A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 86m long and 64m wide. Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer. 64m 86m
Answers
To solve this problem, we have to find the area of the semi circles and the area of the rectangle and add them up together.
The area of the field is equal to 8719.36m^2
Area of the FieldLet us start by finding the area of the rectangle.
Data;
width = 86mlength = 64mArea of a rectangle is given as
[tex]a = length * width \\a = 86 * 64\\a = 5504m^2\\[/tex]
The area of the rectangle is 5504m^2
Area of the semicircle
The formula of a semi circle is given as
[tex]A = \frac{1}{2} \pi r^2[/tex]
But since we have two semi circles here, we can simply multiply it by two and the formula becomes
[tex]A = 2 * \frac{1}{2} \pi r^2\\A = \pi r^2[/tex]
But in the question, we have the diameter of the semi circle as the length of the rectangle.
[tex]radius = \frac{diameter}{2} \\radius = \frac{64}{2} \\radius = 32m[/tex]
The radius of the semicircle is 32m
Area of the semicircle is
[tex]A = \pi r^2\\A = 3.14 * 32^2\\A = 3215.36m^2[/tex]
The area of the field is
[tex]area of field = 3215.36 + 5504\\area = 8719.36m^2[/tex]
The area of the field is equal to 8719.36m^2
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Related Questions
A sequence of transformations that maps ^RST to ^R'S'T' is a _______ followed by a _____.
Answers
Answer: Reflection followed by a translation
Step-by-step explanation:
First, RST is reflected along the x-axis.
Then, RST is translated one unit down into R'S'T' giving us what we're looking for.
need the answer asap
Answers
Answer:
The price for ounce is: $0.25 and she bought 16 ounces of straberris
Step-by-step explanation:
If you have 16 ounces and its 4 dollars you do 4/16 to get 0.25
Divide the number 1080 into two parts with a ratio of 4: 1.
Answers
Answer: It breaks up into 864+216
Reason:
x = some positive real number
The ratio 4:1 scales up to 4x:1x, so we have two parts one is 4x and the other is 1x. Those two parts add up to 1080
4x+1x = 1080
5x = 1080
x = 1080/5
x = 216
We can then find 4x = 4*216 = 864
As a check: 864+216 = 1080, so the answer is confirmed.
x + y = 24
5y = x
The solution to the given system of equations is (x,y). What is the value of y?
Answers
Answer:
The value of y is 4.
Step-by-step explanation:
Note the system of equation:
x + y = 24
5y = x
First, plug in 5y for x in the first equation:
x + y = 24
(5y) + y = 24
Simplify. Combine like terms. Like terms are terms that have the same amount of the same variable:
(5y + y) = 24
(6y) = 24
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Divide 6 from both sides of the equation:
(6y)/6 = (24)/6
y = 24/6 = 4
Now, plug in 4 for y in one of the given equations in the system of equation:
x + y = 24
x + (4) = 24
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 4 from both sides of the answer:
x + 4 = 24
x + 4 (-4) = 24 (-4)
x = 24 - 4
x = 20
x = 20 , y = 4
~
Check. Use the other equation. Plug in 4 for y, and 20 for x:
5y = x
5(4) = (20)
5 * 4 = 20
20 = 20 (True)
~
The value of y is 4.
can you please help me solve the problem
Answers
Answer:
a
Step-by-step explanation:
helppppppppppppppppppppp
Answers
Answer:
10 duh
Step-by-step explanation:
equation for parallel and perpendicular
Answers
Answer:
Parellel: y=-2x+17
Perpendicular: y=2x-3
Step-by-step explanation:
Hope this helps! ;-)
Please help with does 3 questions am trying to get my grade up
Answers
If a fair die is rolled 5 times, what is the probability, rounded to the nearest
thousandth,
of getting at most 2 threes?
Answers
Answer:
0.965 to the nearest thousand.
Step-by-step explanation:
This is a binomial probability distribution.
Prob(getting no 3's) = (5/6)^5 = 0.4019
Prob(getting 1 * 3 ) = 5C1(1/6)(5/6)^4 = 0.4019
Prob (getting 2 3's ) = 5C2(1/6)^2(5/6)^3 = 0.1608
So required probability = 2 * 0.4019 + 0.1608
= 0.9646
When the sun's angle of elevation is 76°, a tree casts an 18-foot shadow on the ground. Find the length of the tree to the nearest tenth of a foot.
Answers
Answer:
56.5 ft
Step-by-step explanation:
See the attached figure which represents the explanation of the problem.
