Given :
A function , x = 2cos t -3sin t .....equation 1.
A differential equation , x'' + x = 0 .....equation 2.
To Find :
Whether the given function is a solution to the given differential equation.
Solution :
First derivative of x :
Now , second derivative :
( Note : derivative of sin t is cos t and cos t is -sin t )
Putting value of x'' and x in equation 2 , we get :
=(-2cos t + 3sin t ) + ( 2cos t -3sin t )
= 0
So , x'' and x satisfy equation 2.
Therefore , x function is a solution of given differential equation .
Hence , this is the required solution .
The future value (A) of a one-time investment of principal amount P at interest rate r compounded n times per year for t years is ...
... A = P(1 +r/n)^(nt)
Putting your given numbers into the formula, we have
... 876.34 = 300(1 +.06/4)^(4t)
Taking logarithms, this becomes the linear equation
... log(876.34) = log(300) + 4t·log(1.015)
Solving for t in the usual way, we get
... log(876.34) -log(300) = 4t·log(1.015) . . . . . . . subtract the constant term on the right
... (log(876.34) -log(300))/(4·log(1.015)) = t ≈ 18.00 . . . . divide by the coefficient of t
It will take <em>18 years</em> for the $300 CD to reach a value of $876.34.
<h2>
Answer with explanation:</h2>
Given : The probability that telephone bills mailed to house-holds in Hong Kong are incorrect.=0.01
<h2>
Binomial distribution :-</h2>
If a sample of 10 bills is selected, then the probability that at least one bill will be incorrect :-
Hence, the probability that at least one bill will be incorrect =0.6513
<h2>
Poisson distribution: </h2>
Mean : 
Then , If a sample of 10 bills is selected, then the probability that at least one bill will be incorrect :-
Hence, the probability that at least one bill will be incorrect =0.6321
Pounds of soil used: 10 x 5/8 = 50/8 = 6 2/8 = 6 1/4 pounds used (in lowest form).
So what was left was: 10 - 6 1/4 = 3 3/4 pounds
