Answer:y=
Acosx+Bsinx +cosx ln(cosx)+x sinx
Step-by-step explanation:
given equation y''+y=secx
auxiliary equation
so CF is y=Acosx+Bsinx
now
using wronskian formula
=
now f(x)=secx
now particular integrals are
PI=cosx ln(cosx)+x sinx
total solution
y= C.F+P.I
y=Acosx+Bsinx +cosx ln(cosx)+x sinx
(I)
Given equation is x²-8x = -16
⇛ x²-8x+16 = 0
⇛ x²-4x-4x+16 = 0
⇛ x(x-4)-4(x-4) = 0
⇛ (x-4)(x-4) = 0
⇛ x-4 = 0 or x-4 = 0
⇛ x = 4 or x = 4
(ii)
Given equation is x²+2x+1 = 0
⇛ x²+x+x+1 = 0
⇛ x(x+1)+1(x+1) = 0
⇛ (x+1)(x+1) = 0
⇛ x+1 = 0 or x+1 = 0
⇛ x = -1 or x = -1
(iii)
Given equation is 4x²-24x-36 = 0
⇛ 4(x²-6x-9) = 0
⇛ x²-6x-9 = 0
⇛ x²-2(x)(3) = 9
On adding 3² both sides then
⇛ x²-2(3)x)+3² = 9+9
⇛ (x-3)² = 18
⇛ (x-3) = ±√18
⇛ x-3 = ±√(2×9)
⇛ x-3 = ±3√2
⇛ x = 3±3√2
⇛ x = 3+3√2 or 3-3√2
Answer:
5mph
Step-by-step explanation:
Let speed of boat in still water is s.
Distance proportional to speed
90/10 = (s+ 4)/(s - 4)
=> 9s - 36 = s + 4
=> 8s = 40
=> s= 5 mph
:-)
Answer:
she earned $288.75 in commissions
Step-by-step explanation:
