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3 years ago

The top of a cylinder is sliced off by a plane. Determine volume of the bottom portion of the cylinder.

Mathematics

1 answer:

notka56 [123]3 years ago

8 0

Answer:

Volume of bottom of cylinder = Volume of entire cylinder - Volume of top of cylinder

Step-by-step explanation:

Here we have the volume of a cylinder given by

Volume of a cylinder = πr²h

Where the cylinder is cut by a plane into portions of heights, bottom a and top b we have

Height of bottom of is then

Height = h - b

Therefore, volume of bottom of cylinder = π·r²h = π·r²(h - b)

Volume of bottom of cylinder = π·r²·h - π·r²b

Volume of bottom of cylinder = Volume of entire cylinder - Volume of top of cylinder.

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A sample of bacteria is being eradicated by an experimental procedure. The population is following a pattern of exponential deca

77julia77 [94]

Answer:

There will be 50 bacteria remaining after 28 minutes.

Step-by-step explanation:

The exponential decay equation is

$N=N_0e^{-rt}$

N= Number of bacteria after t minutes.

$N_0$ = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

$N_0$ = 500

t=11 minutes

r=?

$N=N_0e^{-rt}$

$\therefore 200=500e^{-11r}$

$\Rightarrow e^{-11r}=\frac{200}{500}$

Taking ln both sides

$\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|$

$\Rightarrow {-11r}=ln|\frac{2}{5}|$

$\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}$

To find the time when there will be 50 bacteria remaining, we plug N=50, $N_0$ = 500 and $r}=\frac{ln|\frac{2}{5}|}{-11}$ in exponential decay equation.

$50=500e^{-\frac{ln|\frac25|}{-11}.t}$

$\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|$

$\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}$

$\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}$

$\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}$

$\Rightarrow t\approx 28$ minutes

There will be 50 bacteria remaining after 28 minutes.

3 0

3 years ago

5. BOATING Boat rentals are $50 plus $4 per hour. Write an

KonstantinChe [14]

Answer:

c = 50 + 4h

Step-by-step explanation:

The cost for the boat is 50, and the additional cost for an hour is 4. Then the sdditional cost for h hours is 4h.

So the total cost is 50 + 4h

∴ c = 50 + 4h

8 0

3 years ago

Express 0.31 as a fraction

Ivanshal [37]

31/100 is 0.31 as a fraction

6 0

3 years ago

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Evaluate 8y when y=4

earnstyle [38]

32 cause it’s 32 it be 32 boo

3 0

3 years ago

Carolina paid $15.80 for 4 hamburgers.

jarptica [38.1K]

Answer:

The cost of one hamburger is $3.95.

Step-by-step explanation:

15.80/4=3.95

6 0

3 years ago

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