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:
A plain pizza is $10.50 and a pepperoni pizza is $12.50
Step-by-step explanation:
Create a system of equations where x is the price of a pepperoni pizza and y is the price of a plain pizza:
3x + 2y = 58.5
2x + 4y = 67
Solve by elimination by multiplying the top equation by -2:
-6x - 4y = -117
2x + 4y = 67
Add these together and solve for x:
-4x = -50
x = 12.5
So, a pepperoni pizza is $12.50. Plug in 12.5 as x into one of the equations, and solve for y:
2x + 4y = 67
2(12.5) + 4y = 67
25 + 4y = 67
4y = 42
y = 10.5
So, a plain pizza is $10.50.
A plain pizza is $10.50 and a pepperoni pizza is $12.50
8 × 20= 160; 8 × 4= 32; 160 + 32= 192; 8 × t= 192; 192 ÷ 8= 24; t=24
The answer is t = 24
Hope this helps :)
Answer:
The answer is 25.5.
Step-by-step explanation:
30% of $85 is 25.5.
-6.3 into a fraction is -6 and 3/10. its a mixed number!
