Real world Radical Formula???

C

Cadensmom0608

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I have not been in math for a while and am a little lost. the problem is : C=4(23245)^-1/3 (13.50) I am not sure how to multiply 23245 by the negitive 1/3 exponent. This is the example from class: C = 4[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]d[/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]-1/3[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]b [/FONT][/FONT]
[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]C = 4(8500)-1/3(8.17)C = 4(.049)(8.17)
C = .196(8.17)
C = 1.60

Not sure how she got the .049. Please help.
 
Cadensmom0608 said:
I have not been in math for a while and am a little lost.

the problem is : C = 4 (23245)^(-1/3) (13.50)
Click to expand...

Note the grouping symbols around exponent; very important, to show that the exponent is -1/3 and not just -1.



I am not sure how to multiply 23245 by [-1/3 exponent].
Click to expand...

Oh, we do not ever "multiply by exponent" when evaluating a power.



The number -1/3 is a Rational number.

When exponents are Rational numbers, they indicate taking roots (not multiplying)

x^(1/2) means the square root of x

texted as x^(1/2) = sqrt(x)

x^(1/3) means the cube root of x

texted as x^(1/3) = cuberoot(x)



Negative exponents indicate reciprocals.

x^(-1/2) means 1/sqrt(x)

x^(-1/3) means 1/cuberoot(x)



I think that you need to review the meaning of exponentiation and also roots of numbers. There are a few elementary properties for you to memorize.


This is the example from class: C = 4d-1/3b

C = 4(8500)-1/3(8.17)

C = 4(.049)(8.17)

C = .196(8.17)

C = 1.60

Not sure how she got the .049. Please help.
Click to expand...

She used a scientific calculator to evaluate the power 8500^(-1/3)

That is, she found the value of 1/cuberoot(8500)

Do you have a scientific calculator? If not, there are several free web-based scientific calculators to be found on the Internet. :cool:
 
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Here is what the reciprocal of the cube root of 8500 looks like, using radical-sign notation:

\(\displaystyle 8500^{-1/3} = \dfrac{1}{\sqrt[3]{8500}}\)
 
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Cadensmom0608 said:
not sure how to multiply 23245 by the negative 1/3 exponent
Click to expand...

Oh, another point: where did you get the number 23245?

I see 4(23245) and I see 4(8500) -- which is it supposed to be?

I am concerned that you may not be following the Order of Operations.

Memorizing and understanding how to use the Order of Operations should come before studying radicals. :cool:
 
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23245

I got the 23245 from a word problem I am solving. The problem is: Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2. For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function
dug_09_4356_ch09_p605_1060.png


dug_09_4356_ch09_u024.png



a)Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet.
b)Solve this formula for d.
c)The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?

The 8500 was from an example the teacher gave.
 
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I think that I understand, now. You posted both an exercise and an example mixed together.

We evaluate the reciprocal of the cube root of 23245 in the same way as shown above (where 8500 was the power's base, instead).

23245^(-1/3) = 1/cuberoot(23245)
 
ok think I got it.

Ok so I got 4(.035)(13.5)=1.89
Yay no capsizing.
Now to figure out how to use the same equation but solve for D. I am slow when it comes to math but am getting there. Thanks for your help
 
Ashford University Math

Yes I go to Ashford University and I am lost and praying on passing this is my last math course I believe and it doesnt help that the last math I took was in high school and I am 29 now.

I have another question if you dont mind part b of this question then says solve for d. in her example she has D=1.1g^(-1/4)h
I am confused as to where this comes from. I thought d was 23245. How do I find what I need to solve for d for my equation. I am not sure where she got these numbers/formula from
 
Cadensmom0608 said:
Yes I go to Ashford University and I am lost and praying on passing this is my last math course I believe and it doesnt help that the last math I took was in high school and I am 29 now.

I have another question if you dont mind part b of this question then says solve for d. in her example she has D=1.1g^(-1/4)h

I am confused as to where this comes from. I thought d was 23245. How do I find what I need to solve for d for my equation. I am not sure where she got these numbers/formula from
Click to expand...

Are you mixing up another example with the exercise?

D = 1.1*g^(-1/4)*h

This equation with D, g and h is of the same form as the formula in your exercise using C, d, and b.

C = 4*d^(-1/3)*b


I am guessing that her example shows the steps for solving for g?


You would follow the same steps to solve your equation for d.


My steps would be:

(1) Divide both sides by 4b (to isolate the power of d on the righthand side)

(2) Raise both sides to the power of -4 (this changes the exponent on d from -1/4 to 1)

(3) Simplify expression for d -- that is, rewrite with positive exponent (if your machine teacher requires specific form for on-line entry)


I am curious, if you don't mind answering, did Ashford U make you take a math-placement test, before enrolling in first required math course?
 
still confused!

How did you get the 1/4 when the problem in question is (-1/3)?
And are we supposed to be using the 54 or the 4?
Sorry to jump in but I am just as confused!

mmm4444bot said:
Are you mixing up another example with the exercise?

