Question

I need help now, please. I'm doing a practice exam and it's way harder than anything we've done for the homework...

The first question alone I got wrong and can't go back and change my answers online, so I have no way of checking to see if I'm getting this right to hand it in as written homework, as we were told to do. Here is the first problem:

The relationship between the target heart rate when exercising, R, and a person's age, T, is given by the equation R - H_0 = p(220 - H_0 - T). Assume H_0 and p are positive constants.

Answer 1

Is anyone here good at word problems?

Answer 2

middle school stuff

Answer 3

I forgot to mention this is a two part question, although it's probably better I put this down here like this. Part a asks to find the slope if R is a function of T. The choices are:
a) 220p (which is an incorrect answer, I found out the hard way)
b) p
c) -pT
d) -p
e) PT

Part b asks to find the vertical intercept if R is a function of T. The choices are:
a) 220p - pH_0 + H_0
b) H_0
c) H_0 - 220
d) -pH_0 + 220p (which is wrong, I tried it)
e) 2H_0 - 220

Answer 4

Hey Oris :)
Ok this isn't too bad,
just some tricky algebra steps.

Answer 5

\[\large\rm R - H_0 = p(220 - H_0 - T)\]Distribute p to each term in the brackets,\[\large\rm R - H_0 = 220p - pH_0 - pT\]Add H_o to both sides,\[\large\rm R = 220p - pH_0 - pT+H_0\]R is a function of T,
so we're trying to write this in the form:
R=mT+b
(a linear function)
Where m is the slope.

Answer 6

If you move some stuff around,
you might be able to tell that we're able to write our function as,\[\large\rm R=-pT+(stuff)\]That's the only T term, yes?
There is a bunch of other junk that has nothing to do with slope.

Answer 7

Can you correctly identify the slope when it's in that form? :)\[\large\rm R=mT+(b)\]

Answer 8

So the slope would be -p? Because I feel like the rest of this stuff is for the vertical intercept.

Answer 9

Yes, good :)

Answer 10

For the second question,
we can't simply leave it as "stuff" anymore.
But hopefully it's clear that only the stuff is our vertical-intercept.

Answer 11

Okay, then for part b, the vertical intercept comes out to be \[220p - pH_0 + H_0\]That makes sense. I don't know why I always have such a hard time with calculus. But I'm actually really concerned, because it seems every time I try to take this class the subject material changes, and the teacher never goes over the important stuff for assignments until after it's due, if ever. My main goal right now is to try to learn this stuff as best as I can just to try to pull through with a C.

Answer 12

Thank you for your help. I'm probably going to be up for a while longer trying to finish this and make sure it's done correctly. Hopefully I get this back after it's graded so I can have it to look back on.

Answer 13

Calculus huh? :)
That's was the most exciting class for me (nerd I know).
So much fun stuff to learn!!

Work hard. Study. Be blessed.
Spend more time on OpenStudy if you need,
people love answering Calculus-related questions around here.