The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Answer:
(a) 12 hours
(b) $220
Step-by-step explanation:
(a) First we plug in $364 for C
C=76+24h
364=76+24h
Subtract 76 from both sides
24h=288
Divide both sides by 24
h=12
She spent 12 hours fixing the drain
(b) First we plug 6 hours in for h
C=76+24(6)
Multiply it out
C=76+144
Add
C=220
It costs $220 for fixing a drain that takes 6 hours
Answer:
In algebraic terms this means x-17>33
Step-by-step explanation:
to solve it x−17>33
1 Add 17 to both sides.
x>33+17
2 Simplify 33+17 to 50
x>50
Volume of can, V = pi * r^2 * h
V = 3.14 * (3.5/2)^2 * 5
V = 3.14 * 1.75^2 * 5
V = 3.14 * 3.0625 * 5
V = 48.08125 inches^3
V = 48.08 inches^3
Are there options to this?
