Solve the following two problems using Calculus. Show all of your work on a separate sheet of paper, making clear how you arrived at all your solutions. Please be aware that you are using similar thinking for both of these problems, but you are solving for maximum area in Part A and minimum cost in Part B. Enjoy

A. If the materials for the fence cost $12 per foot, find the dimensions of the
corral for the largest possible area that can be enclosed with $2400 worth of fence.

B. If he only requires an area of 288 square feet for his vegetable garden, find the minimum cost of putting up this fence, if the cost per foot is $10. Indicate the dimensions of the garden that will minimize the cost.​

Answer:

1a:  [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]

1b: See below

1c:  [tex]2\frac{3}{4}[/tex] inches between the beetle and ant

Step-by-step explanation:

1a. To build the equation, we need to see that the beetle started at 3/4th inches below ground level, then "climbed" (which is poor English, it should be descended) a certain distance, and then it ended up at 2 1/2 inches below ground. The distance "climbed" can be represented as 1/3X, where "X" is the ant's current distance. We would do 1/3rd times "X" to figure out how much the beetle climbed down.

So that means, if we added together the starting position of 3/4, plus the distance the beetle descended (1/3X), that would get us TO 2 1/2 inches below ground (the beetle's new current position). So therefore our equation is:

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]

1b. Solve the equation written above from 1a.

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]

-3/4     -3/4   [subtract 3/4 to start the process of getting x by itself]

[tex]\frac{1}{3}x[/tex] = 1[tex]\frac{3}{4}[/tex]

*3/1   *3/1 [Multiply Reciprocal to get X by itself]

x= [tex]5\frac{1}{4}[/tex]

1c. So we take the position of the ant figured out on 1b (5 1/4 inches), and the new current position of the beetle (2 1/2 inches), and subtract them

5 1/4 - 2 1/2 =  [tex]2\frac{3}{4}[/tex]

These answers were found by using this info:

the beetle is 3/4 inch below the ground level. The beetle climbs 1/3 the distance. The beetle is now 2 1/2 inches below ground.

9514 1404 393

Answer:

  (a) 11·10^21

Step-by-step explanation:

"Scientific notation" has a mantissa that has one digit to the left of the decimal point. The number 11·10^21 has two digits to the left of the decimal point, so is not in the form required by scientific notation.

  11·10^21 is not in scientific notation

_____

It would be correctly written in scientific notation as as 1.1·10^22.

Answer:

A) 11 ⋅ 10^21

Answer:

Yes, Each value in the domain goes to only one value in the range.

Step-by-step explanation:

Since each x goes to a different y value, the relation is a function

Each value in the domain goes to only one value in the range.

Answer:

DOMAIN = {3, 4, 5, 6, 7}, RANGE = {2, 1, 9, 12}, the relation is a function.

Step-by-step explanation:

The domain of the relation is the set of points in A which have a tail connected to it.  That is {3, 4, 5, 6, 7}.

The range of the relation is the set of points in B which have a tip connected to it.  That is {2, 1, 9, 12}.

Since each element of the domain of the relation is associated with exactly one element of the range, the relation is a function.

Answer:

7.071067811865475

Step-by-step explanation:

Answer:

B= 40 degress

Step-by-step explanation:

1x+ 5xc /3xc = 40

Answer:

Sean paid 0.25 more cents than Cal.

Step-by-step explanation:

Cal's problem: 2.4 * 2.55 = 6.12

Sean's problem: 2.6 * 2.45 = 6.37

Answer:

I think 0.25

Step-by-step explanation:

Multipled 2.4 and 2.55 then multipled 2.6 and 2.45. I got 6.12 and 6.37 Then subtracted them and got 0.25

Answer:

here's your answer tho: ∞

Step-by-step explanation:

Answer:

1. 23.84

a. Let x = Each mile

5 + 1.57x

b. Let Y = graph position

y = 5 + 1.57x

c. 23.84

2. 27 Miles

Step-by-step explanation:

Step-by-step explanation:

The invention of the microscope allowed human to observe plant and animal cells, and as the technology advanced, scientists have been able to gain more knowledge about these different types of cells. This shows that advancements in technology has paralleled the understanding and knowledge we have about these cells.

The invention of the microscope allowed human to observe plant and animal cells, and as the technology advanced, scientists have been able to gain more knowledge about these different types of cells

In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century, that living organisms are made up of cells, that they are the basic structural/organizational unit of all organisms, and that all cells come from pre-existing cells.

