Answer:
0.5 meters per second.
Step-by-step explanation:
We have been given a graph that represents the distance a ball has traveled x seconds after it was thrown.
We can see from our graph that x is independent variable and distance traveled is dependent variable.
We know that
.
Since the graph represents change is distance with respect to change in time, so we can find average speed of ball by finding the slope of our function using points (2,3) and (8,6).
, where,
= Change in two y-coordinates,
= Change in same x-coordinates of two y-coordinates.
Upon using coordinates of our given points we will get,
![\text{Slope}=\frac{6-3}{8-2}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7B6-3%7D%7B8-2%7D)
![\text{Slope}=\frac{3}{6}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7B3%7D%7B6%7D)
![\text{Slope}=0.5](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D0.5)
Therefore, the average speed of ball between 2 seconds to 8 seconds is 0.5 meters per second.
Answer: c = -0.98
Step-by-step explanation: <u>Differential</u> <u>equation</u> <u>of</u> <u>first</u> <u>order</u> is an equation involving differentiable function and its derivative.
For the differential equation:
, it given a solution function:
![y=x^{2}+cx^{2}](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%2Bcx%5E%7B2%7D)
Factorating the function: ![y=x^{2}(1+c)](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%281%2Bc%29)
So, to determine constant c, use the initial condition:
When x = 10, y = 2:
![2=10^{2}(1+c)](https://tex.z-dn.net/?f=2%3D10%5E%7B2%7D%281%2Bc%29)
![1+c=\frac{2}{100}](https://tex.z-dn.net/?f=1%2Bc%3D%5Cfrac%7B2%7D%7B100%7D)
![1+c=0.02](https://tex.z-dn.net/?f=1%2Bc%3D0.02)
c = -0.98
Constant c that satisfies the initial condition is c = -0.98
Answer:
cubic units
Step-by-step explanation:
vyjf I thvjivgg b j
Answer:
1
Step-by-step explanation:
y-intercept is defined as the point where the graph crosses the y-axis. The value of x coordinate at this point is zero, as along entire y-axis, the value of x coordinate is always zero. So substituting x = 0 in the function will give us the y-coordinate of the y-intercept of the given function.
![f(x)=x^{3}-x^{2} -x+1](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B3%7D-x%5E%7B2%7D%20-x%2B1)
Substituting x = 0 in this function, we get:
![f(0)=0^{3}-0^{2}-0+1=1](https://tex.z-dn.net/?f=f%280%29%3D0%5E%7B3%7D-0%5E%7B2%7D-0%2B1%3D1)
Thus, the y-coordinate of the y-intercept is 1. Therefore the y-intercept of the function in ordered pair will be: (0, 1)
Answer:9
Step-by-step explanation:
The distance between-9 and 0 is 9.