<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
Add all the like terms together so 4x-3x is x or 1x -3y-y is -4y 2z+3z is 5z so put them all together it's x-4y+5z
Answer:
Option D.
Step-by-step explanation:
The formula for total debt ratio is
It can be rewritten as
.... (1)
We know that,
... (2)
Using (1) and (2) we get
Substitute total debt ratio=0.46 in the above equation.
Therefore, the correct option is D.
Answer:
-8x3 - 4x2 + 8x - 4
Step-by-step explanation:
Answer:
x = 64 degree , 2x = 128 degree
Step-by-step explanation:
2x = 128 (being alternate interior angles)
x = 128/2
x = 64 degree
2x
=2*64
=128 degree
