X=-b/2a is the formula for finding the axis of symmetry
So x= -30/2(5)
X=-30/10
X=-3
Because the axis of symmetry is -3, we know where to place our line, and we also know that the parabola is open downwards, which means that the vertex will be maximum. To find the vertex, plug in your values with the axis of symmetry as a midway point. Plug that in for x and so you should have the following:
F(x)
Y(f(x) and y variables are interchangeable) =5(-3)^2-30(-3)+49
Solve for y(f(x))
5(-3)^2-30(-3)+49
(-3)^2=3^2
3^2*5+30*3+49
Multiply
3^2*5+90+49
Add numbers
3^2*5+139
9*5=45
45+139=184
Y=184
So, your vertex would be
(-3,184) and it would be maximum. From there you can plug in the rest of your table of values.
Answer:
Step-by-step explanation:
We have volume of cone as
and for a cone always r/h = constant
Given that r' = rate of change of radius = -7 inches/sec
(Negative sign because decresing)
V' =- 948 in^3/sec
Radius = 99 inches and volume = 525 inches
Height at this instant = 
Let us differentiate the volume equation with respect to t using product rule
![V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%5C%5CV%27%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2rhr%27%2Br%5E2%20h%27%5D%5C%5C-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2%2899%29%28-7%29%28%5Cfrac%7B0.1607%7D%7B%5Cpi%7D%29%2B99%5E2%20h%27%5D%5C%5C)
![-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514](https://tex.z-dn.net/?f=-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2%2899%29%28-7%29%28%5Cfrac%7B0.1607%7D%7B%5Cpi%7D%29%2B99%5E2%20h%27%5D%5C%5C-948%20%3D%2033%283.14%29%28-2.25%2F3.14%20%20%2B%2099%20h%27%29%5C%5C-9.149%3D-0.72%2B99h%27%5C%5C-8.429%20%3D%2099h%27%5C%5Ch%27%20%3D%200.08514)
Rate of change of height = 0.08514 in/sec
Answer:
C
Step-by-step explanation:
divide 14 by 4 to solve it, you get 3.5 or 3 1/2
Answer step-by-step explanation:
We know that the critical t value for a 98% confidence level for a sample of size n = 18:
Finding degrees of freedom (n-1) = 17
-search the information in table t for 0.98 and find that t = 2.567
