It would be 60 because all you do is double the radius because it is only half of the circle
The answer is -4 because -4 times -3 equals -12
Answer:
B
Step-by-step explanation:
To solve for x, we have to get x by itself. To do this, perform the opposite of what is being done to the equation.
5x+14=k
First, subtract 14 from both sides, because 14 is being added on to 5x. Subtraction is the opposite of addition.
5x+14-14=k-14
5x=k-14
Now, divide both sides by 5, because 5 and x are being multiplied. Division is the opposite of multiplication.
5x/5=k-14/5
x=k-14/5
So, the correct answer is choice B
Your answer is <span><span>1^8
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Hope this helps!</span>
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.
