<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 = 8
Step-by-step explanation:
Using the sine or cosine ratio in the right triangle and the exact value
sin30° = 
, then
sin30° = 
= 
= ( cross- multiply )
x = 8
Answer:
I=prt,,60=400*0.05t,,t=3 ..................
this is what i got i hope it is use full to you <3
Step-by-step explanation:
Answer:
C (1,2)
Step-by-step explanation:
The point that is a solution must satisfy both inequalities;
The inequalities are;
Point A
: True
:False
Point B (0,4)
: False
:True
Point C (1,2)
: True
:True
Point D(-2,-4)
: True
:False
The correct answer is C.
