+1 rep point for every problem answered (5+ questions) pre-calc help

[John]

1. find a formula for f^-1(x) given f(x)=ln(2x-5)

2.given f(x)=x^3-4x^2-11x+30 (a)find the zeros and (b) write a linear factorization of the function.

3.You are planning to make an open rectangular box from a 20 by 25in piece of cardboard by cutting congruent squares of side x from the corners and folding up the sides.

(a) write a funtion V(x)for the volume of the box
(b)what is the domain of V?
(c) Graph the function on your calculator and find the maximum volume
(d) what are the dimmensions of the box yielding the maximum volume?

4. Solve algebraically. what is the significance of the solution in terms of the graph of the two equations?
3x-5y=12
6x-10y=14


i will +rep a minimum of one point per answered correct question. different parts (a, b, c, ect all count as there own question.)

also if you answer them all, i will +10 rep you as soon as i can!

[Ana]

4. Solve algebraically. what is the significance of the solution in terms of the graph of the two equations?
3x-5y=12
6y-10y=14

I think in the second equation you're supposed to have an x somewhere in there...

[John]

Aerandria yup, messed that up, edited. i need this done very sson guys. due in an hour.

[Ana]

4. Solve algebraically. what is the significance of the solution in terms of the graph of the two equations?
3x-5y=12
6x-10y=14

3x-5y=12
x = (12+5y)/3

6x-10y=14
6[(12+5y)/3]-10y=14
2(12+5y)-10y=14
24+10y-10y=14
24=14

These is no solution for y (it cancels out), meaning these two lines are parallel

---------- Post added at 08:11 AM ---------- Previous post was at 08:09 AM ----------

1. find a formula for f^-1(x) given f(x)=ln(2x-5)

y=ln(2x-5)

2x-5=e^y

2x=e^y+5

x=(e^y + 5)/2

f^-1(x)=(e^x + 5)/2

---------- Post added at 08:13 AM ---------- Previous post was at 08:11 AM ----------

2.given f(x)=x^3-4x^2-11x+30 (a)find the zeros and (b) write a linear factorization of the function.

a) Zeroes (found through graphing): 5, -3, 2

b) (x-5)(x+3)(x+2)

[John]

Aerandria thank you:D are you planning to try any more or shall i rep now?

[Ana]

I'm working on the last one ^^

[John]

alright:D thanks

[Ana]

3.You are planning to make an open rectangular box from a 20 by 25in piece of cardboard by cutting congruent squares of side x from the corners and folding up the sides.

(a) write a funtion V(x)for the volume of the box
v(x)=x(20-2x)(25-2x)
(b)what is the domain of V?
0<x<10
(c) Graph the function on your calculator and find the maximum volume
I don't have a graphing calculator with me right now, but you can graph the line and then find the maximum
(d) what are the dimmensions of the box yielding the maximum volume?
Use the x value of the maximum as x in the volume equation, and it solve for the other two dimensions. X should be 3. something

[John]

repped:D thanks so much, i owe you 5 more

[Ana]

Found an online graphing calculator
3)
(c) answer is 820.53
(d) x = 3.68
So the dimensions are 3.68 x 12.64 x 17.64