5% sales tax, because the total would be $42 and if you multiply 40 x 0.05 (the equation for tax) you get 2 and that is the amount of tax they charged you
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:
Longer side(L) = 2*sqrt{3} units or 3.46410161514
Step-by-step explanation:
the length of the hypotenuse is twice the length of the shorter side also, the length of the longer side is sqrt{3} times the length of the shorter leg.
So since you haven't given us the actaul equation Im gonna guess that x equals to -7, and lets just say the x equals to uhhhhhh, i dont know how about 42? That sound about right? What im trying to say is next time can you please give out the equation? If you respond I could probably help you next time.