Troubling math!

Ronaldo

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I have some spare time, so I can do the first problem you have up there.

1/5p+3=3/10p-8

I'm assuming you need to have p by itself in this equation, so that's what I'll be aiming for.

2/10p+3=3/10p-8
Subtract 3/10p to both sides.
-1/10p+3=3-8
Subtract 3 to both sides.
-1/1op=-8
divide -1/10 to both sides.
p=80

OR

-1/10p=-8
multiply 10 to both sides to cancel the denominator.
-1p=-80p
divide -1 to both sides.
p=80

Pretty certain that this is the right answer. I'm not that much confident in my algebra solving, but if you're confused with any parts of the work that I did, feel free to ask.
 

soapless

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how about find the first derivative of f(x)=x^3(sin(x))? :D?
Well, you'd have to use the product rule by taking the derivative of x^3 and multiplying that by sin(x), then add that whole mess by the derivative of sin(x) multiplied by x^3. Therefore your answer would be f`(x)= 3x^2(sin(x)) + x^3(cos(x)). You could simplify this further by factoring out x^2 leaving you with f`(x)= x^2(3sin(x) + x(cos(x)))

Calculus!

as for the problems in the orinigal post, WITH STEPS!

6+y=3/t with T=x-5
Express X in Y.

6+y=3/(x-5)
(x-5)(6+y)=3 Multiply both sides by (x-5)
x-5=3/(y+6) divide both side by (y+6)
x=(3/(y+6))+5 add 5 to both sides


1/5p+3=3/10p-8
need clarification on what is in each of the denominators

15/2x-1=3
15/2x = 4 add 1 to both sides
15=8x multiply both sides by 2x
15/8=x divide both sides by 8

2(q=1)=4p-5 (Express P in Q)
2(q-1)+5=4p add 5 to both sides
2q-2+5=4p multiply the 2 into the parentheses
(2q+3)/4 = p divide both sides by 4

q+8-1/p+6=0 (Express P in Q)
need some clarification on this one too
is it supposed to be (q+8)-(1/p)+6, because that's how I'm reading it.

I don't normally do other people's homework, but if you're truly having trouble figuring these out and not being lazy, I'll be happy to help.
 

Mmarz11

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how about find the first derivative of f(x)=x^3(sin(x))? :D?
Wasn't sure if you meant f(x)=x^(3sin(x)) or f(x)=(x^3)(sin(x)). If you meant the second then do what soapless said. Otherwise:

y=x^(3sin(x))
lny=ln(x^(3sin(x)))
lny=(3sin(x))(ln(x))
(1/y)(dy/dx)=(3sin(x))(1/x)+(cos(x))(ln(x))
dy/dx=y(3sin(x))(1/x)+(cos(x))(ln(x))
dy/dx=(x^(3sin(x))((3sin(x)/x)+cos(x)ln(x))
 
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