slope.

Son of Liberty

the answer i get for 17 is 1... is that correct?

glittergirl17

Yes the right answer for 17 is 1

Blademaster

Can you plot them with ti-83? If yes, how does it work?

Andrassy

how can 9 be D? If |h-40| < 10, then 50 and 30 dont work. they are equal to 10, not less than. or is it supposed to be <=

branderson925

well since its between 30 and 50 inches, i assume they mean they can be 30.0001 inches and ride.