<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
Answer:
denotes amount of food that Felicity's dog eats
Step-by-step explanation:
Given:
Felicity's dog eats no more than two cups of dog food per day.
Felicity's dog eats at least one-quarter cup more than one-half of the amount Martin's dog eats.
The amount of food that Martin's dog eats is represented by using 
To find: the inequality that represents the situation
Solution:
Amount of food that Martin's dog eats =
Amount of food that Felicity's dog eats ≤ 2
Also,
Amount of food that Felicity's dog eats 
Therefore,
Amount of food that Felicity's dog eats ≤ 2
Let denotes amount of food that Felicity's dog eats.
≤
Answer:
Mean: 4
Median : 4
Mode: 1, 2, 3, 4, 5, 6, 7
Step-by-step explanation:
Measure of center is:
Mean: Average
Median: Middle number
Mode: Often number
Mean: Add all number then divide by the total number in data set.
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
28/7 = 4
Median: Middle number
1,2,3,4,5,6,7
Mode: most often number
1,2,3,4,5,6,7
<u><em>Kavinsky</em></u>
Answer:
The answer is A)
Step-by-step explanation:
When the plane length increases, the force required gets reduced while the plane height stays the same.
<em>Hope this helps!</em>
