Answer: Can I see the whole questions?
Step-by-step explanation:
The correct question is:
Suppose x = c1e^(-t) + c2e^(3t) a solution to x''- 2x - 3x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c1 as c1 and c2 as c2.)
Answer:
x = c1e^(-t) + c2e^(3t)
is a solution to the differential equation
x''- 2x' - 3x = 0
Step-by-step explanation:
We need to verify that
x = c1e^(-t) + c2e^(3t)
is a solution to the differential equation
x''- 2x' - 3x = 0
We differentiate
x = c1e^(-t) + c2e^(3t)
twice in succession, and substitute the values of x, x', and x'' into the differential equation
x''- 2x' - 3x = 0
and see if it is satisfied.
Let us do that.
x = c1e^(-t) + c2e^(3t)
x' = -c1e^(-t) + 3c2e^(3t)
x'' = c1e^(-t) + 9c2e^(3t)
Now,
x''- 2x' - 3x = [c1e^(-t) + 9c2e^(3t)] - 2[-c1e^(-t) + 3c2e^(3t)] - 3[c1e^(-t) + c2e^(3t)]
= (1 + 2 - 3)c1e^(-t) + (9 - 6 - 3)c2e^(3t)
= 0
Therefore, the differential equation is satisfied, and hence, x is a solution.
(-12 - 2i) + (2 + 2i)
= -12 - 2i + 2 + 2i
= -12 + 2 - 2i + 2i
= -10
Answer: -10
Answer:
Sasha's grandma will need 48 square feet of fabric to sew the umbrella.
Step-by-step explanation:
Since Sasha's grandma is going to sew an umbrella for Sasha, which will be made of 4 identical triangles, if each triangle is 3 feet long and 4 feet high, to determine how many square feet of fabric does Sasha's grandma need, the following calculation must be done:
(3 x 4) x 4 = X
12 x 4 = X
48 = X
Therefore, Sasha's grandma will need 48 square feet of fabric to sew the umbrella.
Answer:
sorry
Step-by-step explanation:
