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amy0799
 one year ago
Find k such that the line y = 2x + 18 is tangent to the graph of the function below.
y=k√x
k=?
amy0799
 one year ago
Find k such that the line y = 2x + 18 is tangent to the graph of the function below. y=k√x k=?

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I told you, take derivative of the curve \(y = k\sqrt x\), what do you get?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440974118718:dw you want y=2x+8 and y=ksqrt(x) to have a common point (a,f(a)) and you also want the derivative of 2x+8 to be equal to the derivative of ksqrt(x) at (a,f(a))

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0right, I understand that, I just don't know how to find it.

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you have 2a+8=k sqrt(a) <since we want 2a+8 to be equal to k sqrt(a) and you also have 2=k/(2sqrt(a))

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Thanks @freckles. Shame on me, I guided him wrong. @amy0799 I am sorry.

freckles
 one year ago
Best ResponseYou've already chosen the best response.3it is just a system of equations to solve

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 2x+8 }{ \sqrt{x}} = k\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2a+8=k \sqrt{a} \\ 2=\frac{k}{2 \sqrt{a}} \implies \sqrt{a}=\frac{k}{4} \implies a=\frac{k^2}{16} \text{ insert into first equation }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3doing that will give you an equation just in terms of k

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0insert it into which equation?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the first equation I wrote above the second equation

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2a+8=k \sqrt{a} \\ 2=\frac{k}{2 \sqrt{a}} \implies \sqrt{a}=\frac{k}{4} \implies a=\frac{k^2}{16} \text{ insert into first equation } \] there are equations I'm playing with here the first equation which is on the first line and the second equation which on the second line the second line I used the second equation to express sqrt(a) in terms o k and I also expressed a in terms of k using the second equation we can now write the first equation which I put on the first line in terms of k

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0so I plug a=k^2/16 into 2a+8=ksqrt(a)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3yes you also plug in k/4 for sqrt(a)

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0\[2(\frac{ k^{2} }{ 16 })+8=k \sqrt{k \sqrt{a}}\] this doesn't make sense

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you are write that equation doesn't make sense you should have gotten something else entirely different

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2a+8=k \sqrt{a} \\ \text{ we determined } \sqrt{a}=\frac{k}{4} \text{ then we squared both sides \to get } a=\frac{k^2}{16} \\ \text{ plug \in both of these results we obtained from the second equation } \\ \text{ into the first } \\ 2(\frac{k^2}{16})+8=k(\frac{k}{4})\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3now solve the equation for k (you will see you have to discard a value that you get for k when solving this equation because of the equation sqrt(a)=k/4 which tells us that sqrt(a) is positive and so k has to be positive )

freckles
 one year ago
Best ResponseYou've already chosen the best response.3do you know how to solve the above quadratic

freckles
 one year ago
Best ResponseYou've already chosen the best response.3k*k=k^2 and 2/16=1/8 you have: \[\frac{k^2}{8}+8=\frac{k^2}{4} \\ \text{ you can multiply both sides by 8 \to get } \\ k^2+64=2k^2 \] can you solve from here?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[64=k^2 \\ k=8 \text{ or } 8 \\ \text{ but we did mentioned that } k>0 \\ \text{ so yes } k=8\]

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0thank you! can u help me with another one?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3before we go on you need to understand this one

freckles
 one year ago
Best ResponseYou've already chosen the best response.3like do you have any questions? do you understand how I solved the system of equations?

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0Consider the following function. f(t) = 2t^2 − 3 (a) Find the average rate of change of the function below over the interval [3, 3.1]. (b) Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. (at t = 3) (at t = 3.1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\text{average rate of change of } f \text{ from }t=a \text{ to } t=b \\ \text{ is given by the formula } \frac{f(b)f(a)}{ba}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\text{ instantaneous rate of change of} f \text{ at } x=c \text{ is given by } f'(c)\]

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0so what's the first step I need to do?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you used the formula above to find the average rate of change from t=3 to t=3.1...

freckles
 one year ago
Best ResponseYou've already chosen the best response.3replace b with 3.1 and a with 3

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ f(3.1)f(3) }{ 3.13 }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3yes now evaluate f(3.1) and f(3) and do the difference on top and bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.3and then the division of the top by the bottom

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand what you mean

freckles
 one year ago
Best ResponseYou've already chosen the best response.3f(t) is given as 2t^23 you are to find f(3.1) and f(3) by using f(t)=2t^23 replace t with 3.1 and get a result for f(3.1) replace t with 3 and get a result for f(3)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{f(3.1)f(3)}{3.13}=\frac{16.2215}{3.13}\] now find the difference for both top and bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the difference of 16.22 and 15 is another way to say 16.2215 if you are confused by the word difference

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0is that the average rate of change?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3yes that is the average rate of change of f(t)=2t^23 from t=3 to t=3.1

freckles
 one year ago
Best ResponseYou've already chosen the best response.3did you find the f'(3) and f'(3.1)

