Quadratic Equations - Trouble with order: SA=2πR2+2πRH

[markl77]

The problem is asking for me to solve the radius of a cylinder with a surface area of 250cm². It also gives me the height which is 7 cm. here are my steps:
SA=2πR²+2πRH
250= 2πR²+2πR(7)
0=2πr²+14πr-250
r=-14π±sqrt((14π)²-4(2π)(-250)/2(2π)

I know that I am only supposed to find the positive x intercept but I keep getting the wrong answer
because I don't know the order to put in my calculator. The answer that I'm supposed to end up with is
r=3.71cm.

 

[stapel]

The problem is asking for me to solve the radius of a cylinder with a surface area of 250cm². It also gives me the height which is 7 cm. here are my steps:
SA=2πR²+2πRH
250= 2πR²+2πR(7)
0=2πr²+14πr-250

I will assume that "R" and "r" are meant, contrary to standard mathematical usage, to represent the same value.

r=-14π±sqrt((14π)²-4(2π)(-250)/2(2π)

I will assume that, contrary to what is posted, you mean the solution, via the Quadratic Formula, to be as follows:

. . . . .\(\displaystyle r\, =\, \dfrac{-14\pi \, \pm\, \sqrt{\strut (14\pi)^2\, -\, 4(2\pi)(-250)\,}}{2(2\pi)}\)

I know that I am only supposed to find the positive x intercept but I keep getting the wrong answer because I don't know the order to put in my calculator. The answer that I'm supposed to end up with is r=3.71cm.

Since we can't see what you're entering in your calculator (and since we don't do tech support on whatever model you have), we cannot advise specifically in this regard. However, in general, there is plenty of simplification you can do before attempting any data-entry for decimal approximations.

Once you've simplified, you can do the data-entry in pieces, such as evaluating inside the square root, then adding or subtracting this value from whatever remains in front of it in the numerator, and then dividing by the denominator. If you get stuck, please reply showing your simplification and then stating your data-entry steps and results. Thank you!

 

[markl77]

I will assume that "R" and "r" are meant, contrary to standard mathematical usage, to represent the same value.


I will assume that, contrary to what is posted, you mean the solution, via the Quadratic Formula, to be as follows:

. . . . .\(\displaystyle r\, =\, \dfrac{-14\pi \, \pm\, \sqrt{\strut (14\pi)^2\, -\, 4(2\pi)(-250)\,}}{2(2\pi)}\)


Since we can't see what you're entering in your calculator (and since we don't do tech support on whatever model you have), we cannot advise specifically in this regard. However, in general, there is plenty of simplification you can do before attempting any data-entry for decimal approximations.

Once you've simplified, you can do the data-entry in pieces, such as evaluating inside the square root, then adding or subtracting this value from whatever remains in front of it in the numerator, and then dividing by the denominator. If you get stuck, please reply showing your simplification and then stating your data-entry steps and results. Thank you!

Thanks for the reply!
I started by evaluating inside the square root: (14π)²-4(2π)(-250) then I stored it as x. I then did -14π+X and divided it all by 2(2π). I know this is the incorrect order, I just need to know what the correct order is.

 

[JeffM]

To supplement stapel's thread.

\(\displaystyle 2 \pi r^2 + 14 \pi r - 250 = 0 \implies pi^2 + 7 \pi - 125 = 0 \implies\)

\(\displaystyle r = \dfrac{-\ 7 \pi \pm \sqrt{49 \pi^2 + 500 \pi}}{2 \pi}.\)

Subtracting the square root obviously leads to a negative radius, which is absurd, so only adding the square root makes sense.

Stapel is absolutely correct that it makes sense to simplify before calculating. Here is a hint.

\(\displaystyle \dfrac{a + \sqrt{b}}{c} = \dfrac{a}{c} + \sqrt{\dfrac{b}{c^2}}.\)

 

[JeffM]

Thanks for the reply!
I started by evaluating inside the square root: (14π)²-4(2π)(-250) then I stored it as x. I then did -14π+X and divided it all by 2(2π). I know this is the incorrect order, I just need to know what the correct order is.

\(\displaystyle (14 \pi )^2 + 4(2 \pi )(250) \approx 8217.63\)

\(\displaystyle \sqrt{8217.63} \approx 90.65.\)

\(\displaystyle \dfrac{90.65 - 14 \pi }{4 \pi} \approx \dfrac{46.67}{4 \pi} \approx 3.71.\)

You are a lot less likely to screw up on your calculator if you simplify before pushing buttons.