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:
There are 19 big marbles
Step-by-step explanation:
10a + 3b = 209
a = 3b
3b = 3b
10a + a = 209
11a = 209
a = 209/11
a = 19
Answer:
(2,-1)
Step-by-step explanation:
The ys in both questions are isolated on one side of the equation in both. The numerical coefficient of both is 1. Therefore you should equate the the left side of each equation to the other left side. The solution is the easiest one to solve because there is only 1 unknown on both sides.
4x - 9 = x - 3 Subtract x from both sides.
4x-x - 9 = -3 Combine
3x -9 = - 3 Add 9 to both sides
3x - 9+9 = - 3+9
3x = 6 Divide by 3
3x/3 = 6/3
x = 2
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Now use the second equation to solve for y
y = x - 3
y = 2 - 3
y = -1
==============
The solution is (2,-1)
Answer:
Step-by-step explanation:
We need to solve 
We know that,
Using the above formula,
![(8m-3n)^2 - (4m+3n)^2=(8m)^2+(3n)^2-2(8m)(3n)-[(4m)^2+(3n)^2+2(4m)(3n)]\\\\=64m^2+9n^2-48mn-(16m^2+9n^2+24mn)\\\\=64m^2+9n^2-48mn-16m^2-9n^2-24mn\\\\=48m^2-48mn-24mn\\\\=48m^2-72mn](https://tex.z-dn.net/?f=%288m-3n%29%5E2%20-%20%284m%2B3n%29%5E2%3D%288m%29%5E2%2B%283n%29%5E2-2%288m%29%283n%29-%5B%284m%29%5E2%2B%283n%29%5E2%2B2%284m%29%283n%29%5D%5C%5C%5C%5C%3D64m%5E2%2B9n%5E2-48mn-%2816m%5E2%2B9n%5E2%2B24mn%29%5C%5C%5C%5C%3D64m%5E2%2B9n%5E2-48mn-16m%5E2-9n%5E2-24mn%5C%5C%5C%5C%3D48m%5E2-48mn-24mn%5C%5C%5C%5C%3D48m%5E2-72mn)
So, the final answer is .
