The speed of the ball is
ds/dt = 32t
At t =1/2 s
ds/dt = 16 ft/s
The distance from the ground
50 - 16(1/2)^2 = 46 ft
The triangles formed are similar
50/46 = (30 + x)/x
x = 345 ft
50 / (50 - s) = (30 + x)/x
Taking the derivative and substituing
ds/dt = 16
and
Solve for dx/dt
Answer:
25/56
Step-by-step explanation:
make 3 1/8 an improper fraction then u should get 25/8 and then multiply the numerator of 1/7 by 25 and then multiply the denominators of the two fractions to get 7*8=56 so your fraction is 25/56
Answer: 37 kilograms of walnuts should be mixed.
Step-by-step explanation:
Let x represent the number of kilograms of peanuts needed to make the mixture.
Let y represent the number of kilograms of walnut needed to make the mixture.
The mixture to be made is 100 kg. It means that
x + y = 100
The worth of the mixture is $3.24 per kilogram. It means that the total worth of the mixture is
3.24 × 100 = $324
peanuts cost $2.50 per kilogram and walnuts cost $4.50 per kilogram. It means that
2.5x + 4.5y = 324- - - - - - - - - -1
Substituting x = 100 - y into equation 1, it becomes
2.5(100 - y) + 4.5y = 324
250 - 2.5y + 4.5y = 324
- 2.5y + 4.5y = 324 - 250
2y = 74
y = 74/2 = 37
x = 100 - y = 100 - 37
x = 63
He put in the value of x into y
and the value of y in x
if that confuse you here this is what it will look like
(x,y)->(y,x)
Volume of Cylinder V = πr²h
diameter = 6 feet, radius = 6/2 = 3 feet
dV/dt = (dV/dh) * (dh/dt) by change rule.
V = <span>πr²h
dV/dh = </span>πr² = π*3² = 9π ft²<span>
dV/dt = 2 ft</span>³/min
<span>dV/dt = (dV/dh) * (dh/dt)
</span>
2 ft³/min = 9π ft² * (dh/dt)
9π ft² * (dh/dt) = 2 ft<span>³/min
</span>
(dh/dt) = (2 ft³/min)/(9π ft<span>²)
(dh/dt) = (2/</span>9π) ft/min
So the water level is rising at (2/9<span>π) ft/min.</span>