Answer:
-50 cm^3/min
Explanation:
The volume of the lollipop is given by

where r is the radius in centimeters.
To find how fast the volume changes, we need to find the rate of change of the volume, which is given by its derivative with respect to time:
(1)
where
dr/dt is the rate of change of the radius
We know that the circumference is

and it decreases by 1 cm per minute, so
(cm/min)
from which we find dr/dt:

Substituting into (1),
(cm^3/min)
And substituting r = 5, we find the rate of change of the volume when the radius is 5 cm:
(cm^3/min)
Answer:
v= 300 m/s
Explanation:
Given that
altitude ,h= 4500 m
The mass ,m = 3 kg
Lets take acceleration due to gravity , g= 10 m/s²
The speed before impact at sea level = v
Initial speed ,u = 0 m/s
We know that
v²=u²+2 g h
v=final speed
u=initial speed
h=height
Now by putting the values in the above equation
v² = 0²+ 2 x 10 x 4500
v²=90000
v= 300 m/s
Therefore the speed at sea level will be 300 m/s.
<span> For this case the volume of the box is given by:
</span>

<span> Substituting values we have:
</span>

<span> Rewriting we have:
</span>

<span> Grouping terms of equal degree we have:
</span>

<span> Adding terms of equal degree we have:
</span>

<span>
Answer: the volume of the box is: All the expressions given.</span>
The vector c has a magnitude of 24.6m and it is in the negative y direction. Therefore

The vector b is 41.4° up from the x-axis. Therefore
![\vec{b} = b[cos(41.4^{o}) \hat{i} + sin(41.4^{o}) \hat{j} ] =b(0.75\hat{i} + 0.6613 \hat{j})](https://tex.z-dn.net/?f=%5Cvec%7Bb%7D%20%3D%20b%5Bcos%2841.4%5E%7Bo%7D%29%20%5Chat%7Bi%7D%20%2B%20sin%2841.4%5E%7Bo%7D%29%20%5Chat%7Bj%7D%20%5D%20%3Db%280.75%5Chat%7Bi%7D%20%2B%200.6613%20%5Chat%7Bj%7D%29)
The vector a is 27.7° up from the x-axis. Therefore
![\vec{a} = a[cos(22.7^{o})\hat{i} + sin(27.7^{o})\hat{j}] = a(0.8854\hat{i} + 0.4648\hat{j})](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%20%3D%20a%5Bcos%2822.7%5E%7Bo%7D%29%5Chat%7Bi%7D%20%2B%20sin%2827.7%5E%7Bo%7D%29%5Chat%7Bj%7D%5D%20%3D%20%20a%280.8854%5Chat%7Bi%7D%20%2B%200.4648%5Chat%7Bj%7D%29)
Because

, the sum of the x and y components should be zero. Therefore,
For the x-component,
0.8854a + 0.75b = 0
or
a + 0.847b = 0 (1)
For the y-component,
0.4648a + 0.6613b - 24.6 = 0
or
a + 1.4228b = 52.926 (2)
Subtract (1) from (2).
0.5758b = 52.926
b = 91.917
a = -0.847b = -77.854
Answer:
The magnitude of vector a is -77.85 m
The magnitude of vector b is 91.92 m