Cells are the basic unit of structure in all organisms and also the basic unit of reproduction.

The invention of the microscope allowed human to observe plant and animal cells, and as the technology advanced, scientists have been able to gain more knowledge about these different types of cells.

This shows that advancements in technology has paralleled the understanding and knowledge we have about these cells.

To know more about cell theory follow

https://brainly.com/question/1594446

Answer:

x=3

Step-by-step explanation:

start with 7x=21

divide each side by 7 to get your answer:

x=3

Answer:

for the first one its the middle answer

Step-by-step explanation:

i speak almost fluent spanish but i am not amazing at math

Answer:

1/2 of an answer is zero

Step-by-step explanation:

Answer:

6/11

Step-by-step explanation:

I don't know that's what my mom said

Answer:

c=6

Step-by-step explanation:

c+7=13

-7        -7

c=13-7

c=6

Here is how you're line should look!

The reasonable amount to pay for 10 gallons of gasoline and 2 quarts of oil will be $27.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A service station on the interstate charges $2.29 per gallon for gasoline and $1.89 per quart for oil.

Now,

Since, A service station on the interstate charges $2.29 per gallon for gasoline and $1.89 per quart for oil.

Hence, We get;

The cost of 10 gallons of gasoline = 10 × $2.29

                                                    = $22.9

And, The cost of 2 quarts of oil = 2 × $1.89

                                                = $3.78

So, The total cost = $3.78 + $22.9

                           = $26.68

                           ≈ $27

Thus, The reasonable amount to pay for 10 gallons of gasoline and 2 quarts of oil will be $27.

Learn more about the multiplication visit:

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Answer:

1.12877

Step-by-step explanation:

You could also round it to the nearest tenth and just say 1.1 pounds

Answer:

1.12877 pounds

Step-by-step explanation:

For an approximate result, divide the mass value by 454.

1 gram = 0.00220462 pounds

Answer:

I believe in the question it only states 4% interest without any time factor so therefore it would be $10 interest for 1 month or 8 months

Is this a trick question?

Step-by-step explanation:

Answer:

guath math

Step-by-step explanation:

There is an app called guath math and it shows you all the steps and everything to a math problem just by scanning it. Also it is fast than asking people on brainly;

Answer:

x ≤ -9 and x ≤ 5

Step-by-step explanation:

2x² + 4x - 85 ≤ -4x +5

2x² + 8x - 85 ≤ 5

2x² + 8x - 90 ≤ 0

x² + 8x -180 ≤ 0

(x + 18)(x - 10) ≤ 0

(x + 9)(x - 5) ≤ 0

x + 9 ≤ 0

x ≤ -9

x - 5 ≤ 0

x ≤ 5

Nominal data, derived from the Latin word 'name,' is just that: a name. Republicans, Democrats, Independents, and so on. You have no idea who or why you're voting for, but you do have a party name, so that's something, right? To make this more quantitative, give each a random number of your choosing (usually small sequential numbers like 1, 2, or 3 but it could be anything). The kinds of statistical analysis you can do with nominal data are severely restricted since the value of the number has no relevance in your environment; it's simply a placeholder.

Ordinal data gives a numerical order to a prior category, such as 'Republican,' although that order does not have to signify anything. Let me explain: suppose you're questioned on a poll to rank your preferred candidate on a scale of 1 to 5. Obviously, a value of '5' is better than a value of '1,' but what does it mean? I'm glad you asked.

Interval data takes ordinal ideas and couples them with schemata that make sense. Using our prior 1-5 scale, for example, 1 degree Fahrenheit is cooler than 5 degrees. Interval data lacks a point of origin, which makes sense when discussing temperatures since 0 degrees Fahrenheit does not indicate a lack of temperature.

Ratio data combines the preceding three ideas and adds a point of origin, or '0' value. The greatest example I could think of was speed. We all realize that 5 mph is quicker than 1 mph, precisely since we all know that 0 mph implies we're not moving at all.

Answer:

0

Step-by-step explanation:

The initial value or y-intercept is the output value when the input of a linear function is zero.

Answer:

The center of the circle is at: C=(−2,3).

The radius of the circle is r=5.

Step-by-step explanation:

A circle with center at (h,k) and a radius of r has equation (x−h)2+(y−k)2=r2.

In this example our circle equation can be written as:

(x−(−2))2+(y−3)2=(5)2

So, we have: h=−2 , k=3 and r=5.

Answer:

Step-by-step explanation: