Answer:
if you multiply 4/3 by 4/4 you get 4/16.
Step-by-step explanation:
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<h2>9.</h2><h3>Given</h3>
<h3>Find</h3>
- linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>
The equation for volume of a sphere is
... V = (4/3)π·r³
Differentiating gives
... dV = 4π·r²·dr
Filling in the given numbers gives
... change in volume ≈ 4π·(15 cm)²·(0.4 cm)
... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick
<h2>11.</h2><h3>Given</h3>
- an x by x by 2x cuboid with surface area 129.6 cm²
- rate of change of x is 0.01 cm/s
<h3>Find</h3>
<h3>Solution</h3>
The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².
The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is
... dV/dt = (d/dt)(2x³) = 6x²·dx/dt
We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...
... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
19,000
Step-by-step explanation:
round down if the hundred is above 5 than round up one number
This is your answer, hope this helps :D !
Answer:
1. y = f(8)
2. So for t which f'(t) > 0, the drug level in the bloodstream is increasing. And for t which f'(t) < 0, it is decreasing.
Step-by-step explanation:
The concentration of the drug in the bloodstream at t hours is:
y = f(t)
1. What is the concentration of the drug in the bloodstream at t= 8 hours?
At t hours, y = f(t)
So at 8 hours, y = f(8)
2. During what time interval is the drug level in the bloodstream increasing? Decreasing?
A function f(t) is increasing when
f'(t) > 0
And is decreasing when
f'(t) < 0
So for t which f'(t) > 0, the drug level in the bloodstream is increasing. And for t which f'(t) < 0, it is decreasing.