An oval track is made by erecting semicircles on each end of a 46 m by 92 m rectangle. Find the length of the track and
the area enclosed by the track.
Answers
Answer:
[tex]Length\,\, of\,\, the\,\, track=420.44\,m\\\\Area\,\,covered \,\,by\,\, the\,\, track=5893.06\,m^2[/tex]
Step-by-step explanation:
Length of the Track:
Perimeter of the rectangle + Circumference of the two semicircle
Perimeter of the rectangle= [tex]2(Length+Width)[/tex]
[tex]Length=92\,m\\Width=46\,m[/tex]
Perimeter of the rectangle:
[tex]=2(92+46)\\\\=2(138)\\\\=276\,m[/tex]
Circumference of Two Semicircle with same radius:
[tex]r=\dfrac{46}{2} =23\,m[/tex]
[tex]Circumference=2\times \pi \times r\\\\[/tex]
[tex]=2\times 3.14\times 23\\\\=6.28 \times 23\\\\=144.44\,m[/tex]
Total Length of the track is :
[tex]=276+144.44\\\\=420.44\,m[/tex]
Area Covered by the track is :
Area of the two semicircle + Area of the rectangle
[tex]=(\pi \times r^2) + (Length\times Width)\\\\=(3.14\times (23\times 23 ))+(92\times 46)\\\\=1661.06 +4232\\\\=5893.06\,m^2[/tex]
The total length of the oval track is 420.51m and the area enclosed by the track is 5893.90m².
Explanation:The dimensions of the rectangular part of the track are 46m and 92m respectively. Thus, the total distance around the rectangle (perimeter) is 2*(46m + 92m) = 276m. The two semicircles on either end of the rectangle form a complete circle with a diameter of 46m. The circumference of this circle (which equates to the remaining path length of the race track) is given by the formula πd or π*46m ≈ 144.51m. Thus, the total length of the track is 276m + 144.51m = 420.51m.
As for the area enclosed by the track, it consists of two main parts: the area of the rectangle and the area of the circle. The area of the rectangle is given by the formula L*W, or 46m*92m = 4232m². The area of the circle is given by the formula π(r²), where r is the radius of the circle. So, π(23m²) equals approximately 1661.90m². Adding the two results together, the total area enclosed by the track is 4232m² + 1661.90m² = 5893.90m².
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Related Questions
What does it mean when we write √100 = 10 in terms of squares and side lengths? Explain. *
Answers
Step-by-step explanation:
[tex]\sqrt{100}=10[/tex] because [tex]10^{2}=100[/tex]. 10 is the square root of 100, which means that 10 multiplied by itself (10×10=[tex]10^2[/tex]) is equal to 100. So, when you are trying to find the square root of a number, the square root is itself multiplied by itself.
For example 16squared=4 because 4 x 4 = 16
Hope this helped :)
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Which function is represented by the graph?
Answers
Answer:
Step-by-step explanation:
b
Answer:b
Step-by-step explanation:
6x^2=726
[tex]6x^2 = 726[/tex]
Answers
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
Step 1: Divide both sides by 6
[tex]6x^2 / 6 = 726 / 6[/tex]
[tex]x^2 = 121[/tex]
Step 2: Square root both sides
[tex]\sqrt{x^2} = \sqrt{121}[/tex]
[tex]x = 11[/tex]
Answer: [tex]x=11[/tex]
Answer:
[tex]6 {x}^{2} = 726 \\ \frac{6 {x}^{2} }{6} = \frac{726}{6} \\ {x}^{2} = 121 \\ x = \sqrt{121} \\ x = 11[/tex]
Complete the following table with the properties used to solve 4(x + 3) =20
Statements Proof:
4(x + 3) = 20:
4x + 12 = 20:
4x = 8:
x =2:
Answers
Answer:
distributive property, subtraction, division
Step-by-step explanation:
i don't know the exact name of the last two but that's what i'm assuming they're called lol
The properties used to solve the equation 4(x + 3) = 20 are the distributive property, subtraction property of equality, and division property of equality. First, the distributive property is used to expand the left-hand side, then subtraction is used to isolate 4x. Finally, division is used to find x = 2.
