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Zolol [24]
2 years ago
5

2. Bacterial Culture Problem: When you grow a

Mathematics
1 answer:
nignag [31]2 years ago
6 0

The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases

<h3>Find the area at times t = 0, t = 5, and t = 10.</h3>

The function is given as:

A(t) = 9 * (1.1)^t

Substitute t = 0, t = 5, and t = 10.

A(0) = 9 * (1.1)^0 = 9

A(5) = 9 * (1.1)^5 = 14.5

A(10) = 9 * (1.1)^10 = 23.3

The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases

<h3>Use the results of part a to find the radius of the culture at these three times</h3>

The area of a circle is

A = πr^2

Make r the subject

r = √(A/π)

So, we have:

r = √(9/π) =  1.7

r = √(14.5/π) =  2.1

r = √(23.3/π) =  2.7

The radius is changing at an increasing rate

<h3>Write an equation for the composite function R(A(t)).</h3>

In (b), we have:

r = √(A/π)

Express as a function

r(A(t)) = √(A/π)

Hence, the equation for the composite function is R(A(t)) = √(A/π)

<h3>The restriction for the function R * A</h3>

We have:

r(A(t)) = √(A/π)

A(t) = 9 * (1.1)^t

This gives

r(A(t)) = √(9 * (1.1)^t/π)

The radius is 30.

So, we have:

√(9 * (1.1)^t/π) = 30

Square both sides

(9 * (1.1)^t/π)= 900

Divide by 9

(1.1)^t/π= 100

Multiply by π

(1.1)^t= 314

Take the logarithms of both sides

t * log(1.1) = log(314)

Solve for t

t = 60

Hence, the restriction on the domain is 0 <= t <= 60

Read more about composite functions at:

brainly.com/question/13502804

#SPJ1

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Reika [66]

Answer:

\frac{p}{3}  = 5

p = 15

\frac{15}{3}  = 5

4 0
2 years ago
Find the scale factor where the pre-image is the small triangle and the image is the large triangle.
allsm [11]

Scale factor is the ratio of two corresponding sides.

Here we have two triangles, where the preimage is the smaller triangle and the image is the larger triangle.

So scale factor =14/18 = 7/9

And to find the missing variable, we need to set the ratio.

7/9 = 28/x

Cross multiplying both sides

7x = 28*9

x = 36

8 0
3 years ago
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What adds to 1 but multiples to -72
andre [41]

Using a system of equations, the numbers that add to 1 and multiply to -72 are given as follows:

9 and -8.

<h3>What is a system of equations?</h3>

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable.

In the context of this problem, the two numbers are the variables. They are unknown, hence they are going to be defined as follows:

x and y.

They add to 1, hence:

x + y = 1.

They multiply to -72, hence:

xy = -72.

From the first equation, we have the following relation:

y = 1 - x.

Replacing in the second, we have that:

x(1 - x) = -72.

x - x² = -72.

x² - x - 72 = 0.

The quadratic function can be factored as follows:

(x - 9)(x + 8) = 0.

Hence the amounts are given as follows:

  • x - 9 = 0 -> x = 9.
  • x + 8 = 0 -> x = -8.

Which are the two numbers representing the solution to the system of equations.

More can be learned about a system of equations at brainly.com/question/24342899

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7 0
1 year ago
the elephants water tank holds 2,560 gallons of water. After two weeks, the zookeeper measures and finds that the tank has 1,944
nadezda [96]
The answer is 58 whole days
6 0
3 years ago
4x-6+3(2-x)=2x-(x-4)<br> How many solutions are there to this equation?
Svetach [21]

Answer:

No solution (0 solutions)

Step-by-step explanation:

Simplify it as shown below:

4x-6+3(2-x)=2x-(x-4)

4x-6+6-3x=2x-x+4. (on the left side the negative 6 and the positive 6 cancel out, and then combine like terms on both sides)

x=x+4

No solution

3 0
3 years ago
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