Answer:
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Step-by-step explanation:
∫ 15 sin(√(at)) dt
Use substitution:
If x = √(at), then:
dx = ½ (at)^-½ (a dt)
dx = a / (2√(at)) dt
dx = a/(2x) dt
dt = (2/a) x dx
Plugging in:
∫ 15 sin x (2/a) x dx
30/a ∫ x sin x dx
Integrate by parts:
If u = x, then du = dx.
If dv = sin x dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 30/a (-x cos x − ∫ -cos x dx)
= 30/a (-x cos x + ∫ cos x dx)
= 30/a (-x cos x + sin x + C)
Substitute back:
30/a (-√(at) cos(√(at)) + sin(√(at)) + C)
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Answer:
x =
, y = -1.71
Step-by-step explanation:
sub y = x+4 in the first equation to get:
12 x - 5 (x+4) = -20
Simplify:
12 x - 5 x + 20 = -20
Further simplify:
7 x = - 40
Divie both sides by 7 to get:
x =
--> x = -5.7
Sub x =
in the second equation to get:
y =
+ 4 = -1.71
1c. New Value=64.8 and Decrease=15.2
1e. Original Value= $70 and Decrease=$21
1f) Original Level=11 and New value=44
Answer:
45
Step-by-step explanation:
45% = 0.45
45/100 = 0.45
Answer:
3 is known as the power of 2.