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Kitty [74]
2 years ago
8

The population in a small town is increasing annually by 1.8%. What is the quarterly rate of population increase

Mathematics
1 answer:
almond37 [142]2 years ago
4 0
0.4 because 1.8 divided by 4
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What is 363 rounded to the nearest ten
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Analyze the key features of the graph f(x) = 1/x+3 -2
tia_tia [17]
<h2>Explanation:</h2><h2></h2>

Here we have the following rational function:

f(x) = \frac{1}{x+3} -2

So the graph of this function is shown in the First Figure below. Let's define another function which is a parent function:

g(x)=\frac{1}{x}

Whose graph is shown in the second figure below. So we can get the graph of f from the graph of g this way:

Step 1. Shift the graph 3 units to the left:

f_{1}(x) = \frac{1}{x+3}

Step 2. Shift the graph 2 units down:

f(x) = \frac{1}{x+3}-2

Finally, the features of the graph of f are:

The graph of this function comes from the parent function g and the transformations are:

  • A shifting 3 units to the left
  • A shifting 2 units down

8 0
3 years ago
What us tge initial value of the linear function y= 5x - 6
Dovator [93]
X=1/5y+6/5
hope this helps!
3 0
3 years ago
Arnold is trying to make packing boxes out of 6 foot by 6 foot pieces of cardboard from the local grocer. Help Arnold decide how
lions [1.4K]
<span>Part I: Determining Dimensions

Arnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with the same size variable cut from each corner.

*You don't have to draw one, just explain what it would look like*


Answer:

Base of the box:

     it is a square
     side of the base = 6 foot - x - x. = 6 - 2x

Height of the box: x

Part II: Analyze

How does each variable expression relate to the length, width, and height of the box when folded?

Answer:

length = width = 6 - 2x
height = x


Part III: Extend your Findings
a. Based upon the variables you used in Part II, write a product for the volume.

Answer:

Volume = area of the base × height


Volume = (6 - 2x)² x

b. Expand the product to write a volume function.

Answer:

Volume = (36 - 24x + 4x²)x

Volume = 36x - 24x² + 4x³


c. What domain makes sense for the volume?

Answer:

Since x is a physical dimension x is greater than 0

Since the lenght of the cardboarc sheet is 6 and two squares are cut off, x has to be less than 3

So, the domain is (0, 3)


d. Guess and check values to find the size cut that produces a maximum volume.
*Six guesses are required*

Answer:

x              </span>Volume = 36x - 24x² + 4x³

0.1           36(0.1) - 24(0.1)² + 4(0.1)³ = 3.36
0.5           36(0.5) - 24(0.5)² + 4(0.5)³ = 12.5
1.0           36 - 24 + 4 = 16
1.5           36(1.5) - 24(1.5)² + 4(1.5)³ = 13.5
2.0           36(2) - 24(2)² + 4(2)³ = 8
1.7           36(1.7) - 24(1.7)² + 4 (1.7)³ = 11.49
1.2           36(1.2) - 24(1.2)² + 4(1.2)³ = 15.55

Then you can guess that the maximum volume is pretty close to 16 and it is whenx is close to 1.
2.9

7 0
3 years ago
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