Explanation:The question provides an algebraic equation and uses properties to solve for the variable 'x'. The steps taken demonstrate the following properties:
Distributive property: The equation starts as 4(x + 3) = 20. Through the distributive property (a*(b + c) = a*b + a*c), this is expanded to 4x + 12 = 20.Subtraction property of equality: Next, 12 is subtracted on both the sides giving 4x = 8. This property states that we can subtract the same value from both sides of the equation and it will still hold true.Division property of equality: Finally, the equation is divided by 4 on both sides, which results in x = 2. This property tells us that if we divide both sides of the equation by the same non-zero number, the equation will still be equal.Learn more about Algebraic Properties here:https://brainly.com/question/32858114
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What is the distance between the points (-3,-5) and (3, 3)?
A. 14
B. 2
C. 10
D. -2
Answers
Answer:
-2
Step-by-step explanation:
Answer: IT IS NOT -2 IT IS 10
Step-by-step explanation:
Simplify 9 to the 2nd over 9 to the 7th. (4 points)
Group of answer choices
95
1 over 9 to the 9th
1 over 9 to the negative 5th
1 over 9 to the 5th
Answers
Answer:
[tex]\frac{1}{9^{5} }[/tex]
Step-by-step explanation:
[tex]\frac{9^{2} }{9^{7} } \to 9^{2-7} \to 9^{-5} \to \frac{1}{9^{5} }[/tex]
Helper's Message:
Hi! I hope this helped you :)
I wouldn't mind a Brainliest or a five-star rating!
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Mitchell has decided to give his dog a longer leash to roam in the backyard. If the new 7 ft. leash is tied to the center pole in the yard, how much area in the yard does the dog have to move around?
Answers
Answer:
153.94
Step-by-step explanation:
William's typical running speed is 6 mi/h. The difference between his fastest speed and his typical speed is 1.5 min. The equatio
f-1.5 = 6 can be used to represent this problem, where fis William's fastest speed. What is William's fastest speed?
A) 4.5 mi/h
B) 5.5 mi/h
C)6.5mi/h
D) 7.5 mi/h
Answers
Answer:
D) 7.5 mi/h. hcbhcvu yc yv. y yv yh
Answer:
D
Step-by-step explanation:
7.5
Express as simply as possible with a rational denominator. 1/root13
Answers
Answer: root13/13
Step-by-step explanation:
Answer:
root13/13
Step-by-step explanation:
Factor: 6a²−378a²−384a.
Answers
Answer:
=-372a^2-384a
Step-by-step explanation:
6a^2-378a^2-384a
=-372a^2-384a
Write the ratios 20:40:60 in its simplest form?
Answers
Answer:
1:2:3
Step-by-step explanation:
The ratio 20:40:60 is simplified by dividing each number by the greatest common divisor (GCD), which is 20, giving us the simplest form of the ratio as 1:2:3.
Explanation:To write a ratio in simplest form, you have to find the greatest common divisor (GCD) of the numbers and then divide all numbers by the GCD. In the ratio 20:40:60, the GCD is 20. Therefore, when you divide each number of the ratio by the GCD you get 1:2:3. So, the ratio 20:40:60 in its simplest form is 1:2:3.
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How would you classify number 125?
A perfect square
B perfect cube
C both a perfect cube and a perfect square
D neither a perfect square nor a perfect cube
Answers
Answer:B (perfect cube)
Step-by-step explanation: 125 is the cube of 5
Write an equation for the line shown
Answers
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Answers
Answer:
~102 per square mile.
Step-by-step explanation:
9883640 divided by 96,716 is 102.19 so rounding down to 102.
How are the solutions to the inequality -2x ≥ 10 different from the solutions to -2x > 10?
Explain your reasoning.
Answers
Answer:
First lets find the solutions to each inequality.
-2x[tex]\geq \\[/tex]10 and -2x>10 (divide both sides by -2 to solve)
x[tex]\leq[/tex]-5 and x<-5
x[tex]\leq[/tex]-5 tell us that x could be -5 or less.
x<-5 tells us that x could be -6 or less.
The first one is less than or equal to which tells you that there is a possibility that the number is shows is could be an answer
Hope this helps ;)
Maten forgot some of her 12 facts. She wants to find 6x12 , but all she can remember is 5x12=60 . How could she use the fact 5x12=60 to find 6x12? Explain
Answers
Answer:
5 times 12 = 12 times 5
Step-by-step explanation:
You flipped the factors since they were the same. 5 times 12 = 60 when you flip the factors 12 times 5 = 60
a movie theater charges $10.50 per ticket and $5 per bucket le popcorn. you never buy the popcorn because you think it's too expensive
Answers
Answer:
any other info pls tell me
Step-by-step explanation:
Answer:the answer is yes
Step-by-step explanation:
I need help with this please. I don’t understand how to do this
Answers
Answer:
i can help!
Step-by-step explanation:
all you have to do is first add all the # after you should be left with 2 # multiply them together and there you have your answer!
Select the correct answer.
Cesar had a part-time job last year. He worked every week for the year and made $23 an hour. He worked 28 hours each week. Cesar saved
what was left of his earnings after paying all of his monthly expenses. At the end of the year, he had saved $3,360. What were Cesar's average
monthly expenses, rounded to the nearest dollar?
A
$1,288
B. $1,680
C. $2,403
D. $2,511
E. $2,791
Answers
Answer:
D. $2,511
Step-by-step explanation:
First off, we need to write down the facts we know.
There are about 52.177 weeks in a year
Cesar works 28 hours each week
Cesar makes $23 an hour
There are 12 months in a year
Cesar has $3,360 after his monthly expenses
To figure out how many hours are in a "work year," multiply the number of work hours in a week by the number of weeks in a year. In other words, multiply Cesar's 28 hour work week by about 52.177 weeks. That makes 1,456 hours in his work year. That means he makes $33,492 a year. If you multiply $2,511 by the months in a year (12), you get $30132. Finally, subtract his annual salary by $30132 to get $3,360, which is what was left of Cesar's earnings after paying all of his monthly expenses. This means that your answer is: D. $2,511.
Answer:
D. $2,511
Step-by-step explanation:
$23 x 28 x 52 = $33,488
$33,488 ÷ 12 = $2,790.66 = $2,791
12($2,791) - $3,360 = 30,132
$30,132 ÷ 12 = [$2,511]
Matti built a greenhouse in his backyard as shown below.
How much cubic space is in Matti's greenhouse?
A. 191.1 ft 3
B. 367.5 ft
C. 382.2 ft3
D. 735.0 ft
Answers
Answer:
B) 367.5 ft
Step-by-step explanation:
BECAUSE ITS NOT A
Answer:
the answer is b
Step-by-step explanation:
........................................................................................
Answers
Answer:
[tex]125.9 ft^2[/tex]
Step-by-step explanation:
Missing question:
An artist is making a rectangular canvas for a custom painting. the canvas has a width of 9 1/2 feet and a length of 13 1/4 feet . what is the area of canvas in square feet?
The area of a rectangle is given by the formula
[tex]A=L\cdot w[/tex] (1)
where
A is the area
L is the length
w is the width
In this problem, we have a rectangular canvas, so we want to find its area.
We know that:
[tex]w=9\frac{1}{2}ft[/tex] is the width, converting into an improper fraction,
[tex]w=\frac{9\cdot 2+1}{2}=\frac{19}{2}[/tex] ft
[tex]L=13\frac{1}{4}ft[/tex] is the length, converting into improper fraction,
[tex]L=\frac{13\cdot 4+1}{4}=\frac{53}{4}[/tex] ft
Substituting into eq (1), we can find the area of the canvas:
[tex]A=\frac{19}{2}\cdot \frac{53}{4}=\frac{1007}{8}=125.9 ft^2[/tex]
Consider the geometric sequence 4,20, 100, 500, 2500, 12500, 62500, 312500. Give the values of g1, r, n.
Answers
Which number should each side of the equation 2/3x=10 be multiplied by to produce the equivalent equation of x = 15?
−2/3
1/3
3/2
3
Answers
Answer:
3/2
Step-by-step explanation:
If you want to get the coefficient of x to be 1, you multiply by the reciprocal of the coefficient. The reciprocal is 3/2, so you multiple by 3/2
A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 26, 13, 19, 2, 12. The third column is labeled predicted with entries 22.2, 18.3, 14.4, 10.5, 6.6. The fourth column is labeled residual with entries 3.8, negative 5.3, 4.6, negative 8.5, 5.4.
For the given table, which point lies on the residual plot?
(1, 26)
(2, 18.3)
(3, 4.6)
(4, 19)
Answers
Answer:
Sample 1: 1.5
Sample 2: -2.5
Sample 3: 5.5
Step-by-step explanation: I just did it
Answer:
(3, 4.6)
Step-by-step explanation:
Took the test on edge.
A circle with area 36 π has a central angle of 11/6 π radians
Answers
Answer:
33pi or 103.62 square units
Step-by-step explanation:
central \: angle \: ( \theta) \\ = \frac{11}{6} {\pi}^{c} = \frac{11}{6} \times 180 \degree = 330 \degree \\ \\ area \: of \: sector \\ = \frac{ \theta}{360 \degree} \times area \: of \: circle \\ \\ = \frac{ 330 \degree}{360 \degree} \times 36 \: \pi \\ \\ = \frac{ 330 }{10 } \pi \\ \\ = \red{ \bold{33\pi}} \: {units}^{2} \\ = 33 \times 3.14 \\ = 103.62 \: {units}^{2} \\
At a raffle, 250 tickets are sold at $1 each for 3 prizes of $100, $50, and $10. You buy 1 ticket. What is the expected value of your gain? Should you play this game? 1. Explain HOW to determine the expected value. (one paragraph) 2. Interpret the meaning of the expected value for this scenario. (one paragraph)
Answers
Answer:
enervsorry it glitched, but the expected value would be 50
Step-by-step explanation:
How do you think inequalities are different from equations you have worked with before?
Answers
Answer:
The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses.
Hope this helps, and have a nice day
Step-by-step explanation:
Good luck! :)
Answer:yes they are different
Step-by-step explanation:
1. An equation is an equality of two mathematical expressions. That's why it has an equal(=) sign . For example:
12x=10x +2x
Or
3x+4y=5
2. While an inequation is an inequality of two expressions and here the greater than and lower than signs are used with equal sign i.e. >,< or=
For example
4y+5a > 5
Or
8a< 7b
help me plzzzzzzzzzz im begging youuuuu
Answers
Answer:
If the poster is enlarged by the scale factor 5/2 then,
length=12×5/2=30ft
And,
breadth=3×5/2=7ft
>>>>correct ans is 7.5 by 30
Answer:
7.5 feet by 30 feet
Step-by-step explanation:
i believe you would take 12 and divide it by 2 and then multiply it by 5=30. And then do the same for 3. 3 divided by 2 =1.5 and 1.5 multiplied by 5 =7.5
The answer would be 7.5 feet by 30 feet
(02.02)
The length of a rectangle is 24 units. Can the perimeter x of the rectangle be 60 units when its width y is 11 units? (1 point)
Select one
O a. No, the rectangle cannot have x = 60 and y = 11 because x = 48 + 2y
b. No, the rectangle cannot have x = 60 and y = 11 because x = 24 + 2y
c. Yes, the rectangle can have x = 60 and y = 11 because x + y is greater than 48
d. Yes, the rectangle can have x = 60 and y = 11 because x + y is greater than 24
Answers
Let
L--------> the length of the rectangle
y------> the width of the rectangle
x------> the perimeter of the rectangle
we know that
The perimeter of the rectangle is equal to
In this problem we have
For a width
Find the value of the perimeter
so
therefore
the answer is the option A
No, the rectangle cannot have x = 60 and y = 11 because x = 48 + 2y. .
What is the value of the expression when a = 4, b = 3 ,and c = 10?
3a4b−c
1
4
6
12
Answers
Step-by-step explanation:
hope it will help you....