Answer:
(a) 2 feet.
(b) 2 feet.
Step-by-step explanation:
We have been given that the velocity function 
in feet per second, is given for a particle moving along a straight line.
(a) We are asked to find the displacement over the interval 
.
Since velocity is derivative of position function , so to find the displacement (position shift) from the velocity function, we need to integrate the velocity function.
Using power rule, we will get:
![\left[\frac{t^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}}\right] ^4_1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cfrac%7Bt%5E%7B-%5Cfrac%7B1%7D%7B2%7D%2B1%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%2B1%7D%7D%5Cright%5D%20%5E4_1)
![\left[\frac{t^{\frac{1}{2}}}{\frac{1}{2}}}\right] ^4_1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cfrac%7Bt%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%5Cright%5D%20%5E4_1)
![\left[2t^{\frac{1}{2}}\right] ^4_1](https://tex.z-dn.net/?f=%5Cleft%5B2t%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%5D%20%5E4_1)
Therefore, the total displacement on the interval would be 2 feet.
(b). For distance we need to integrate the absolute value of the velocity function.
Since square root is not defined for negative numbers, so our integral would be .
We already figured out that the value of is 2 feet, therefore, the total distance over the interval would be 2 feet.
Answer:
There are 8 more girls
Step-by-step explanation:
If you divide 32 by 8 (since the ratio is 3:5 which is 8 parts (3+5)). You get 4.
Thus, there are 12 boys and 20 because 3*4 is 12 and 5*4 is 20. 12+20 is 32.
Answer:
b
Step-by-step explanation:
Given y = x² then y = x² + c is a vertical translation of y = x²
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here c = - 12 < 0
Thus y = x² - 12 is the graph of y = x² shifted 12 units down → b
Answer:
$900
Step-by-step explanation:
add 200 to 50 times 14
Answer:
3 7/23
Step-by-step explanation:
Hope this helps.
