Graphf(x)=x and g(x)=5x+1.

Water is leaking out of an inverted conical tank at a rate of 12,000 cm3/min at the same time that water is being pumped into th

Bas_tet [7]

Answer:

$291111.1cm^3/min$

Step-by-step explanation:

We are given that

$\frac{dV}{dt}_{out}=12000 cm^3/min$

Height of tank,h=6 m

Diameter of top,d=4 m

Radius,r= $\frac{d}{2}=\frac{4}{2}=2 m$

$\frac{dh}{dt}=20 cm/min$

$\frac{r}{h}=\frac{2}{6}=\frac{1}{3}$

$r=\frac{1}{3} h$

We have to find rate at which water is being pumped into the tank.

Volume of conical ,V= $\frac{1}{3}\pi r^2 h$

$V=\frac{1}{3}\pi(\frac{1}{3} h)^2h=\frac{1}{27}\pi h^3$

$\frac{dV}{dt}=\frac{1}{9}\pi h^2(\frac{dh}{dt})$

h=2 m=200 cm

1m=100 cm

$\frac{dV}{dt}_{in}-12000=\frac{1}{9}\pi(200)^2\times 20$

$\frac{dV}{dt}_{in}=12000+\frac{1}{9}\pi (40000)\times 20$

$\frac{dV}{dt}_{in}=291111.1cm^3/min$

4 0

3 years ago

10 people are attending a chess tournament, and they are from Team A, Team B and Team C. Every person will complete each of the

Ber [7]

Answer:

Team A = 4 players

Team B = 5 players

Team C = 1 players

Step-by-step explanation:

Each player will compete in nine matches, for a maximum total of nine points possible. Since Team C has an average score of 9, Team C can only have one player because it would be impossible for more than on player to score a nine.

The possible total scores for team B are:

$B =3.6x\\x=1; B=3.6\\x=2; B=7.2\\x=3; B=10.8\\x=4; B=14.4\\x=5; B=18.0\\x=6; B=21.6\\x=7; B=25.2\\x=8; B=28.8\\x=9; B=32.4$

Since the scoring possibilities are 0, 0.5 and 1, total team score must be a multiple of 0.5. Therefore, the only possible number of players for team B is 5 (for a total score of 18.0).

If there are 10 players in total, 5 are from team B and 1 is from team C, the remaining 4 players are part of team A.

Team A = 4 players

Team B = 5 players

Team C = 1 players

3 0

3 years ago

I need help please !!

AnnyKZ [126]

Answer:

59

Step-by-step explanation:

it has the most dots

8 0

2 years ago

Miley drove 288 miles in 41/2 hours.what was miley average speed in miles phr

KiRa [710]

I am going to assume you meant 4 and one half hours. So you want to divide the distance by time. So 288 divided by 4.5 hours is 64. So Miley's average speed is 64 miles per hour.

4 0

3 years ago

At the end of each month for 20 years, you deposit $150 into a savings plan. You then make no further deposits, but leave the mo

adoni [48]

The balance resulting from 20 years' payments into the plan is the sum of a geometric series with first term $150 and common ratio 1+.055/12 (the monthly balance increase). That balance is
.. $550*((1 +.055/12)^240 -1)/(.055/12) ≈ $239,595.07

This balance is increased by the factor (1 +.055/12) each month for 120 months, so it is multiplied by (1 +.055/12)^120 over the 10 years.
.. $239,595.07*(1 +.055/12)^120 = $414,757.38

At the end of the 30-year period, the balance will be $414,757.38.

5 0

3 years ago