<span>Xsquared -5x= 2x-6
x^2 - 5x - 2x + 6 = 0
x^2 - 7x + 6 = 0
(x -6)(x-1) = 0
x-6 = 0, x = 6
x - 1 = 0, x = 1
answer
solutions
x = 1 and x =6</span>
Answer:
The height of cone is decreasing at a rate of 0.085131 inch per second.
Step-by-step explanation:
We are given the following information in the question:
The radius of a cone is decreasing at a constant rate.
![\displaystyle\frac{dr}{dt} = -7\text{ inch per second}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%20-7%5Ctext%7B%20inch%20per%20second%7D)
The volume is decreasing at a constant rate.
![\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20-948%5Ctext%7B%20cubic%20inch%20per%20second%7D)
Instant radius = 99 inch
Instant Volume = 525 cubic inches
We have to find the rate of change of height with respect to time.
Volume of cone =
![V = \displaystyle\frac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h)
Instant volume =
![525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}](https://tex.z-dn.net/?f=525%20%3D%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%2899%29%5E2h%5C%5C%5C%5C%5Ctext%7BInstant%20heigth%7D%20%3D%20h%20%3D%20%5Cfrac%7B525%5Ctimes%203%7D%7B%5Cpi%2899%29%5E2%7D)
Differentiating with respect to t,
![\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Cbigg%282r%5Cfrac%7Bdr%7D%7Bdt%7Dh%20%2B%20r%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%5Cbigg%29)
Putting all the values, we get,
![\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Cbigg%282r%5Cfrac%7Bdr%7D%7Bdt%7Dh%20%2B%20r%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%5Cbigg%29%5C%5C%5C%5C-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Cbigg%282%2899%29%28-7%29%28%5Cfrac%7B525%5Ctimes%203%7D%7B%5Cpi%2899%29%5E2%7D%29%20%2B%20%2899%29%2899%29%5Cfrac%7Bdh%7D%7Bdt%7D%5Cbigg%29%5C%5C%5C%5C%5Cfrac%7B-948%5Ctimes%203%7D%7B%5Cpi%7D%20%2B%20%5Cfrac%7B2%5Ctimes%207%5Ctimes%20525%5Ctimes%203%7D%7B99%5Ctimes%20%5Cpi%7D%20%3D%20%2899%29%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7B%2899%29%5E2%7D%5Cbigg%28%5Cfrac%7B-948%5Ctimes%203%7D%7B%5Cpi%7D%20%2B%20%5Cfrac%7B2%5Ctimes%207%5Ctimes%20525%5Ctimes%203%7D%7B99%5Ctimes%20%5Cpi%7D%5Cbigg%29%20%3D%20%5Cfrac%7Bdh%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20-0.085131)
Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.
Answer:
d
Step-by-step explanation:
The co ordinates of P' is (-7,-2) and Q' is (-16, -8)
<u><em>Explanation</em></u>
PQ is rotated 180 degrees clockwise about P. It means <u>P and P' are the same points</u>.
According to the graph, the coordinates of P is (-7, -2) and Q is (2, 4)
When PQ is rotated 180 degrees clockwise about P, then <u>P or P' will be the mid-point of Q and Q' </u>
Suppose, the co ordinate of Q' is (x, y)
Now according to the mid-point formula, the coordinate of P or P' will be:
, which is actually at (-7, -2)
Thus.....
![\frac{x+2}{2}=-7\\ \\ x+2=-14\\ \\ x= -16\\ \\ and\\ \\ \frac{y+4}{2}= -2\\ \\ y+4= -4\\ \\ y= -8](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B2%7D%3D-7%5C%5C%20%5C%5C%20x%2B2%3D-14%5C%5C%20%5C%5C%20x%3D%20-16%5C%5C%20%5C%5C%20and%5C%5C%20%5C%5C%20%5Cfrac%7By%2B4%7D%7B2%7D%3D%20-2%5C%5C%20%5C%5C%20y%2B4%3D%20-4%5C%5C%20%5C%5C%20y%3D%20-8)
So, the co ordinates of P' is (-7,-2) and Q' is (-16, -8)
Answer:
That will be;
3x^2 + 5x -6 = 0
Step-by-step explanation:
Here, we want to write 3x^2 + 5x = 6 in the form
ax^2 + bx + c = 0
That will be;
3x^2 + 5x -6 = 0
We can simply get it by bringing the value 6 from the right hand side of the equation to the left hand side of the equation