Answer:
2160 cm³/hour
Step-by-step explanation:
By default, we know that the volume of a cube is given as s³
Thus, the Volume function, V = s³
When we differentiate with respect to time we have
dV/dt = 3s² (ds/dt), where ds/dt = 0.2
Then we go ahead and substitute all the given parameters
dV/dt = 3 x 60 x 60 x 0.2
dV/dt = 10800 * 0.2
dV/dt = 2160 cm³/hour
This means that the volume decreases by a rate of 2160 cm³/hour at the instant its edge is 60 cm
Dup= 72 miles
<span>ddown= 120 miles </span>
<span>v= riverspeed </span>
<span>rup= 32mph - v </span>
<span>rdown= 32mph + v </span>
<span>t both ways= t </span>
<span>d=r*t </span>
<span>d/r=t </span>
<span>t=ddown/rdown </span>
<span>t=dup/rup </span>
<span>dup/rup = ddown/rdown </span>
<span>(72)/(32-v)=(120)/(32+v) </span>
<span>3840-120v=2304+72v </span>
<span>1536=192v </span>
<span>v=8</span>
Answer:
see explanation
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
(11)
- 81 + x² = - y² ( add y² to both sides )
- 81 + x² + y² = 0 ( add 81 to both sides )
x² + y² = 81 ← in standard form
with centre = (0, 0 ) and r = 
= 9
(12)
y² + x² - 196 = 0 ( add 196 to both sides )
x² + y² = 196 ← in standard form
with centre = (0, 0 ) and r = 
= 14
Figure on top is 8 times 9 (to find volume)
the figure on top has a volume of 72 cm<span>^3
the volume of the lower figure:
3 times 9 times 5 = 135 cm</span><span>^3
72+135=207 cm</span><span>^3
the volume of both figures is 207 cm</span><span>^3</span>
Your proof is correct and very well done
