#1, your dy/dt is correct
b) correct, to the right when v(t) > 0
but they probably want to know when that happens
look at your derivative, the denominator will always be positive, since it is something squared.
So the ± of your v(t) is only determined by the numberator which is 1 - t^2
By the "Just look at it" theorem you should be able to see that it is positive for x's between -1 and +1 , and negative for x < -1 or x> +1
c) total distance ???
find s(4) - s(0)
2. a) yes , but it asked for the max height.
the max height will be reached at 2.5 sec
so s = 80t - 16(2.5)^2 = 100
b) when s = 96
96 = -16t^2 + 80t
t^2 - 5t + 6 = 0
(t-2)(t-3) = 0
t = 2 or t = 3
so t = 2 must be on its way up and v(2) = 80 - 32(2) = 16 m/s
and t-3, on its way down v(3) = 80-3(32) = -16 m/se
3. I know nothing about Torricelli's Law, but your equation is a quadratic.
When you differentiate it, you get a linear function, and setting that equal to zero would only produce one answer, and that would give us the time when we have a minimum.
I think there is something amiss in your equation
1. A particle moves along the x-axis, it's position at timer given by x(t)=t/(1+t^2), t greater than or equal to 0,where t is measured in seconds and x in meters.
a) find the velocity at time t.
I am a little confused.. Do I find the derivative by using the quotient rule? What would the answer be? I am not sure with mine..
My answer: s'(t)=v(t)=(-t^2 + 1)/(t^4 +2t^2 +1)??
b) when is the particle moving to the right? When is it moving to the left?
Particle moving right when v(t) is greater than zero?? Left when v(t) is less than zero??
c) find the total distance traveled during the first 4s.
??
2.If a ball is thrown vertically upward with a velocity of 80 ft/sec, then it's height after t sec is s=80t-16t^2.
a) what is the maximum height reached by the ball?
Derivative of s =o ????
Is it 2.5 sec?
b) what is the velocity of the ball when it is in 96 ft above the ground on its way up? On its way down?
s(t)=0????
3. If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as
V=5000(1-t/40)^2
t is greater than or equal to 0 and less than or equal to 40
Find the rate at which water is draining from the tank after
5 min? 3828.125 gallons/min?
10 min? 2812.5 gallons/min?
20 min? 1250 gallons / min?
40 min? 0 gal/ min?
At what time is the water flowing out the fastest?
5min-10min?
The slowest? Summarize your findings.
20min-40min?
2 answers
Pascale,You never actually eoxprt a GeoGebra file, though you do start by choosing Export Dynamic Worksheet as Webpage. On the Advanced tab, the default value on the dropdown menu in the lower right is “File: html�. Change this to “Clipboard: html�. This will replace the button labeled “Export� with a button labeled “Clipboard�. When you click this button, the code you need is copied to your clipboard and you just paste into the HTML Snippets area on your WordPress dashboard. After I did this and pasted the shortcode generated by the plugin into my WordPress post, the applet ran.The only problem I had was that the font information in HTML code generated by GeoGebra changed the font on my entire site. I fixed this by removing the style information in the header section of the code that I pasted from the clipboard. This fixed that minor problem. I didn’t change anything else in the code that I pasted.I hope this makes sense even though you’re working in a different language! Bonne chance!-Laura
2 answers