Misc Math Problems

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A few more to look over please....Thanks for any and all help! Pig's mommy


1. What is the average rate of change of f(x)=x^3-x in the interval {-2,2}?
a. 6
B. -3 THIS is her answer!
c. 3
d. 0
e. none of these

2. If a+bi is a complex number, llet {a+bi}=(sqrt)a^2+b^2. What is n[(3+4ai)^3]?
a. 625
b.125
c.5
d. (sqrt)91 which is 9
e. none of these THIS is her answer!!!


3. What is the sum of the solutions of 4^x -3 *2^x=2 + 32=0?
a. log^UNDERSCORE 2 (8/3)
b.2 THIS is her answer!
c. 5
D. -5
e. none of these

4. X+Y+Z, wher (x,y,z) is the solutionto the following linear system:
X+2Y+3Z=1
Y+2Z=2
Z=3

a. 7 This is her answer
b. 9
c.0
d. 1
e. none of these

5.Simplify the expression ln(81)+lm(27)+in(9) all over / ln(27)-ln(9) + ln (3)

a. ln(117)/lm(21)
b. 9/2
c. 7ln(3) This is here answer
d. 4.51
e. none of these

hope I wrote these so you can understand them...thanks!
 
1) How did she get her answer?

2) What is the meaning of the "n[]" notation?

3) There appears to be a typo, as the equation should not have two "equals" signs in it.

4) Should we assume that x, y, and z are the same as X, Y, and Z, respectively? If not, how are the six variables related? Also, please show the steps she did to obtain her answer.

5) Is the expression as posted, or is it actually "[ln(81) + ln(27) + ln(9)] / [ln(27) - ln(9) + ln(3)]"? Please show the steps she used to obtain her answer.

Thank you.

Eliz.
 
1. I'm not sure as she's at a music contest and I'm trying to check over her work?

2. should be let n{a+bi}=(sqrt)a^2+b^2. What is n[(3+4ai)^3]

3. should be 4^x -3 *2^x+2 + 32=0

4. yes x=X, y=Y, and z=Z and again I'm not sure her books and stuff are with her I only have this paper to check????

5. Yes the way you wrote it's correct
[ln(81) + ln(27) + ln(9)] / [ln(27) - ln(9) + ln(3)]


Thanks for any help you can give a mom with this to check adn 3 otests to study with kids and a soc. studies project to help finish! H
 
It would help if the student could reply, showing what she had tried and stating what her thoughts are. It is difficult, if not impossible, to divine what her sticking points might be, from looking at your report of what answer option you think she's chosen.

You started posting, if I recall correctly, before she'd left for school this morning. She'd then had some after-school activities (dance class?), but I'm sure she's home by now, and can post her work and her thoughts. This would be very helpful in letting the tutors know where she is needing assistance.

Thank you.

Eliz.
 
...the daughter(Kelle)

Hola!

Thanks for all of the help you've given to my mother...which she has shown me. To be truly honest, some of these problems I had no idea what to do with...so I guess and tested or worked through them in different ways than are probably correct. If you could continue giving me assistance, I'm not asking for the answer...but if you could show me the correct steps for some of these problems.

I'm not sure which question my mom started with but one problem I'm having more trouble with than I should is: finding the average rate of change of f(x)=x^3-x in the interval [-2,2]. would i put in -2 for x and see what f(x) becomes? If so wouldn't it be 8?

a+bi is a complex number, which is a given. We are supposed to let n[a+bi] equal the square root of a^2=b^2. If that is true then n[(3+4i)^3] would equal 625 correct? Because it would be 25^3?

I honestly have no idea how to solve the sum of the solutions for a problem. I know to follow the order of operations but would my first step in the problem: 4^x-3*2^x+2+32=0: be to subtract 32 from each side? I answered 2 because It seemed to be the most reasonable solution. Is there a specific formula for these types of equations?

I solved the x+y+z problem on my own after looking at the question and realizing it was similar to problems I was confident in doing, but thank you for looking at it anyway!

For the ln(81)+ln(27)+ln(9) over ln(27)-ln(9)+ln(3). I solved it to be 4.5 or 9/2, I simply used the ln function on my calculator, is that reliable or is there a formula to solving it that would be closer to correct? I remeber learning how to do something like this in math class but I can not remember the names of them.

I had one additional question that I"m not sure my mom had posted. This question seems really easy to me but for some reason I"m not sure where to start. We are supposed to find the sum of the first 100 terms of the arithmetic sequence 19,13,7. They are all subtracting 6, so would the easiest solution be to add the numbers on my own? If so the answer is definately larger than any of those listed.

I hope that this helps you to figure out what I need help with, from what I have seen and heard you are already a lot of great help:D

Thank you so much!!
 
Re: ...the daughter(Kelle)

4 little piggies mom said:
I had one additional question that I"m not sure my mom had posted. This question seems really easy to me but for some reason I"m not sure where to start. We are supposed to find the sum of the first 100 terms of the arithmetic sequence 19,13,7. They are all subtracting 6, so would the easiest solution be to add the numbers on my own? If so the answer is definately larger than any of those listed.
Click to expand...
S = N(F + L) / 2
where:
S = Sum
N = Number of terms
F = First term
L = Last term

We need to calculate the Last term:
L = F + D(N - 1) where D is the Difference, -6 in your problem:
L = 19 -6(100 - 1)
L = 19 -6(99)
L = 19 - 594
L = -575
So terms are: 19,13,7,1,-5,-11 ..... -569,-575.

Now we get the sum:
S = N(F + L) / 2
S = 100(19 + (-575)) / 2
S = 100(19 - 575) / 2
S = 100(-556) / 2
S = -55600 / 2
S = -27800

Tatoo them 2 formulas on the inside of your left hand, and you're set :wink:
 
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