We need to find the length of the tree to which is the length of AD
From the graph ∠BAC = 90° and ∠ABD = 76°, AB = 18 ft
At ΔABD:
∠BAD = ∠BAC - ∠DAC = 90° - 4° = 86°
∠ADB = 180° - ( ∠BAD + ∠ABD) = 180 - (86+76) = 180 - 162 = 18°
Apply the sine rule at ΔABD
∴[tex]\frac{AB}{SinD} =\frac{AD}{sinB}[/tex]
∴ 18/sin 18 = AD/sin 76
∴ AD = 18 * (sin 76)/(sin 18) ≈ 56.5 (to the nearest tenth of a foot)
So, The length of the tree = 56.5 ft.
The answer is 56.5 ft
Find the volume of the rectangular prism pictured below if LM = 25 in, LO = 28 in, and
PR = 9 in, and OR = 3 in.
P
R
M
62 in
6300 in?
248 in
3
o 2354 in
3
Answers
Answer:
B. 6300
Step-by-step explanation:
Karissa liked to measure the snowpack at her house. On Tuesday, the snowpack was 6 inches deep. On Wednesday, 2 inches had melted. How
much snowpack was left?
Answers
The perimeter of a rectangular field is 48m, if the length is twice the width . Find the area of the field.
Answers
Answer:
Step-by-step explanation:
→Perimeter (P) = 2×(L+W) Perimeter = 48m
But Length = 2 × Width
∴ P = 2×( 2W + W)
= 2×(3W)
48 = 6W
Divide both sides by 6
[tex]\frac{48}{6}[/tex] = [tex]\frac{6}{6}[/tex] W
∴Width (W) = 8m
→This means Length = 2W
= 2×8m
L = 16m
→Area of a rectangle = L × W
= 8m × 16m
∴ Area of the rectangular field= [tex]128m^{2}[/tex]
Please graph y=log3(x+2) and then find the asymptote domain and range
Answers
Answer:
Step-by-step explanation:
y = a * log_b (x - h) + k
(h,k) = (x,y)
h = shift right/left
k = shift up/down
Original Points of y = log_3
y = log_3 (x + 2)
h = -2 thus shift left.
Asymptote: x = -2
Domain: [-2 , +inf)
Range: (-inf , +inf)
2(1 + 4)2 x (9-6)
3
Answer please
Answers
2(1+4)2 x (9-6)3
4(5) x 3(3)
20 x 9
180
3/4 : 6/x = 3/8 : 4/5 : 6/7
Answers
The value of x will be equal to 3 for the given expression.
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts.
Given expression is solved as:-
[tex]\dfrac{\dfrac{3}{4} }{\dfrac{6}{x}} = \dfrac{3}{8}[/tex]
[tex]\dfrac{3}{4}\times \dfrac{x}{6}=\dfrac{3}{8}[/tex]
[tex]\dfrac{x}{8}=\dfrac{3}{8}[/tex]
x = 3
The value of x will be equal to 3 for the given expression.
Therefore the value of x will be equal to 3 for the given expression.
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PLS HELPPPPPP!!!!!!
The functions graphed shows the distances, in miles, for two drivers x hours after driving.
Select ALL correct statements about the graph.
Question 5 options:
The intersection (1, 60) indicates the time in hours when Celia and Tayvin are traveling at the same speed.
Celia drove at a faster rate than Tayvin.
Tayvin drove at a faster rate than Celia.
The intersection (1, 60) indicates the time in hours when Celia and Tayvin are the same distance from the city.
Answers
Answer:
selection 1 ,2
Step-by-step explanation:
Celia. 60km/hr
Tayvin. 50km/hr
Which one geos first to last 3/4 or 1/3 or 5/8
Answers
pls, help! and explain
Answers
Answer:
I can't seem to work out the other two, sorry
Step-by-step explanation:
1. -> c. because there are 10 letters in total and there are 4 vowels, so it would be 4/10, then we'd simplify by 2, and I gives us 2/5
4. -> g. because there are 10 letters so it's 10/10 which gives us 1
Answer:
CEFG
Step-by-step explanation:
1. P = 4/10 = 2/5
2. P= (4/10)(4/10)=16/100=4/25
3. P= (4/10)(3/9) = 12/90 = 2/15
4. P = 12/12 = 1
Hope this helps
Solve for x in the first equation, then solve the system using substitution. Write your answer as (x, y).
