anonymous
  • anonymous
A function is given below. Determine the average rate of change of the function between x = -3 and x = -3 + h. f(t) = √-7t
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I have \[\sqrt{-7h}/h\] but it says that is wrong and I can't figure out why
anonymous
  • anonymous
Well, the 'average' rate of change for some interval \([a,b]\) (non-calculus, please tell me if you need otherwise) would be: \[ \Delta f_{avg}=\frac{f(b)-f(a)}{b-a} \]Try using that.
anonymous
  • anonymous
This is pre-calc

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
All right, then that should be the case.
anonymous
  • anonymous
so you are telling me my answer is right?
anonymous
  • anonymous
/correct
anonymous
  • anonymous
Nope, sorry. Using the above, we find, for \(f(t)=\sqrt{-7t}\) \[ \frac{f(-3+h)-f(-3)}{-3+h+3}=\frac{\sqrt{21-7h}-\sqrt{21}}{h} \]If you need further simplification of the above, please tell me.
anonymous
  • anonymous
how did you get -7h out from under the root?
anonymous
  • anonymous
How does one? You can't, you'd have to multiply both the numerator and denominator by \(\sqrt{21-7h}+\sqrt{21}\), but then it would end up on the denominator.
anonymous
  • anonymous
This is only useful for evaluating the limit.
anonymous
  • anonymous
I have no idea what you mean by that
anonymous
  • anonymous
why would I multiply the numerator and denominator by that?
anonymous
  • anonymous
@LolWolf
anonymous
  • anonymous
My 7 sub 2 is \[\sqrt{21-7h}\]
anonymous
  • anonymous
Y sub 2*
anonymous
  • anonymous
If you wish to remove the \(h\) from the radical, you'd have to do that, but, of course, then the top expression ends up in the denominator. So, the point is that one cannot remove the \(h\) from such.
anonymous
  • anonymous
yours simplifies to -7
anonymous
  • anonymous
f(-3+h) = \[\sqrt{-7(3+h)}\]
anonymous
  • anonymous
My equation does not simplify. And, yes, that last statement is correct. Keep in mind: \[ \sqrt{a+b}-\sqrt{a}=\sqrt{b}\\ \]Is *not* necessarily true (In fact, it is mainly true if b=0 or a=0).
anonymous
  • anonymous
The original problem looks like the square root goes over the "t"
anonymous
  • anonymous
Yes, and that's how I computed it. What do you feel is wrong with my expression?
anonymous
  • anonymous
I don't understand how there is no square root sign over the 7h in your third comment
anonymous
  • anonymous
@LolWolf
anonymous
  • anonymous
Where is there not a square root sign?
anonymous
  • anonymous
Over the "7h"
anonymous
  • anonymous
the 7h that is in the numerator of your third comment
anonymous
  • anonymous
http://imgur.com/1fwvB This is what I have in my browser and what has been typed.
anonymous
  • anonymous
oh that is weird it doesn't look like that in my browser
anonymous
  • anonymous
so my first comment is correct then
anonymous
  • anonymous
Square root of (-7h) divided by h
anonymous
  • anonymous
No, it is not, as they are not equivalent statements.
anonymous
  • anonymous
yeah it is because square root of (x+y) is equal to square root of x plus square root of y right?
anonymous
  • anonymous
No, it does not. \[ \sqrt{a+b}\ne\sqrt{a}+\sqrt{b} \]Unless a or b is zero.
anonymous
  • anonymous
oh jesus I feel like an idiot. So then your third comment does not simplify any further in pre calc?
anonymous
  • anonymous
Nope. I don't think there is any need to, unless you're taking limits.
anonymous
  • anonymous
so last thing square root of x*y is equal to square root of x times the square root of y?
anonymous
  • anonymous
Never mind I just proved it.
anonymous
  • anonymous
Thanks again I'll have to look up a khan academy video on that
anonymous
  • anonymous
Yes, that statement is true. Since: \[ a^2=n\\ b^2=m \]So we say: \[ nm=a^2b^2=(ab)^2 \]And all right, sure thing.

Looking for something else?

Not the answer you are looking for? Search for more explanations.