The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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<u>ANSWER:
</u>
Rate per annum at which CI will amount from RS 2000 to RS 2315.35 in 3 years is 5%
<u>SOLUTION:
</u>
Given,
P = RS 2000
C.I = RS 2315.35
T = 3 years
We need to find the rate per annum. i.e. R = ?
We know that,
When interest is compound Annually:
Where p = principal amount
r = rate of interest
n = number of years
![$1+\frac{R}{100}=\sqrt[3]{1.157}$](https://tex.z-dn.net/?f=%241%2B%5Cfrac%7BR%7D%7B100%7D%3D%5Csqrt%5B3%5D%7B1.157%7D%24)
R = 5%
Hence, rate per annum is 5 percent.
Step-by-step explanation:
If you plug in the respective numbers (x,y) you'll get the answer choice C. 19=4(4)+3 : 19=19
Answer:
Step-by-step explanation:
Givens
d1 = d
d2 = 75 - d
r1 = x
r2 = x + 7
t = 3
Equation
x*t + (x + 7)*t = 75
This equation represents the total distance travelled. Neither one of the cyclists have gone 75 miles, but they both have gone distances that equal a total of 75 miles.
Solution
3x + (x + 7)*3 = 75
3x + 3x + 21 = 75
6x + 21 = 75
6x = 54
6x/6 = 54/6
x = 9
Answer
The first cyclist is going 9 miles / hr
The second cyclist is going 16 miles / hour
