MATHEMATICS HIGH SCHOOL

: Sergio wants to fence in a circular portion of his backyard for a play space for his dog. Determine the area of the largest portion of the yard he can enclose with 72 feet of fencing. Use 3.14 for π.

Answers

Answer 1

Answer:

For this case we have to:

If Sergio has 72 feet of fence then we have that the circumference of the fence (whose space is circular) is 72.

By definition, the circumference of a circle is given by:

$C = \pi * d$

Where:

d: It is the diameter of the circumference

So:

$72 = \pi * d\nd = \frac {72} {\pi}\nd = \frac {72} {3.14}\nd = 22.93 \ ft$

Then, the radius will be given by: r = 11.45 \ ft

Thus, the area of the circular portion will be:

$A = \pi * r ^ 2\nA = 3.14 * (11.45) ^ 2\nA = 3.14 * 131.1025\nA = 411.66 \ ft ^ 2$

Thus, the area of the playing space is: $A = 411.66 \ ft ^ 2$

Answer:

$A = 411.66 \ ft ^ 2$

Related Questions

Solve each equation (steps as to how appreciated)
Which of the following is a point-slope equation for a line with the point(-2, 4) and a slope of 3?O A. y-2-3(x-4)B. y-4-3(x-2)O C. y +2 = 3(x-4)O D. y - 4 - 3(x+2)
I am confused on number 15, the instructions are at the top.
On one of the day you went to the gym, the ratio of men to women was 3 : 2. If 120 men used the gym, how many women were there?
The table below shows the total cost of buying printer ink cartridges for both members and nonmembers of a shopping club.Price of Ink at Shopping ClubNumber of ink cartridges purchasedTotal cost formembers(with membership fee)Total cost for nonmembers0$3001$40$252$50$503$60$75Which statement is supported by the table?The relationship between the number of cartridges purchased and the total cost is proportional for nonmembers but not for members.The relationship between the number of cartridges purchased and the total cost is proportional for members but not for nonmembers.The relationship between the number of cartridges purchased and the total cost is proportional for neither members nor nonmembers.The relationship between the number of cartridges purchased and the total cost is proportional for both members and nonmembers.

The bar graph in the following graphic represents fictional net exports in billions of dollars for five countries. Net exports are obtained by subtracting total imports from total exports; a negative net export means the country imported more goods than it exported.What is the sum of net exports for Germany and China ?
a.
-80 billion dollars
c.
90 billion dollars
b.
180 billion dollars
d.
150 billion dollars

Answers

Answer:

d.) 150 billion dollars

Step-by-step explanation:

As per the given bar graph, we can draw the following conclusions:

Net exports for United States = ~ -110 Billion Dollars (It means import of 110 Billion Dollars)

Net exports for Denmark = ~ -30 Billion Dollars (It means import of 30 Billion Dollars)

Net exports for China = ~ 115 Billion Dollars

Net exports for Germany = ~ 35 Billion Dollars

We have to find the sum of net exports of Germany and China:

$\Rightarrow$ 35 + 115 = 150 Billion Dollars.

Hence, correct answer is d. 150 Billion Dollars.

Answer: d

Step-by-step explanation:

150 billion dollars

The measure of W is 134°, the measure of Y is 46°, and the measure of Z is 134°.What is the measure of X?
a 40°
b 46°
c 134°
d 90°

Answers

The angles in any quadrilateral must add up to 360 degrees.
A trapezoid is a quadrilateral, because it has four sides.

$W+X+Y+Z=360 \n \n (134)+X+(46)+(134)=360 \n \n 314+X=360 \n \n X=46$

Angle X is (b) 46 degrees.

B. 46 because the measure of all of the angles in a quadrilateral is 360. If you add 134+46+134 it equals 314, and 360-314 is 46.

Write a whole number and a fraction greater than 1 to name the part filled.Think : 1 container = 12 boxes with 4 shaded circles in each

Answers

I'll answer the second question it is 2x4 which = 8 boxes

How do you rename each additive inverse without parentheses
-(2x+7)

Answers

-2x+7 or -2x-7or anything else idk

In a certain country, a letter up to 1 ounce requires postage in the amount of $0.42, and each additional ounce (or fraction of an ounce) has an additional cost. The function below represents the cost of mailing one letter in this country.f(c)=0.42 + 0.20[x-1]

Josiah has two letters. The first weighs 2.9 ounces, and the second weighs 4.1 ounces. What is the total amount Josiah can expect to pay for postage?
$1.62
$1.64
$1.84

Answers

Answer:

$1.84

Step-by-step explanation:

We are given that a letter up to 1 ounce requires postage in the amount of $0.42, and each additional ounce (or fraction of an ounce) has an additional cost.

The function which represents the situation:

$f(c)=0.42 + 0.20[x-1]$

Now Joseph has two letters .

The weight of first letter = 2.9 ounces

Cost of first letter = $0.42 + 0.20[2.9-1]$

= $0.8$

Now , second letter weighs 4.1 ounces

So, cost of second letter = $0.42 + 0.20[4.1-1]$

= $1.04$

Thus the total amount Josiah can expect to pay for postage = $0.8+$1.04

=$1.84

Hence the total amount Josiah can expect to pay for postage is $1.84

Answer:

$1.84

Step-by-step explanation:

Wade's grandmother gave him $100 for his birthday. Wade wants to save his money to buy a new MP3 player that cost $275. Each month, he adds $25 to his MP3 savings. Write an equation in slope-intercept form for x, the number of months that it will take Wade to save $275

Answers

Answer:

The answer is:

275 = 25X + 100

Step-by-step explanation:

1.The equation for the slope- intercept is:

y = mx + b

2. Recognize and value variables

x = number of months

y = the expected range to arrive

m = is the amount Wade earns per month

b = the amount of money saved.

3. Solve the equation for X which is the unknown.

275 - 100 = 25X

175 / 25 = X

X = 7

4. . Show the result

275 = 25(7) + 100

275 = 275

5. Wade will take 7 months to buy your MP3 if he saves 25 for each month.

7 months because after the 100 dollars u add u 25 7 times to get 275

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Sharon’s turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?

Convert to fractional notation 1 4/7

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If You have a full cylindrical glass of water that stands 8 inches tall and has a radius of 1.5 inches. If you pour the water into a larger cylindrical glass that stands 12 inches tall and has a radius of 2.5 inches, how much more water would the larger glass be able to hold? Round it to the nearest hundredth.