Find the next number is the sequence<br><br> 1, 2, 6, 21, 4, 0, ?

A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 min

Leya [2.2K]

Answer:

127.53 liters left after 10 minutes

Step-by-step explanation:

Let

$A \to Amount$

$t \to time$

Given

$A(0) = 200$ --- initial

$A(5) = 200 * (1 - 20\%) = 160$ --- the amount left, after 5 minutes

Required

$A(10)$ --- amount left after 5 minutes

To do this, we make use of:

$A(t) = A(0) * e^{kt}$

$A(5) = 160$ implies that:

$160 = 200 * e^{k*5}$

Divide both sides by 200

$0.80 = e^{k*5}$

Take natural logarithm of both sides

$\ln(0.80) = \ln(e^{k*5})$

$\ln(0.80) = \ln(e^{5k})$

$\ln(0.80) = 5k\ln(e)$

So, we have:

$-0.223 = 5k$

Divide by 5

$k = -0.045$

So, the function is:

$A(t) = A(0) * e^{kt}$

$A(t) = 200 * e^{-0.045t}$

The amount after 10 minutes is:

$A(10) = 200 * e^{-0.045*10}$

$A(10) = 200 * e^{-0.45}$

$A(10) = 127.53$

3 0

3 years ago

If a cylinder holds a volume of 100 cm3, and is 30 cm tall, which is the area of the bottom of the cylinder?

Vesna [10]

=πr2h

Area of circle
=πr2

=V/h
=100/30
≈3.33cm

4 0

3 years ago

I neeeeed help please

Sedbober [7]

6 = 2(1) + 2(w)

6 = 2 + 2w

Subtract 2 from both sides to isolate 2w.

4 = 2w

Divide 2 on both sides to isolate w.

2 = w

6 0

4 years ago

The smallest object visible with your eyes is similar to the width of a piece of hair, which is 1×10−4 meters wide. Using an opt

Sloan [31]

Answer:

B. $5\times10^{2}$

Step-by-step explanation:

We are told that the smallest object visible with our eyes is similar to the width of a piece of hair, which is $1\times 10^{-4}$ meters wide.

Using an optical microscope, we can see items up to $2\times 10^{-7}$ meters wide.

To find the objects we can see with our eyes are how much larger than the objects we can see with an optical microscope, we can set an equation as:

$\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=\frac{1*10^{-4}}{2*10^{-7}}$

Using the exponent rule of quotient $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=\frac{1}{2}*10^{-4-(-7)}$

$\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10^{-4+7}$

$\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10^{3}$

$\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10\times 10^{3-1}$

$\text{The object we can see with our eyes}=5\times10^{2}*\text{The objects we can see with microscope}$

Therefore, the objects we can see with our eyes are $5\times10^{2}$ times larger than the objects we can see with an optical microscope and option B is the correct choice.

3 0

3 years ago

A bat and ball both costs £1:10c, If the bat costs a dollar more how musch does the ball cost

kodGreya [7K]

5 Cent
because dollar more right?
so 10 cent left then divide half and half

8 0

3 years ago

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Find the next number is the sequence 1, 2, 6, 21, 4, 0, ?