Answer: (a) (i)50.42 m/s (ii) 51.35 m/s (iii) 52.094 m/s (iv) 52.2614 m/s (v) 52.27814 m/s
(b) 54.14 m/s
Step-by-step explanation:
The average speed over the given time interval [a,b]: = ![\frac{y(b)-y(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7By%28b%29-y%28a%29%7D%7Bb-a%7D)
Given: If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by ![y = 56t − 1.86t^2.](https://tex.z-dn.net/?f=y%20%3D%2056t%20%E2%88%92%201.86t%5E2.)
(a)
(i) average speed = ![\frac{y(2)-y(1)}{2-1}](https://tex.z-dn.net/?f=%5Cfrac%7By%282%29-y%281%29%7D%7B2-1%7D)
![=\frac{56(2)-1.86(2)^2-(56(1)-1.86(1)^2)}{1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B56%282%29-1.86%282%29%5E2-%2856%281%29-1.86%281%29%5E2%29%7D%7B1%7D)
m/s
(ii) average speed = ![\frac{y(1.5)-y(1)}{1.5-1}](https://tex.z-dn.net/?f=%5Cfrac%7By%281.5%29-y%281%29%7D%7B1.5-1%7D)
![=\frac{56(1.5)-1.86(1.5)^2-(56(1)-1.86(1)^2)}{0.5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B56%281.5%29-1.86%281.5%29%5E2-%2856%281%29-1.86%281%29%5E2%29%7D%7B0.5%7D)
m/s
(iii) average speed = ![\frac{y(1.1)-y(1)}{1.1-1}](https://tex.z-dn.net/?f=%5Cfrac%7By%281.1%29-y%281%29%7D%7B1.1-1%7D)
![=\frac{56(1.1)-1.86(1.1)^2-(56(1)-1.86(1)^2)}{0.1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B56%281.1%29-1.86%281.1%29%5E2-%2856%281%29-1.86%281%29%5E2%29%7D%7B0.1%7D)
m/s
(iv) average speed = ![\frac{y(1.01)-y(1)}{1.01-01}](https://tex.z-dn.net/?f=%5Cfrac%7By%281.01%29-y%281%29%7D%7B1.01-01%7D)
![=\frac{56(1.01)-1.86(1.01)^2-(56(1)-1.86(1)^2)}{0.01}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B56%281.01%29-1.86%281.01%29%5E2-%2856%281%29-1.86%281%29%5E2%29%7D%7B0.01%7D)
m/s
(v) average speed = ![\frac{y(1.001)-y(1)}{1.001-01}](https://tex.z-dn.net/?f=%5Cfrac%7By%281.001%29-y%281%29%7D%7B1.001-01%7D)
![=\frac{56(1.001)-1.86(1.001)^2-(56(1)-1.86(1)^2)}{0.001}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B56%281.001%29-1.86%281.001%29%5E2-%2856%281%29-1.86%281%29%5E2%29%7D%7B0.001%7D)
m/s
(b) ![y(1)=56(1)-1.86(1)^2](https://tex.z-dn.net/?f=y%281%29%3D56%281%29-1.86%281%29%5E2)
![=56-1.86](https://tex.z-dn.net/?f=%3D56-1.86)
m/s
Answer:
7) -2 and 3
8) -2 and 3
9) Discrete
Step-by-step explanation:
Its the third and the fourth one
Answer:
64 adult tickets were sold
Step-by-step explanation:
Let a = adult tickets sold
c = child tickets sold
a+c = 90 since there were 90 tickets sold
12a+7c = 950 since the amount of money collect is 950
c = 90-a
Substitute this into the second equation
12a +7( 90-a) = 950
Distribute
12a + 630-7a = 950
Combine like terms
5a +630 = 950
Subtract 630 from each side
5a = 950-630
5a = 320
Divide by 5
5a/5 = 320/5
a =64
64 adult tickets were sold