2x-6y=14
4x - y = 9
Answers
Answer:
( 18.4, 4.6 )
Step-by-step explanation:
2x - 6y = 14
Add 6y to both sides
2x = 6y + 14
divide both sides by 2
x = (3y + 7)
Substitute this ^ for x in the othe equation
4 (3y + y) - y = 9
distribute the 4
12y + 4y - y = 9
combine like terms
15y = 9
divide both sides by 15
y = 4.6
Now substitute this value for y in the equation we previously substituted .to find the value of x
x = 3 (4.6) + 4.6
x = 13.8 + 4.6
x = 18.4
Hope this makes sense and was helpful!
Please solve (20 points)
Answers
Answer:
104.65 m
Step-by-step explanation:
The plane with the smaller angle of depression is closer to the raft.
Taking the tan values of both planes :
Plane 1 (57°)
tan 57° = 3000 + x / h1.54 = 3000 + x / hh = 3000 + x / 1.54 (Equation 1)Plane 2 (48°)
tan 48° = x / h1.11 = x/hh = x/1.11 (Equation 2)Equate Equations 1 and 2 :
3000 + x / 1.54 = x/1.111.11 (3000 + x) = 1.54x3330 + 1.11x = 1.54x0.43x = 3330x = 77.44 mTaking the sin ratio to find distance :
sin 48° = 77.44/distance0.74 = 77.44/distancedistance = 77.44/0.74distance = 104.65 m1. Kayla and Heidi each buy a tiger. Kayla pays for her tiger using a $10 bill and two $1 bills. Heidi pays for her tiger using a $20 bill and a quarter. How much change does each girl receive? a tiger costs 11.23$
Answers
Answer:
Kayla gets $0.77 back, Heidi gets $9.02 back
Step-by-step explanation:
12 - 11.23 = 0.77 (how I got 12 is the $10 dollar bill and TWO $1 dollar bills)
20.25 - 11.23 = 9.02 (how I got 20.25 is the $20 dollar bill and the quarter which is worth $0.25)
PLEASE HELP quick
………
Answers
Answer:
50
Step-by-step explanation:
1/2 x base x height
In this problem: (It's times 2 because I split it up into 2 triangles.)
1/2 x 10 x 5 x 2 =
50
hope this helps
have a good day
What’s a good estimate for 2,745 x 6.9? Show how you got you estimate.
Answers
Answer:
21000
Step-by-step explanation:
2745 -> 3000
6.9 -> 7
3000 x 7 =
21000
Find the center of the circle whose equation is (x - 5) 2 + (y + 3) 2 = 6.
Answers
Answer:
(5, -3)
Step-by-step explanation:
Solve for x and solve for y by making each set of brackets equal to 0
16. Farhan bought a bag and a wallet at a discount from a store. He was
given a discount of 30% for the bag. For the wallet, a discount was also
given. He saved a total of $66.60.
He paid a total of $121.40 for the 2 items and paid $46.60 more for the
bag than the wallet.
a) What was the price of the bag without discount?
b) What was the percentage discount given for the wallet?
Answers
A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.
PercentagesGiven that Farhan bought a bag and a wallet at a discount from a store, and he was given a discount of 30% for the bag, and for the wallet, a discount was also given, and he saved a total of $66.60, and he paid a total of $121.40 for the 2 items and paid $46.60 more for the bag than the wallet, to determine A) what was the price of the bag without discount, and B) what was the percentage discount given for the wallet, the following calculations must be performed:
(121.4 - 46.6) / 2 = Wallet37.4 = Wallet1-0.3 = 0.70.7 = 841 = X84 / 0.7 = X120 = X66.6 - (120 - 84) = X66.6 - 36 = X30.6 = X68 = 10037.4 = X37.4 x 100 / 68 = X55 = XTherefore, A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.
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Answer:A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.
Step-by-step explanation:
The universal set is the set that contains no elements.
True
False
Answers
Answer:
False,
Step-by-step explanation:
The set that contains no elements is the null set Ф.
Answer: True
Step-by-step explanation: Where all inclusive set comprises of a set of all elements, the purge set contains no elements of the subsets.
Please help me! I would appreciate it a lot!
Answers
Answer:
d
Step-by-step explanation:
The number of pupils in Pooti Junior School increased by x% form 800 pupils to 960. Find the value of x
Answers
5/3 ÷ 1/9
list answer below
Answers
Answer:
5
Step-by-step explanation:
just calculated and got it
Answer:
15
Step-by-step explanation:
First, change it to multiplication and flip the second fraction
5/3×9/1
Then you multiply 5×9 and 3×1. This gets you 45/3
45/3 can be simplified down to 15 so the answer is 15