(New Message) |
Ready at 8:30 |
are we gonna have time in class to work on these problems too |
We will have about 35 minutes tomorrow and after school hours. |
are we still having additional homework tomorrow night |
Hey Everybody! |
@Your Name
No, just these problems, pease put your name next time!  |
Yep..... |
yay! Okay, so i guess ill start off my many questions with a question about number 12. I'm kinda lost on where to begin. I drew my picture and everything but i dont know where to go from there... |
Anybody know how to make my screen refresh automatically when someone posts a new question or answer? I keep having to press F5 every minute or so. :-( |
@Mullins No, it might just be Megan and us tonite!! |
haha im okay with that that means I can ask all my questions! |
Well, Megan, I hope you get all your questions answered! |
@Megan...this is sortof like 9, where you will create a proportion.and take the derivative 2/y = x/12 where y represents the wall shadow and x represents the distance to the wall... |
Um.. about number 9, I'm confused as to how to find the distance between the man and the lamppost and the distance between the man and the shadow. I know you're supposed to do a proportion, but I don't know exactly how to do it. |
Here are my steps, but i dont get the answer....
yx=24 x=24/y (now i took the derivative) and got dx/dt= -24(1.6) / 24 which gives me -1.6, not -0.6 |
Allo... My name is D M Ray, you have joined the Calculus forum. prepare to learn |
Sorry the no name post before was me |
@Megan... the 24 is the problem, the denominator is y^2. Since they are 4 away from the wall, the y value is 12-4 = |
@Ray. As You Wish. |
Awesome. |
Hey everybody,
I'm working on #12 too, but I used the product rule to take the deriv. of 24 = xy, will that work? |
@Sharon it should still work... use your proportion to find the missing x value. |
Sharon, I had the same as you. 24 = xy. They I divided by x to get y=24/x. Then I took the derivative with respect to time. That worked for me. |
Here's what I did:
24=xy 0=x dy/dt +y dx/dt 0 = 4 dy/dt + (3 * 1.6) I got -1.2...but I'm not sure where I went wrong |
Sharon - Are you saying that y = 3, if I'm reading your equation right? Where did you get 3? If it's not the y value, what is it? |
@Sharon the problem was your x value, it should be 12-4....
Because the whole distance is 12 and the distance from the man to the wall is 4, so the distance from the light is... |
My x value represented the distance from the person to the wall--should it have been the distance from the light to the person?
And, I got y = 3 using the proportion: 2/8 = y/12 24 = 8y 3 = y |
Im confused about#12, I got to the 24= xy step, and I dont know what to do.... |
@Sharon, yes, it should be the distance from the light to the person b/cthe rate 1.6 represents the rate of that distance. Your 3 is gud. |
@ other Megan product rule on right, 0 on left |
Never mind! I got it. the only thing that I was iffy with was why you multiplied x by dy/dt instead of dx/dt... |
Aha! I got the right answer!  |
@other Megan ... cool beans other Megan, cool beans |
So when you have a speed with respect to x, the x-value is always the distance the object/person has traveled? |
@Sharon insert happy dance |
For #13, my picture is kind of crazy. But the sides are 9300, 500, and 9313.43. Am I on the right track? |
Go Sharon! Woot! Woot! |
Megan, I'm happy with your sides for 13. |
@Sharon... essentially yes, you should have your variable represent the value that is changing or rate you are given. So if you are given the rate from the light, you should call x the distance from the light... if that makes sense! |
how does the picture for #12 look? is it similar to #9? |
@Julia yes and your set up is very similar.... derivative of the proportion |
So the picture for #13 should be a right triangle? I wound up with 2 right triangles, 1 going up and the other going down, and they share a base of 500' |
Are the rates for #13 4 and 5? so you have 4800(4)+ 4500(5) = 9313.43 dz/dt ? |
@Sharon... true, true, but you can slidethat 500 side up to create a right triangle .... |
Sharon, your picture for 13 sounds like mine. I think you're on the right track. |
Sharon, i dropped a line down and across and made it one big triangle. if that makes sense. |
Megan, I did not use 4 and 5 in my rates for my equation |
so the sides of the triangle would be 500, the the distances traveled of both people combined, and then the hypotenuse? |
Isn't 4= dx/dt and 5=dy/dt ? |
@Megan...the 4800 and 4500 are incorrect... hrmm, try to think of it as one big triangle than two small ones.. the base is 500, the height is 9300 and the hypot is 9313.43.
NOW use pyth thm on that triangle.... help? |
@Sharon... Oui, si, yes
@Megan Yes |
Megan, Well the man is walking N at 4 ft/s, and the woman is walking S at 5 ft/s. So the way I set mine up was having the man walk "up" my paper, and having the woman walk "down". I have two triangles. So the rate of change of the people is 9 ft/s. |
I don't know if this will help for 13, but I did keep the two triangles. But I thought of this like the distance formula (which is derived from the pythogorean thm). I don't know, but it worked for me. |
@Megan.... try this drop that 500 side to the bottom. Now the triangle has a base of 500, a height of x+y, and a hypotenuse of z. Now use pyth thm on those three sides. Take the deriv of (x+y)^2 (USING chain rule) and z^2. |
i got the right answer using 9 ft/s as the rate, but why wouldn't the overall rate be 1 ft/s since the people are going in opposite directions? |
Im still getting 5 or 4 ish... 9300(4)+ 500(5) = 9313.43 dz/dt... is that not right? |
Ahhh.. two ways to do the same problem. Both works, use the one that akes the best sense to you! |
@Megan the derivative of (x+y)^2 is (x+y)(dx/dt + dy/dt).... since x+y = 9300, you can distribute to dx/dt and dy.dt. This should now work. |
The equation that I posted gives me 4.262... I dont know where I went wrong. |
@Sharon since the distance is Increasing, thier rates would add, not subtract |
@Megan - i used the equation 500 * 0 + 9300 *9 = 9313.431 dz/dt, because 500 is not changing. It's just a number, so it's deriv. is 0. |
@Megan it sounds like you are almost there, lets look at it in the morning and I can see whats happening |
Mrs. Ray, where did the ^2 disappear to when you took the derivative? |
@Megan, I like what Sharon is saying... good dealio |
@Megan since the derivative of z^2 is 2z dz/dt, I diided both sides by 2... so you have (x+y)(dx/dt + dy/dt) = z dz/dt |
@Megan: Good luck!
@Ms. Ray & Ms. Mullins: Thanks! |
Got it Sharon, thanks! |
Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun! See what happens when you guys keep me up late???? |
Sorry to do this gals, but my contacts are tellin me it is time for bed. See you in the AM and thank you for joinging us!! |
@Ms. Ray: |
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