Answer:
9r
Step-by-step explanation:
1.5r - 3r + 10.5r
10.5r + 1.5r = 12r
12r - 3r = 9r
Final Answer = 9r
The fourth choice - 5/104.
In one cube, there are 3 even numbers - 2,4,6. For two cubes, the total probability is 36.
3*3 / 36 = 9/36
For letters, there are five vowels over 26 letters = 5 / 26
Multiply the two probabilities to get the probability of rolling two even numbers and selecting one of the vowels.
9/36 * 5/26 = 5/104
Answer:
97°
Step-by-step explanation:
you do 
and then 
which is the total sum of the two unknown vertical angles. once you have that, divide it by 2 to get 
as the measure of each individual unknow vertical angle
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
4 4/5 is the answer. :)
or.. 4.8!
