The change of the weather balloon would be 90% increase. to get the percentage of change we have to subtract 50 ft to 95 ft, it will then give us the 45 ft change. Then we have to divide 45 ft by 50 ft times 100, it will give us 90%. Then since the change and percentage of change is positive then the change could be describe as increasing.
Number of points Jill scored in the first 4 games = 4 * 4 = 16
number of points Jill scored in the first 4 games = 6 * 9 = 54
total points Jill scored in 10 games 16 + 54 = 70
the average number of points after 10 games = 70 / 10 = 7 points
Answer:
-0.8 is less than -0.3
Step-by-step explanation:
when dealing with decimals the closer it is to 1 the greater it is
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.
