Step-by-step explanation:
The slope is described by the the initial and final value of one quantity over the difference between the initial and final of the other
Rate: for points on a Cartesian plane,(x1, y1) and (x2, y2)
the slope, m= (y2 - y1)/(x2 - x1)
The rate of change on the other hand is mostly refers to how much a quantity is changing with time i.e the rate of change of y from y1 to y2 can be expressed as
rate = (y2 - y1)/(t2 - t1)...where t1 and t2 are the various time in y1 and y2 respectively...
Answer:
x−2x4+2x3−7x2−8x+12=x3+4x2+x−6
The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that x=-2x=−2 is a root, since (-2)^3+4(-2)^2+(-2)-6=0(−2)3+4(−2)2+(−2)−6=0 , so x+2x+2 is also a factor and we have
\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3(x−2)(x+2)x4+2x3−7x2−8x+12=x2+2x−3
Finally, we can factorize the remaining quotient easily:
x^2+2x-3=(x+3)(x-1)x2+2x−3=(x+3)(x−1)
so the other factors are x+2x+2 , x+3x+3 , and x-1x−1 .
Answer:
The work done to pump all of the kerosene from the tank to an outlet is 
Step-by-step explanation:
The work is defined by:
(1)
The force here will be the product between the volume and the kerosene weighing, so we have :
This force will be in-lbs.
Where R is the radius (3 feet)
Then using (1), we have:
Here 8-y is a distance at some point of the tank. Now, to get the work done from the base to the top of the tank we will need to take integral from 0 to 8 feet.
Therefore, the work done to pump all of the kerosene from the tank to an outlet is
I hope it helps you!
GH: chord
M: point of tangency
MJ: diameter
J: center
MH: radius
GH: secant
Answer:
B
Step-by-step explanation:
