Answer:
13
Step-by-step explanation:

Hope this helps..
Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
Answer:
50 degrees ( Vertically opposite)
Hope it helps
Step-by-step explanation:
It would take 26 years.
The equation will be in the form y = a(1+r)ˣ, where a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. Using our information we have
y = 18450(1+0.027)ˣ = 18450(1.027)ˣ
We want the population to be doubled; 18450*2 = 36900:
36900 = 18450(1.027)ˣ
Divide both sides by 18450:
36900/18450 = 18450(1.027)ˣ/18450
2 = 1.027ˣ
Using logarithms, we have
This problem can be solved by manipulating the formula for power, which is: P = VI. Where:
P = Power in watts
V= Voltage in volts
I = Current in amperes
Since we are already given the power and voltage, simple substitution can be done.
P = VI
3.5 watts = 120 volts * I
I = 3.5 / 120
I = 0.0292 Amperes or 29.2 milliAmperes
Therefore, the current through the bulb is 29.2mA