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:
Thanks kind stranger! :)
Step-by-step explanation:
Answer:
(1,7.5)
Step-by-step explanation:
(x₁ + x₂ / 2 , y₁ + y₂ / 2)
(-2 + 4 / 2 , 6 + 9 / 2)
(2 / 2 , 15 / 2)
(1,7.5)
Answer:
y-8x=-2
Step-by-step explanation:
so the slope of the perpendicular line has to the negative receprical of the slope of this line which gives
-(-8)=8
let us put all the equations into slope intercept form
a.y=-8x+6
b.y=-1/8x-5
c.y=1/8x-5
d. y=8x-2
y=mx+b
as you can see the only line with a slope of 8 is y-8x=-2
