15% as decimal is 0.15 so 90g*0.15= 13.5
so the equation is 90g*15%=13.5
Answer:
The answer is below
Step-by-step explanation:
The volume of the cylinder with radius (r) and height (h) is given as:
Volume = πr²h
17 = πr²h
h = 17 / πr²
Let k represent the cost of the side and 2k the cost of the bottom.
The area of the side = 2πrh, hence the cost of the side = k(2πrh)
The area of the top and bottom = 2πr², hence the cost of the top and bottom = 2k(2πr²)
The total cost (T) = cost of side + cost of the top and bottom
T = k(2πrh) + 2k(2πr²)
T = 2kπ(rh + 2r²)
Put h = 17/πr²
T = 2kπ (r×17/πr² + 2r²)
T = 2kπ(17/πr + 2r²)
The minimal cost is at dT/dr = 0
![\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2} =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdr%7D%20%3D0%3D%5Cfrac%7Bd%7D%7Bdr%7D%20%5B2k%5Cpi%28%5Cfrac%7B17%7D%7B%5Cpi%20r%7D%20%2B2r%5E2%29%5D%5C%5C%5C%5C4r-%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%3D0%5C%5C%5C%5C4r%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%5C%5C%5C%5Cr%5E3%3D%5Cfrac%7B17%7D%7B4%5Cpi%20%7D%3D1.35%5C%5C%5C%5Cr%3D%5Csqrt%5B3%5D%7B1.35%7D%5C%5C%5C%5Cr%3D1.1%5C%20m%5C%5C%5C%5Ch%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%20%3D%5Cfrac%7B17%7D%7B%5Cpi%20%281.1%29%5E2%7D%20%5C%5C%5C%5Ch%3D4.42%5C%20m)
Answer:
combined velocity of the system = 0.033 m/s.
Step-by-step explanation:
taking the bullet and block as single system since there is no external force involved momentum is conserved .
initial momentum of the bullet = mv
where m is the mass of bullet and v is velocity of bullet.
and initial momentum of block = 0 since its velocity is 0.
therefore initial momentum of the system = mv
= 0.005×40
= 0.2
when the bullet stick of together with the block let the combined velocity of the system be V
therefore applying conservation of momentum
mv = (M+m)V
0.2=(6+0.005)V
therefore V = 0.033 m/s
Answer:
$1449.15
Step-by-step explanation:
currently paying 815
to pay next year: 41% increase + 25 extra per month
⇒ 141%·815 + 12·25
= 1149.15 + 300
= 1449.15
