Answer: y= -1/3x + 3
Step-by-step explanation:
To write it in slope intercept form we need just the slope and the y intercept. Here we are given the slope but we need to find the y intercept using the coordinates.
Using the slope intercept formula y= mx + b where m is the slope and b is the y intercept.
We will plot in the x and y coordinates and the slope to find the y intercept.
4 = -1/3(-3) + b
4= 1 + b
-1 -1
b =3 The y intercept in this case is 3.
so y = -1/3 + 3
Answer:
60
Step-by-step explanation:
The given function is:
![h(t)=-16t^2+120t+6](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%2B120t%2B6)
The average rate of change of h(t) from t=a to t=b is given by:
![\frac{h(b)-h(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%28b%29-h%28a%29%7D%7Bb-a%7D)
We can rewrite this function as: ![h(t)=-16(t-3.75)^2+231](https://tex.z-dn.net/?f=h%28t%29%3D-16%28t-3.75%29%5E2%2B231)
The maximum height of the rocket is 231 and it occurs at t=3.75
![\implies h(3.75)=231](https://tex.z-dn.net/?f=%5Cimplies%20h%283.75%29%3D231)
The initial launch occurs at: t=0
and ![h(0)=-16(0)^2+120(0)+6=6](https://tex.z-dn.net/?f=h%280%29%3D-16%280%29%5E2%2B120%280%29%2B6%3D6)
The average rate of change from the initial launch to the maximum height is
![\frac{h(3.75)-h(0)}{3.75-0}=\frac{231-6}{3.75-0} =60](https://tex.z-dn.net/?f=%5Cfrac%7Bh%283.75%29-h%280%29%7D%7B3.75-0%7D%3D%5Cfrac%7B231-6%7D%7B3.75-0%7D%20%3D60)
Answer:
The following classification is found:
- Absolute minimum
- Absolute maximum
Step-by-step explanation:
Let be
, we need to find first and second derivatives of this expression at first:
First derivative
(Eq. 1)
Second derivative
(Eq. 2)
Critical points are points that equals first derivative to zero and that may be maxima or minima. That is:
![375\cdot x^{2} -15 = 0](https://tex.z-dn.net/?f=375%5Ccdot%20x%5E%7B2%7D%20-15%20%3D%200)
![x = \pm \sqrt{\frac{15}{375} }](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B15%7D%7B375%7D%20%7D)
Which leads to the following critical points:
and ![x_{2} \approx -0.2](https://tex.z-dn.net/?f=x_%7B2%7D%20%5Capprox%20-0.2)
Now we evaluate each result in second derivative expression:
![f''(x_{1}) = 750\cdot (0.2)](https://tex.z-dn.net/?f=f%27%27%28x_%7B1%7D%29%20%3D%20750%5Ccdot%20%280.2%29)
(Absolute minimum)
![f''(x_{2})= 750\cdot (-0.2)](https://tex.z-dn.net/?f=f%27%27%28x_%7B2%7D%29%3D%20750%5Ccdot%20%28-0.2%29)
(Absolute maximum)
Lastly we evaluate the function at each critical point:
![f(x_{1})= 125\cdot (0.2)^{3}-15\cdot (0.2)+8](https://tex.z-dn.net/?f=f%28x_%7B1%7D%29%3D%20125%5Ccdot%20%280.2%29%5E%7B3%7D-15%5Ccdot%20%280.2%29%2B8)
![f(x_{1})= 6](https://tex.z-dn.net/?f=f%28x_%7B1%7D%29%3D%206)
![f(x_{2})= 125\cdot (-0.2)^{3}-15\cdot (-0.2)+8](https://tex.z-dn.net/?f=f%28x_%7B2%7D%29%3D%20125%5Ccdot%20%28-0.2%29%5E%7B3%7D-15%5Ccdot%20%28-0.2%29%2B8)
![f(x_{2}) = 10](https://tex.z-dn.net/?f=f%28x_%7B2%7D%29%20%3D%2010)
And the following classification is found:
- Absolute minimum
- Absolute maximum
Split the number into its whole number component and decimal component.
for the decimal component, 0.2 is the same as 2/10
Find the GCF of both 2 and 10 and that would be 2
divide both the numerator and denominator by the GCF
simplify and you get 1/5
Lastly combine the whole number component with the fraction and your answer would be 1 1/5.