<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:
x=-17
Step-by-step explanation:
subtract 6 from each side and simplify and you'll get -17
Given:
The expression is
To find:
The expression in repeated multiplication form and then write the expression as a power.
Solution:
We have,
The repeated multiplication form of this expression is
![=[(-8)\cdot (-8)\cdot (-8)]\cdot [(-8)\cdot (-8)\cdot (-8)\cdot (-8)]](https://tex.z-dn.net/?f=%3D%5B%28-8%29%5Ccdot%20%28-8%29%5Ccdot%20%28-8%29%5D%5Ccdot%20%5B%28-8%29%5Ccdot%20%28-8%29%5Ccdot%20%28-8%29%5Ccdot%20%28-8%29%5D)
Clearly, (-8) is multiplied seven times by itself. So,
Therefore, the repeated multiplication form of the given expression is 
and the expression as single power is 
.
Answer:
140 because half which is (%50) of 350 is 175 so 40% of 350 is 140
