fractions kill me

"Here's the actual problem:

m = 7/8, (7,-8)

My answer: y = 7/8x - 120/8

Correct answer: y = 7/8x - 113/8"

-8=49/8+x
x= -64/8-49/8
x=-113/8

K, exam #2 coming up this weekend. Stuck on a few problems and would like these problems explained and broken down for me. Please!!

Problem #1

4+3i / 3-i

I know the answer is 9/10 + 13/10 i

how?

Problem #2

x^2=14x+10

I answered: -√59/35, √59/35

Correct answer: 7+√59, 7-√59

How?

Problem #3

1/6x+24 - 2/x^2-16=7/x-4

Correct answer: -184/41

How?



That's all for now. Thanks!

Problem 1
(4+3i)/ (3-i) when you have a complex number in the denominator you want to multiply by its complex conjugate (multiply to numerator and denominator)

(4+3i)/ (3-i) * (3+i)/(3+i)

simplifying gives

(12 + 13i +3i^2) / (9 - i^2)

remember i^2 = -1

(12 + 13i -3) / 10

9/10 + (13/10)i

Problem 2

x^2=14x+10

rearrange all terms onto one side

x^2 -14x -10 = 0

use quadratic equation

x = [14 +/- sqrt[(14)^2 - 4(1)(-10)]]/ 2(1)

x = 7 +/- sqrt(196 +40)/2
x = 7 +/- sqrt(236)/2

236 = 59 * 4

x = 7 +/- sqrt(59 * 4)/2
x = 7 +/- 2sqrt(59)/2
x = 7 +/- sqrt(59)

Problem 3
1/(6x+24) - 2/(x^2-16)=7/(x-4)

multiply both sides by (x^2-16)

(1/6)(x-4) - 2 = 7(x+4)
(x/6) -24 -2 = 7x + 4
(x/6) - 7x = 30

mutltiply both sides by 6

x - 42x = 180
-41x = 180
x= -180/41

Got this word problem (?) and I have absolutely no idea how to solve it. Can someone explain it to me?

im assuming that it says log base 6

The student is incorrect. You can check by exponentiating both sides with base 6

6^(log₆(x/y)) = 6^(log₆(x-y))

x/y = x-y which is not true for all x,y

The student incorrectly used the log properties

Correct answer:

log₆(x/y) = log₆x - log₆y

Ok, final exam tomorrow and I need help with a few problems.

I know the answer to all these problems, I just need help finding out how to get there. Thanks!

Problem One:

e^t=702

Problem Two:

Given that f(x)=3x+1 and g(x)=x^3, find (f * g)(-4)

Problem Three:

f(x)=2x^2-16x+34

Find the vertex, minimum/maximum, range, increasing, decreasing

e^t = 702

ln both sides

ln(e^t) = ln(702) ---- ln(e^t) = t
t = ln(702)
t = 6.5539

------------------------------

f(x) = 3x+1 g(x) = x^3 find (f(g(-4)) <- assuming this is how it is really written (f of g of -4)
g(-4) = (-4)^3 = -64
f(-64) = 3(-64) + 1 = -191

-----------------------------

f(x) = 2x^2 - 16x + 34
f'(x) = 4x - 16
f''(x) = 4

Min/Max when f'(x) = 0, incr when f''(x) is +, decr when f''(x) is -, range is -inf, inf because there is nowhere it is undefined

f'(x) = 0 when x = 4 (local min/max) - since we know that f''(x) is always positive (concave up), then there is a local minimum (or vertex) at x = 4

vertex: (4, f(4)) or (4, 2)
minimum: 2 @ x = 4
maximum: no local maximum, absolute maximum would be checked at endpoints of range or at infinity
range: stated above, there is nothing that limits range (i.e. denominators) and it is not given so the range is (-inf,inf)
increasing: wherever f'(x) is positive -> (4, inf)
decreasing: wherever f'(x) is negative -> (-inf,4)

I know the answer. Can you explain how to solve? Thanks!

Same with this:



This post was edited by Dune1 on Dec 5 2014 06:33pm

s = -16t^2 + 160t
v = s' = -32t + 160
a = v' = s'' = -32

Max height when v = 0, -32t + 160 = 0, t = 5
s(5) = -16(25) + 160(5)
Max Height = 400 ft

-------------------

Need a common denominator, which will be all of the denominators multiplied together.

Common Denominator is going to simply be: (5x+20)(x^2-16)(x-4) for now

(x^2-16)(x-4)/(5x+20)(x^2-16)(x-4) - 3(5x+20)(x-4)/(5x+20)(x^2-16)(x-4) = 8(5x+20)(x^2-16)/(5x+20)(x^2-16)(x-4)

To find out what x cannot be, you solve the common denominator: (5x+20)(x^2-16)(x-4) = 0

Then, use the numerators only to solve for x (what x really is).

x cannot be: -4, 4 (would make one or more original denominator as well as the common denominator equal to 0 -> undefined)

(x^2-16)(x-4) - 3(5x+20)(x-4) = 8(5x+20)(x^2-16)

Now multiply this out and solve for x normally

Really don't want to do this on a keyboard because I'll likely make mistakes, but you should know how to do this by hand.

Wolframalpha gives the x solution as -179/39
http://www.wolframalpha.com/input/?i=1%2F%285x%2B20%29+-+3%2F%28x^2-16%29+%3D+8%2F%28x-4%29

This post was edited by Dontrunaway on Dec 5 2014 07:40pm