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:
y=-3x+2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-5)/(1-(-1))
m=-6/(1+1)
m=-6/2
m=-3
y-y1=m(x-x1)
y-5=-3(x-(-1))
y-5=-3(x+1)
y=-3(x+1)+5
y=-3x-3+5
y=-3x+2
Answer:
g(-5) = -6
Step-by-step explanation:
We need to find value of g(-5)
Looking at the graph in figure when g = -5, the value on the graph is -6 as it is highlighted with blue point.
because we have x = -5 so, we will look at graph that passes through x and y when x= -5, so we get y=-6
So, g(-5) = -6
Answer:
V = 205 in^3 to the nearest whole number
Step-by-step explanation:
V = 4/3 π r^3
Plugging in the given information:
V = 4/3 * 3.14 * 7^2
V = 205.147.
