Answer:β=√10 or 3.16 (rounded to 2 decimal places)
Step-by-step explanation:
To find the value of β :
- we will differentiate the y(x) equation twice to get a second order differential equation.
- We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β
y(x)=c1cosβx+c2sinβx
we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.
Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.
lastly the differential of sinx= cosx and for cosx = -sinx.
Knowing all these we can proceed to solving the problem.
y=c1cosβx+c2sinβx
y'= β×c1×-sinβx+β×c2×cosβx
y'=-c1βsinβx+c2βcosβx
y''=β×-c1β×cosβx + (β×c2β×-sinβx)
y''= -c1β²cosβx -c2β²sinβx
factorize -β²
y''= -β²(c1cosβx +c2sinβx)
y(x)=c1cosβx+c2sinβx
therefore y'' = -β²y
y''+β²y=0
now we compare this with the second order D.E provided in the question
y''+10y=0
this means that β²y=10y
β²=10
B=√10 or 3.16(2 d.p)
Answer:
Future amount (A) = $1,258.77 (Approx)
Step-by-step explanation:
Given:
Amount deposit (p) = $693
Rate of interest monthly (r) = 4.9% / 12 = 0.003833
Number of month (n) = 13 × 12 = 156
Find:
Future amount (A)
Computation:
![A = p [1+r]^n \\\\ A = 693 [1+0.003833]^{156}\\\\ A= 693[1.8163]\\\\ A = 1258.77](https://tex.z-dn.net/?f=A%20%3D%20p%20%5B1%2Br%5D%5En%20%5C%5C%5C%5C%20A%20%3D%20693%20%5B1%2B0.003833%5D%5E%7B156%7D%5C%5C%5C%5C%20A%3D%20693%5B1.8163%5D%5C%5C%5C%5C%20A%20%3D%201258.77)
Future amount (A) = $1,258.77 (Approx)
Answer:
113.1in²
Step-by-step explanation:
The answer for this question will be 113.1in²
As we know the diameter that is 12 inches.
Thats how we got the area for this question.
Hope this helps
Because the probability of getting heads is 1/2, in a scenario in which it is tossed 3 times, the probability of getting exactly one head is 1/3.
Answer: $9
Step-by-step explanation: 9•8=72
9+5=14
14•3=42
42+72=114
