Answer:
y_c = 2 + 10*x
Step-by-step explanation:
Given:
y'' = 0
Find:
- The solution to ODE such that y(0) = 2, y'(0) = 10
Solution:
- Assuming a solution y = Ce^(mt)
So, y' = C*me^(mt)
y'' = C*m^2e^(mt)
- Back substitute into given ODE, we get:
y'' = C*m^2e^(mt) = 0
e^(mt) can not be equal to zero
- Hence, m^2 = 0
m = 0 , 0 - (repeated roots)
- The complimentary function for repeated roots is:
y_c = (C1 + C2*x)*e^(m*t)
y_c = C1 + C2*x
- Evaluate @ y(0) = 2
2 = C1 + C2*0
C1 = 2
-Evaluate @ y'(0) = 10
y'(t) = C2 = 10
Hence, y_c = 2 + 10*x
Answer:
32x - 8
Step-by-step explanation:
8 x 4 = 32
(-)2 x 4 = -8
32x - 8
hope this helps and that it's right :)
Answer:
25/11 divided by 5/22 = 10
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 11 on the left side and the dividend 25 on the right side like this:
1 1 ⟌ 2 5
Step 2:
The divisor (11) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:
0
1 1 ⟌ 2 5
Step 3:
Multiply the divisor by the result in the previous step (11 x 0 = 0) and write that answer below the dividend.
0
1 1 ⟌ 2 5
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.
0
1 1 ⟌ 2 5
- 0
2
Step 5:
Move down the 2nd digit of the dividend (5) like this:
0
1 1 ⟌ 2 5
- 0
2 5
Step 6:
The divisor (11) goes into the bottom number (25), 2 time(s). Therefore, put 2 on top:
0 2
1 1 ⟌ 2 5
- 0
2 5
Step 7:
Multiply the divisor by the result in the previous step (11 x 2 = 22) and write that answer at the bottom:
0 2
1 1 ⟌ 2 5
- 0
2 5
2 2
Step 8:
Subtract the result in the previous step from the number written above it. (25 - 22 = 3) and write the answer at the bottom.
0 2
1 1 ⟌ 2 5
- 0
2 5
- 2 2
3
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 25 divided by 11 calculated using Long Division is:
Answer:
A. ^3√5 is the answer.
Step-by-step explanation:
5^( 1 / 3 ) = ^3√5