D = 1.1*g^(-1/4)*h

This equation with D, g and h is of the same form as the formula in your exercise using C, d, and b.

C = 4*d^(-1/3)*b


I am guessing that her example shows the steps for solving for g?


You would follow the same steps to solve your equation for d.


My steps would be:

(1) Divide both sides by 4b (to isolate the power of d on the righthand side)

(2) Raise both sides to the power of -4 (this changes the exponent on d from -1/4 to 1)

(3) Simplify expression for d -- that is, rewrite with positive exponent (if your machine teacher requires specific form for on-line entry)


I am curious, if you don't mind answering, did Ashford U make you take a math-placement test, before enrolling in first required math course?
Click to expand...
 
My Week 3 Assignment

I am also currently in this class @ Ashford, and I'm sorry guys, but the entire chapter is on radicals, I don't see anything resembling what I came up with in your posts...

Please comment on my methodology, as I'm pasting the relevant paragraph from my assignment.

According to the text, “The strategy for evaluating a-m/n: 1. Find the nth root of a. 2. Raise your result to the mth power. 3. Find the reciprocal” (Dugopolski, 2012, p. 571). In this case, the cube root of 92980 is raised to itself and then flipped to the reciprocal. Written out this would look like: 1/3√92980×13.5. We must eliminate the cube root in the denominator by rationalizing it. This is accomplished by “multiplying both the numerator and denominator by another radical that makes the denominator rational” (Dugopolski, 2012, p. 587). It just so happens, that we need to build up the denominator to be the cube root of a perfect cube so we multiply both the top and the bottom by 3√4356. This makes the top 3√4356, or 16.33, and the bottom 3√97339, or 46, so we now have 16.33/46×13.5 which leaves you with the value of C = 4.79. It is safe to say, that if my calculations are correct, then this boat is not seaworthy.


Thanks!
 
xdleet said:
I am also currently in this class @ Ashford, and I'm sorry guys, but the entire chapter is on radicals, I don't see anything resembling what I came up with in your posts...

Please comment on my methodology, as I'm pasting the relevant paragraph from my assignment.

According to the text, “The strategy for evaluating a-m/n: 1. Find the nth root of a. 2. Raise your result to the mth power. 3. Find the reciprocal” (Dugopolski, 2012, p. 571). In this case, the cube root of 92980 is raised to itself raised to 92980? and then flipped to the reciprocal. Written out this would look like: 1/3√92980×13.5. We must eliminate the cube root in the denominator by rationalizing it. This is accomplished by “multiplying both the numerator and denominator by another radical that makes the denominator rational” (Dugopolski, 2012, p. 587). It just so happens, that we need to build up the denominator to be the cube root of a perfect cube so we multiply both the top and the bottom by 3√4356. This makes the top 3√4356, or 16.33, and the bottom 3√97339, or 46, so we now have 16.33/46×13.5 which leaves you with the value of C = 4.79. It is safe to say, that if my calculations are correct, then this boat is not seaworthy.


Thanks!
Click to expand...
Please start your own thread to ask a question. The quotation from your book makes sense. Nothing else does. Where did 92980 come from? "In this case": in what case?
 
how about graphing an exponential function ifexponent is a fraction F(x)=3 to (.5x)

How do you graph an exponential function if exponent is a fraction - problem is f(x)=3 to the .5x. So if x is 1, f(x) is square root of 3. If x is 2, f(x) is 3. If x is 3, f(x) is 3 times the square root of 3......but is there pointers to how to graph this?
 
JeffM said:
Please start your own thread to ask a question. The quotation from your book makes sense. Nothing else does. Where did 92980 come from? "In this case": in what case?
Click to expand...

Naw it's cool, I just cubed the whole **** thing and said forget about it... The reason I replied to this thread was because we were working the same problem, and it's in the chapter about manipulating radicals, and NO ONE was even touching on that area, WHICH WAS THE ENTIRE QUESTION - LOL. The answer is all fine and dandy, but what *I* was looking for, and ANYONE ELSE ASSIGNED THIS PROBLEM, was how to eliminate the radical from the exponent... Sorry. I'm deleting this acct...
 
xdleet said:
Naw it's cool, I just cubed the whole **** thing and said forget about it... The reason I replied to this thread was because we were working the same problem, and it's in the chapter about manipulating radicals, and NO ONE was even touching on that area, WHICH WAS THE ENTIRE QUESTION - LOL. The answer is all fine and dandy, but what *I* was looking for, and ANYONE ELSE ASSIGNED THIS PROBLEM, was how to eliminate the radical from the exponent... Sorry. I'm deleting this acct...
Click to expand...
And how do we we know what the problem asks and what your chapter is about unless you tell us?

I point out that as originally given to us, there is no radical in an exponent so it is highly unlikely that anyone would have thought to discuss what to do with one.
 
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