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0yea isn't it 16.22 and 15?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3f' means to find the derivative of f

freckles
 one year ago
Best ResponseYou've already chosen the best response.3and you just plugged into original function

freckles
 one year ago
Best ResponseYou've already chosen the best response.3did you not look earlier at how I said to find the instantaneous rate of change?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I posted the following two comments: \[\text{average rate of change of } f \text{ from }t=a \text{ to } t=b \\ \text{ is given by the formula } \frac{f(b)f(a)}{ba}\] \[\text{ instantaneous rate of change of} f \text{ at } x=c \text{ is given by } f'(c)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you don't know how to find the derivative of 2t^23?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3do you know power rule and constant rule? if not use the definition of derivative

freckles
 one year ago
Best ResponseYou've already chosen the best response.3yes so what do you not understand?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you have f'(t)=4t and you are asked to evaluate f'(t) at the endpoints

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the endpoints are 3 and 3.1

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0my very first question. I got k=8 wrong

freckles
 one year ago
Best ResponseYou've already chosen the best response.3did you look at what we wrote and what you asked?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you should see we changed 18 to 8

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you know the line being y=2x+18 instead of y=2x+8

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the answer is k=8 if the question involved y=2x+8 but the equation was y=2x+18 please look at our work and your question our answer was for if the line was y=2x+8 which I started over and over but the equation was y=2x+18 so just redo the work for the equation being y=2x+18 instead of it being y=2x+8

freckles
 one year ago
Best ResponseYou've already chosen the best response.3which I stated over and over in the answer*

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the question was: Find k such that the line y = 2x + 18 is tangent to the graph of the function below. y=k√x k=? however our work was for: Find k such that the line y = 2x + 8 is tangent to the graph of the function below. y=k√x k=?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you should be able to do your question now if you actually understand the work we did to find k for this other question

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0can you help me with it? @freckles

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I thought you said you understand the process?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\text{ solve the system of equations } \\ (2x+18)'_{x=a}=(k \sqrt{x})'_{x=a} \\ 2a+18=k \sqrt{a}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3it is the same process we did above

freckles
 one year ago
Best ResponseYou've already chosen the best response.3except there is just a little number change

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0I understood how you solved the quadratic, but not how you got a

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2a+8=k \sqrt{a} \\ 2=\frac{k}{2 \sqrt{a}} \implies \sqrt{a}=\frac{k}{4} \implies a=\frac{k^2}{16} \text{ insert into first equation } \] is this what you are talking about? you don't know how I solved the second equation for sqrt(a)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2=\frac{k}{2 \sqrt{a}} \\ \text{ I just multiplied } 2 \sqrt{a} \text{ on both sides } 2(2 \sqrt{a})=k \\ 4 \sqrt{a}=k \\ \text{ and then divided both sides by } 4\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3and the only different and this set of equations is 8 is supposed to be 18

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2a+18=k \sqrt{a} \\ \sqrt{a}=\frac{k}{4} \text{ squaring both sides gives } a=\frac{k^2}{16} \text{ replace the items in the first equation }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3how did you get that?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3did you replace a with k^2/16 and sqrt(a) with k/4?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[2a+18=k \sqrt{a} \\ 2(\frac{k^2}{16})+18=k(\frac{k}{4})\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3solve the equation for k

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 18k^{2} }{ 8 }+324=\frac{ 18k ^{2} }{ 4 }\] is this right so far?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3why did you choose to multiply both sides by 18

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0that's how u did it before

freckles
 one year ago
Best ResponseYou've already chosen the best response.3no I multiplied both sides by something to clear the fractions not to make the problem more fractionie (I know that isn't a word) \[\frac{2}{16}=\frac{1}{8} \\ k \cdot k=k^2 \\ \text{ you have } \\ 2(\frac{k^2}{16})+18=k(\frac{k}{4}) \\ \text{ so this is equivlant to } \\ \frac{k^2}{8}+18=\frac{k^2}{4} \\ \text{ if you multiply both sides by 8 } \text{ you can clear the fractions }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the denominators were same in previous previous problem and I chose to multiply both sides by 8 then so it shouldn't change here

freckles
 one year ago
Best ResponseYou've already chosen the best response.3unless you want to make the problem more complicated looking :p

freckles
 one year ago
Best ResponseYou've already chosen the best response.3yes \[k^2+8(18)=2k^2 \\ 8(18)=k^2 \\ 16(9)=k^2 \\ 4(3)=k \\ k=12\] and again we chose 12 instead of 12 because we wanted k to be positive @amy0799 you might want to go and review how to solve algebraic equations practice, practice and you can get better at this I promise

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0yeaa I know >.< I have one more I need help with

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you can post it but brb

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0Consider the following function. \[f(x)=\sqrt{9x^{2}}\] Find the derivative from the left at x = 3. If it does not exist, enter NONE. Find the derivative from the right at x = 3. If it does not exist, enter NONE.

freckles
 one year ago
Best ResponseYou've already chosen the best response.3do you know what the function looks like?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440979836143:dw does the function exist to the right of x=3?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3so we already know one answer is does not exist... now let's look at the left side: \[\text{ \left derivative of } f \text{ at } x=3 \text{ is given by } \lim_{x \rightarrow 3^}\frac{f(x)f(3)}{x3} \\ \]

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0it doesn't exist either

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0thank you so so much and I'm really sorry if I took up ur time!!

freckles
 one year ago
Best ResponseYou've already chosen the best response.3It is only fine if you take up my time if you have learned something

freckles
 one year ago
Best ResponseYou've already chosen the best response.3do you feel like you learned anything

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0I learned a lot. thank you!
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