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:
A set of parametric equations for the line y = 4x - 5 is;
x = t
y = 4t - 5
Step-by-step explanation:
To find a set of parametric equations for the line y = 4x - 5;
We can assign either variable x or y equal to the parameter t, in this case we can easily let x = t
We then substitute x = t in the original equation;
y = 4t - 5
Therefore, a set of parametric equations for the line y = 4x - 5 is;
x = t
y = 4t - 5
your question answer is 12360
.0562 is the smallest number
Answer:
volume = 7 * 4 * 24 = 672 m 3
Step-by-step explanation:
a^2 = 25^2 - 7^2 = 576
-> a = 24
volume = 7 * 4 * 24 = 672 m 3
