solve t = q/(1 + (g/p)) for p; simplify ((6z)^(7/2))/((4z)^(

[kpx001]

i've forgotten my basic algebra. can someone please show me the steps to completing this problem? i tend to multiply the entire denominator across the = but i dont get the same answer as the back of the book does. thanks


and for this problem how would i simplify the numbers into like a root form? i know how to simplify the variables

 

[stapel]

If the images of text are not viewable, these are the exercises:

1) Solve t = q / [1 + (g/p)] for p.

2) Simplify the following expression: [ 1 / (4z)^(5/2) ] * [ (6z)^(7/2) ]

 

[stapel]

1) Solve t = q / [1 + (g/p)] for p.

Simplify 1 + (g/p).

Since you're dividing by (the simplified form of 1 + (g/p), which is) a fraction, invert and convert to multiplication with (q/1).

Multiply both sides of the resulting equation by the denominator of the right-hand side. You should end up with p + g = pq.

Get both terms containing "p" on one side of the equation, with the "g" on the other.

Factor out the variable you want, and divide whatever is left to the other side of the equation.

2) Simplify the following expression: [ 1 / (4z)^(5/2) ] * [ (6z)^(7/2) ]

What is 4[sup:i5h6z981]4/2[/sup:i5h6z981] = 4[sup:i5h6z981]2[/sup:i5h6z981]? What is 4[sup:i5h6z981]1/2[/sup:i5h6z981] = sqrt[4]? What is the value of 4/2 + 1/2? What then is the value of 4[sup:i5h6z981]5/2[/sup:i5h6z981]?

Apply the same reasoning to 6[sup:i5h6z981]7/2[/sup:i5h6z981].

What is the simplified form of (x[sup:i5h6z981]7[/sup:i5h6z981]) / (x[sup:i5h6z981]5[/sup:i5h6z981])? What then is the simplified form of your expression?

If you get stuck on either exercise, kindly please reply with a clear listing of all of your work and reasoning so far. Thank you!

Eliz.

 

[Deleted member 4993]

Re: help please. basic algebra + a simplification

i've forgotten my basic algebra. can someone please show me the steps to completing this problem?

i tend to multiply the entire denominator across the = Please show us your work so that we know where to begin to help you

but i dont get the same answer as the back of the book does. thanks


and for this problem how would i simplify the numbers into like a root form? i know how to simplify the variables

hint:

\(\displaystyle \frac{z^n}{z^m} \, = \, z^{(n - m)}\)

 

[kpx001]

Re: help please. basic algebra + a simplification

i dont understand what u mean by flipping but this is what i did

t(1 + (9/p)) = q
q/t - 1 = 9/p
(q/t -1)p = 9
p = 9/(q/t - 1)

the 2nd problem i get is
6^(7/2) * z / 4^(5/2)
how do i get = constants for 6 and 4?
i could do 2^5 for the denominator but that does nothing. is there like a root i can take or something?

 

[Deleted member 4993]

Re: help please. basic algebra + a simplification

i dont understand what u mean by flipping but this is what i did

t(1 + (9/p)) = q
q/t - 1 = 9/p
(q/t -1)p = 9
p = 9/(q/t - 1) <<< Correct

the 2nd problem i get is
6^(7/2) * z / 4^(5/2)
how do i get = constants for 6 and 4?
i could do 2^5 for the denominator but that does nothing. is there like a root i can take or something?

use 6 = 3 * 2 and reduce

Then leave it radical form (unless otherwise instructed)

 

[stapel]

i dont understand what u mean by flipping

To learn how to divide by a fraction (which you will need to know, in order to simplify expressions), try some online lessons:

. . . . .Google results for "divide by fraction"

Short version: To divide by a fraction, instead multiply by it's reciprocal.

how do i get = constants for 6 and 4?

To learn how to simplify radical expressions, try here:

. . . . .Google results for "simplifying square roots"

Have fun!

Eliz.

 

[skeeter]

Re: help please. basic algebra + a simplification

i dont understand what u mean by flipping but this is what i did

t(1 + (9/p)) = q
q/t - 1 = 9/p
(q/t -1)p = 9
p = 9/(q/t - 1)
this is fine ... I'd multiply numerator and denominator by t just to clear the fraction in the denominator
p = 9t/(q - t)

the 2nd problem i get is
6^(7/2) * z / 4^(5/2)
how do i get = constants for 6 and 4?
i could do 2^5 for the denominator but that does nothing. is there like a root i can take or something?

6[sup:wu0jzzlr]7/2[/sup:wu0jzzlr] = (2*3)[sup:wu0jzzlr]7/2[/sup:wu0jzzlr] = 2[sup:wu0jzzlr]7/2[/sup:wu0jzzlr]*3[sup:wu0jzzlr]7/2[/sup:wu0jzzlr]
so ...
2[sup:wu0jzzlr]7/2[/sup:wu0jzzlr]*3[sup:wu0jzzlr]7/2[/sup:wu0jzzlr]*z/2[sup:wu0jzzlr]5[/sup:wu0jzzlr] = 3[sup:wu0jzzlr]7/2[/sup:wu0jzzlr]*z/2[sup:wu0jzzlr]3/2[/sup:wu0jzzlr] = z(3[sup:wu0jzzlr]7[/sup:wu0jzzlr]/2[sup:wu0jzzlr]3[/sup:wu0jzzlr])[sup:wu0jzzlr]1/2[/sup:wu0jzzlr], or z*sqrt(3[sup:wu0jzzlr]7[/sup:wu0jzzlr]/2[sup:wu0jzzlr]3[/sup:wu0jzzlr])

 

[Denis]

Re: help please. basic algebra + a simplification

i dont understand what u mean by flipping but this is what i did
t(1 + (9/p)) = q

Ok, but save yourself "contortions" by next going this way (complete left side multiplication):
t + 9t/p = q
Now multiply each term by p:
pt + 9t = pq
Finish off:
pq - pt = 9t
p(q - t) = 9t
p = 9t / (q - t)

Hokay??

 

[kpx001]

Re: help please. basic algebra + a simplification

the answer for simplifying should be (27/2)*sqroot(3/2)z , but i dunno how they got to that. i can simplify up to the splitting of the number part.

 

[Deleted member 4993]

Re: help please. basic algebra + a simplification

So you are saying - you cannot prove37/23)1/2

\(\displaystyle {(\frac{3^7}{2^3})}^{\frac{1}{2}} \, = \, \frac{27}{2}\cdot \sqrt{\frac{3}{2}}\)

do you see

\(\displaystyle 3^{\frac{6}{2}} \, = \, 27\)

Now continue.....

 

[Denis]

Re: help please. basic algebra + a simplification

Anybody else confused when looking at the last 2 posts? :shock:

 

[mmm4444bot]

My Attempt ...



Hi KPX:

the answer for simplifying should be (27/2)*sqroot(3/2)z

I think that is wrong. I think it is (27/4) * ?6 * z

Of course, I could be wrong. Here's my work:

~ Mark

 

[Deleted member 4993]

Re: My Attempt ...

Hi KPX:

the answer for simplifying should be (27/2)*sqroot(3/2)z

I think that is wrong. I think it is (27/4) * ?6 * z = (27/2) * ?(3*2)/(2) * z = (27/2)*sqroot[3 * 2/(2*2)]z = (27/2)*sqroot(3/2)z

Of course, I could be wrong. Here's my work:

~ Mark

 

[mmm4444bot]

Re: My Attempt ...

the answer for simplifying should be (27/2)*sqroot(3/2)z

I think that is wrong. I think it is (27/4) * ?6 * z = (27/2) * ?(3*2)/(2) * z = (27/2)*sqroot[3 * 2/(2*2)]z = (27/2)*sqroot(3/2)z

My apologies to Subhotosh for only glancing at those previous posts. My apologies to the original poster for my ignorance in not recognizing the equivalency of all our results.

Does anybody want to state a case, in the absense of context, as to why one of the following expressions is "simpler". :wink:

\(\displaystyle \frac{27}{2}\;\sqrt{\frac{3}{2}}\)

\(\displaystyle \frac{27}{4}\;\sqrt{6}\)

~ Mark