Answer:
dh/dt=9.82x10^-3 ft/min
Step-by-step explanation:
1. You have that the rate is10 ft³/min. Then:
dV/dt=10
2. The formula for calculate the volume of a cone, is:
V=1/3(πr²h)
"r" is the radius and "h" is the height.
3. The diameter of the base of the cone is approximately 3 times the altitude. Then, the radius is:
r=diameter/2
diameter=3h
r=3h/2
4. When you susbstitute r=3h/2 into the formula V=πr²h/3, you have:
V=1/3(πr²h)
V=1/3(π(3h/2)²(h)
V=1/3(π9h²/4)(h)
V=9πh³/12
5. Therefore:
dV/dt=(9πh²/4)dh/dt
h=12
dV/dt=10
6. When you substitute the values of dV/dt and h into dV/dt=(9π(12)²/4)dh/dt, you have:
dV/dt=(9π(12)²/4)dh/dt
10=(1017.876)
7. Finally, you obtain:
dh/dt=10/1017.876
dh/dt=9.82x10^-3 ft/min
Answer:
y = 16.
Step-by-step explanation:
The ratio of corresponding sides of similar triangles are the same.
The small and large triangles are similar ( - that is corresponding angles are congruent).
So 2/(2+8) = x / 20
2/10 = x/20
10x = 40
x = 4.
Therefore y = 20 -4 = 16.
x = k/2 + 11/2
Step-by-step explanation:
hope this helped :)
Answer:
Susan makes 5 fruit cups
each fruit cup has 5 strawberries and 3 kiwis
so the number of strawberries used is - 5 x 5 = 25 strawberries
and the number of kiwis used - 5 x 3 = 15 kiwis
so the total number of fruits - 25 + 15 = 40 fruits
Joanna uses 40 fruits to make 4 fruit cups
each cup she uses 8 strawberries
therefore total number of strawberries she uses - 8x 4 = 32 strawberries
she has 40 fruits in total and 32 of those are strawberries
the rest are kiwis
number of kiwis = 40 -32 = 8
8 kiwis are there and she has to make 4 cups
so for each cup number of kiwis = 8 / 4 = 2
so each cup has 2 kiwis
Step-by-step explanation:
