Help thread for SAT blue CB book questions

[i_lose]

I thought this would be helpful since the blue CB book doesn't have explanations. I guess I'll start. MANY THANKS!

(p657, #18)

h(t)=c-(d-4t)^2

At time t=0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t=2.5, what was the height, in feet, of the ball at time t=1?

Why is the answer 70?

[jksbond007]

good thinking, the only way to get explanatinos is to pay for the cb online course!

[i_lose]

HAH. Isn't that thing like $60.

[zach447]

You have to use the given information to solve for c and d.

Here's what's given:

h(0) = 6 --> (0, 6)
h(2.5) = 106 --> (2.5, 100)

And now we'll solve using that information...

h(0) = c - (d - 0)^2 = c - d^2 = 6 --> c = 6 + d^2

h(2.5) = c - (d - 4(2.5))^2 = c - (d - 10)^2 = c - d^2 + 20d - 100 = 106 (because h(2.5) = 106, which was given)

So now we have:

c - d^2 + 20d - 100 = 106

and we can substitute the bolded equation above to put everything in terms of d:

(6 + d^2) - d^2 + 20d - 100 = 106

The d^2 and -d^2 cancel out and we're left with:

6 + 20d - 100 = 106
20d = 200 --> d = 10

Plug that back into the bolded equation above:

6 + d^2 = c
6 + (10)^2 = c --> c = 106

And now that we have c (106) and d (10), we can use h(t) to solve for h(1):

h(1) = c - (d - 4t)^2
h(1) = (106) - ((10) - 4(1))^2 = 70

I know that looks really involved, but really it's just a couple of substitutions.

zach, did you get an 800 on the math?

[everzinny]

Pg 783 # 25 (writing section)

(For the past) hundred years or more, Yellowstone National Park (was) a kind of sociological laboratory (in which) North Americans have been exploring (the meaning of) the nation-park concept. (No error)


why is this answer (was)? can someone explain why and what that is supposed to be?

[tweeeek]

It should be "has been" because the phrase "For the past x amount of time" implies that the action is still occurring

You're also given a clue later in the sentence that it is still happening because it says "North Americans have been exploring"

[bost88]

This is just a guess but I think that it should be: has been.

It is an ongoing action and it is still happening (since it says "for the past hundred years").

[zach447]

No, I got a 700, but my incorrect answers were all due to careless errors. I'll try my best to avoid those this time around by paying more attention to what I'm doing and hopefully get an 800...

And as for the Writing question, it's because the tenses have to match; "have been" is a form of the Present Perfect, so "was" is incorrect, as it is the Simple Past (or Preterite).

[rhs06]

It's only $19.95.

[k0w]

all the more for not giving cb more money :l
neway, please help on page 464 #20.

there are 75 more women than men enrolled in Linda College. If there are n men enrolled, then, in terms n, what percent of thsoe enrolled are men

100n/2n +75

[rhs06]

I also had trouble with this one at first. Say there are 25 men: therefore there are 100 women, and there are 125 people total; not just n+75, but rather 2n+75. Percent = part/whole*100 --> n/2n+75 *100.

[k0w]

wow i never thought of that. thanks thx06

i think the answers wrong, but im realy puzzled about this one

the eggs in a certain basket are either white or brown. If the ratio of teh number of white eggs to the number of brown eggs is 2/3, each of the gollowing could be the number of eggs in the basket EXCEPT

12

i got 10 because 3 isnt divisible in it, but...yea.

[zach447]

You actually have to add the two parts of the ratio together. For every 2 white eggs there are also 3 brown eggs, or 5 eggs total. So the TOTAL number of eggs will be a multiple of 5, and thus 12 isn't a possible amount.