Why is the answer 2y/x^2 and not 2x^-2*y?

x^(-a) = 1/x^a
x^(-2) = 1/x^2
Therefore, 2y/x^2 and 2x^(-2)y are equal
But often, you will be asked to use positive exponents,
so it's best to answer 2y/x^2

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How do you solve 7+3t over 4 =-t over 8?

This is: ?
(7+3t)/4 = -t/8
If it was the equation above do the following..
multiply both sides with 8 which gives you:
2(7+3t) = -t (get 2 due to (8/4 = 2))
14 + 6t = -t
6t + t = -14
t = -2

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Describe the effect of each number on the graph of f(x) =7 (-1x + 1)^3 +4.?

Describe the effect of each number on the graph of f(x) =7 (-1x + 1)^3 +4.
Match:
7
1
4
-1
3
Match with:
a. shifts the graph up
b. identifies the common graph to be used
c. shifts the graph to the left
d. stretch
e. reflects the graph over the y axis

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differentiation of exponential functions?

you have fraction, note that
[a/b]' = (a'b-b'a)/b^2
in your case a=x
b=e^x
as you know
x'=1
(e^x)' = e^x
so we get
(1*e^x - xe^x)/e^(2x)

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Find all the zeros of each equation.?

1. x^5 – 3x^4 – 15x^3 + 45x^2 – 16x + 48 = 0
A. 3, 4, i
B. 4, –4, i,–i
C, 3, 4, –4, i, –i
D. 3, –4, –i
2. x^3 – x^2 + 5x – 5 = 0
A. i, –i, 1
B. i, –i, –1
C. , –, –1
D. i, 1
3. 7x^2 – 144 = –x^4
A. 3, –3, 4i, 0
B. 3, 4i
C. 3, –3, 4i, –4i
D. –3, –4i

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Given that x²+y²=14x+6y+6,find the largest possible value of the expression E=3x+4y?

x^2-14x +y^2-6y=6
(x-7)^2 +(y-3)^2 = 6+49+9 = 64 = 8^2
this is a circle centre (7,3) radius 8
y = 3 + 8 sin[theta]
x= 7+ 8 cos[theta]
E= 3(7+8cos( theta)) +4 (3 +8 sin[theta])
= 21 +24 cos (theta) + 12 +32 sin (theta)
= 33 +24 cos (theta)+ 32 sin(theta)
dE/ d (theta)= -24sin(theta) +32cos (theta)=0
32cos theta=24sin (theta)
tan (theta) = 32/24 = 4/3
theta = arctan(4/3)
E= 33 +24 cos (arctan(4/3)) + 32 sin(arctan(4/3)
=73

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For a cubic graph, how do you know if it goes below the x axis or above the x axis?

every cubic (or in general, every polynomial of odd order) crosses x-axis.
to find where that happens, you solve for y=0.
for example if you have cubic, it would be ax^3+bx^2+cx+d=0

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Quick! Do arithmetic sequences have to be addition and subtraction?

I am learning about arithmetic sequences, and my book only shows addition and subtraction. Are multipication patterns arithmetic sequences too?
Examples:
I know 2, 4, 6, 8, 10 is an arithmetic sequence. +2
But is 1, 3, 9, 27 an arithmetic sequence too? x3

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Back pain help?!?!?!?!?!?!?!?!?

Don't trust those links. They look like virus links. Well it doesn't sound like something a medical Dr. could help you with. Maybe you should try a chiropractor. I've used them off and on my whole life and they have performed miracles on me.
Truthfully though, it just sounds like you are making your body do something that it's not really good for it. I don't know if you are in a circus or what, but just because your parents did it, doesn't mean it's right for you.
There is also at least one back stretching piece of equipment out there that might help you. Try this site for items you have seen on tv. The one I remember is you lay on your back and put your legs over it like it's a chair or something like that.
Well I can't find it on that site, but I'm still looking. This machine you would put your legs over it and it would automatically move your legs around. I'll keep looking for a while.

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What is wrong with my calf?

About a month ago i kinda strained my calf. However it started poping throughout the month and feeling strained or pain. When im walking down stairs the calf pops and a tendon or something feels out of place and pops in again.
I had a meniscus repair in July. At first i thought it was my knee but it seems to be a muscle between the thigh and my upper side calf in the back of my leg.
Yes im seeing my doctor next week but i would like to see some other opinions first

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