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:
circumference of circle = 2×pi×r
circumference of circle = 2×3.14×12.7
circumference of circle = 79.756 in
Answer:
x=35/3 or 11 2/3 or 11.67
Step-by-step explanation:
I=prt
700=p(5)(12)
700=60p
700/60=p
p=11.67
Answer:
Step-by-step explanation:
The equation of a linear function in point-slope form is y – y1 = m(x – x1)
The point is A (x1 , y1)
in this exercice : x1 = 3 and y1 =2
let A(3,2) B(-9,6)
the slope is : m = (YB - YA)/(XB -XA)
(6-2)/(-9-3) =4/(-12) = -1/3
the slope is m = -1/3
The equation is : y – y1 = m(x – x1)
y-2 =-1/3 ( x-3)
or : 3y-6 = -x+3
Answer: x = 9, y = -14
Explanation:
4x + y = 16
2x + y = -2<span>
</span> 4x + y = 16
- 2x + y = -2
-------------------
2x + 0 = 18
-------------------
2x = 18
x = 9 <<<<< ¯\_(ツ)_/¯ For the value of x
Plug x = 9 into 2x + y = -2
2(9) + y = -2
12 + y = -2
y = -14 <<<<< ¯\_(ツ)_/¯ For the value of y
