The first step u should do is (3+2)
<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:
11.2 feet
Step-by-step explanation:
The two furthest corners of the bed are at (8, 6) and (5, 10). To determine which is the furthest from the origin, use the distance formula.
d = √((x₂ − x₁)² + (y₂ − y₁)²)
d = √((8 − 0)² + (6 − 0)²)
d = 10
d = √((x₂ − x₁)² + (y₂ − y₁)²)
d = √((5 − 0)² + (10 − 0)²)
d = 5√5
d ≈ 11.2
Therefore, the corner at (5, 10) is the furthest from the origin, about 11.2 feet away.
Answer:
y=5×+2
Step-by-step explanation:
5(1)+2=7
5(2)+2=12
5(3)+2=17
5(4)+2=22
Answer: 0.29 or 29 cents each :)
anymore questions ask me ;)
