Answer:
p = 1
Step-by-step explanation:
4 - 5(p + 3/5) = -4
Find P
4 - 5(p + 3/5) = -4
4 - 5p -15/5 = -4
4 - 5p - 3 = -4
-5p + 1 = -4
-5p = -4 - 1
-5p = -5
p = -5/-5
p = 1
Check:
4 - 5(p + 3/5) = -4
4 - 5(1 + 3/5) = -4
4 - 5 - 15/5 = -4
4 - 5 - 3 = -4
4 - 8 = -4
-4 = -4
We're going to assume that x = # of days.
Plug 12 in as x:
4 × 12 = 48
48 + 6 = 54
They produced 54 boats in 12 days.
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)
3ab...when a = 2 and b = 3
(3)(2)(3) = 6(3) = 18
