(-3,7)
5(-3)+2(7)=-1
-15+14=-1
(4x−101)(2x+3)
Apply the distributive property by multiplying each term of 4x−101 by each term of 2x+3.
8x²+12x−202x−303
Combine 12x and −202x.
8x²−190x−303
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29
We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)
We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify
The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
There can be more then 1 mode.
Sometimes, there is not even a mode.....and other times, there is 1 mode.
Answer:
4
Step-by-step explanation:
Equating the y-values gives an equation in x.
4x -10 = (x -2)^2 +2
0 = x^2 -4x +4 +2 -4x +10 . . . . . . . . eliminate parentheses, subtract 4x-10
x^2 -8x +16 = 0
(x -4)^2 = 0
x = 4
The x-coordinate of the one point of intersection is x = 4.
