Answer:
Step-by-step explanation:
We are given the following in the question:
We have to evaluate:
Putting values, we get
Answer:
5,2
Step-by-step explanation:
Clockwise rotations for 90 is
The preimage of (x,y), or for this problem, (-2,5) into (y,-x).
So, a clockwise rotation is from x,y into y,-x
So we do -2,5 into 5,2
We flipped the x and y, and the 2 became positive because two negatives equal a positive
The points of intersection are at (3, 6) and (-1, -2).
Since both of these equations have y isolated, we can set them equal to each other:
2x=x²-3
We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x
Write the quadratic in standard form:
0=x²-2x-3
This is easily factorable, as there are factors of -3 that will sum to -2. -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)
Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.
Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2
Therefore the coordinates are (3, 6) and (-1, -2).
Answer:
7x4+2x3-4x2-5
Step-by-step explanation:
We will start solving this question by opening the bracket first
So let's solve
(7x4+2x3-3)-(4x2-9x+2)
7x4+2x3-3-4x2+9x-2
Collect like terms
7x4+2x3-4x2-3-2
7x4+2x3-4x2-5
So the final answer is 7x4+2x3-4x2-5
<h3>Given</h3>
p'(t) = kp²
p(0) = 12; p(10) = 24
<h3>Find</h3>
a) p(t)
b) t such that p(t) = 48
c) the behavior of p(t) after the time of part b
<h3>Solution</h3>
a) The differential equation is separable, so can be solved by separating the variables and integrating.
Plugging in the given boundary conditions, we can solve for k and C to find
b) The population doubles when the time to t=20 is cut in half. The first doubling occurred in 10 years; the second one will occur in half that time, 5 years. There will be 48 alligators in the swamp in 2003.
c) The population doubles again in half the time of the previous doubling, so is predicted to be infinite in 2008.