Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.
Answers
The area bounded by a chord and arc it intercepts is known as a segment of a circle segment of a circle
The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units
The reason the above value is correct is as follows:
The given parameters in the question are;
The radius of the circle, r = 11
The length of the chord PL = 16
The measure of angle ∠PAL = 93°
Required:
The area of part of the circle enclosed by chord PL and arc PL
Solution:
The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL
The area of a segment of a circle is given by the following formula;
Area of segment = Area of the sector - Area of the triangle
Area of segment = Area of minor sector APL - Area of triangle APL
Area of minor sector APL:
Area of a sector = (θ/360)×π·r²
Where;
r = The radius of the circle
θ = The angle of the sector of the circle
Plugging in the the values of r and θ, we get;
Area of the minor sector APL = (93°/360°) × π × 11² ≈ 98.2 square units
Area of Triangle APL:
Area of a triangle = (1/2) × Base length × Height
Therefore;
The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units
Required shaded area enclosed by line PL and arc PL:
Therefore, the area of shaded segment enclosed by line PL and arc PL is found as follows;
Area of the required segment PL ≈ (98.2 - 60.58) square units = 37.62 square units
The area of the circle enclosed by line PL and arc PL ≈ 37.62 square units
Learn more about the finding the area of a segment can be found here:
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The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
The calculation of the area between line segment PL and circle arc PL is described below:
1) Calculation of the area of the circle arc.
2) Calculation of the area of the triangle.
3) Subtracting the area found in 2) from the area found in 1).
Step 1:
The area of a circle arc is determined by the following formula:
[tex]A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}[/tex] (1)
Where:
[tex]A_{ca}[/tex] - Area of the circle arc.
[tex]\alpha[/tex] - Arc angle, in sexagesimal degrees.
[tex]r[/tex] - Radius.
If we know that [tex]\alpha = 93^{\circ}[/tex] and [tex]r = 11[/tex], then the area of the circle arc is:
[tex]A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}[/tex]
[tex]A_{ca} \approx 98.201[/tex]
Step 2:
The area of the triangle is determined by Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}[/tex] (2)
[tex]s = \frac{l + 2\cdot r}{2}[/tex]
Where:
[tex]A_{t}[/tex] - Area of the triangle.
[tex]r[/tex] - Radius.
[tex]l[/tex] - Length of the line segment PL.
If we know that [tex]l = 16[/tex] and [tex]r = 11[/tex], then the area of the triangle is:
[tex]s = \frac{16+2\cdot (11)}{2}[/tex]
[tex]s = 19[/tex]
[tex]A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}[/tex]
[tex]A_{t} \approx 60.399[/tex]
Step 3:
And the area between the line segment PL and the circle arc PL is:
[tex]A_{s} = A_{ca}-A_{t}[/tex]
[tex]A_{s} = 98.201 - 60.399[/tex]
[tex]A_{s} = 37.802[/tex]
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
Related Questions
Please tell me answer not by directly step by step please don't write answer only please please please
Answers
y + z + r + x = 360
2x + 3x + 4x + x = 360
10x = 360
x = 360/10
x = 36
Now
x = 36
y = 72
z = 108
r = 144
Answered by Gauthmath must click thanks and mark brainliest
Using the order of operations, what is the last calculation that should be done to evaluate 4(8 - 6952 - 6+(-3)
4(8 - 6352 – 6 + (-3)
4(2)52 - 6+(-3)
4(2)(25) - 6+(-3)
200 - 6+(-3)
200 - (-2)
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Answer:
200 + 2
Step-by-step explanation:
you know that two (2) negatives multiplying each other is = +
=200 +2
=202
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Answer:
17000
Step-by-step explanation:
17^1 * 10^3
17 * 10*10*10
17*1000
17000
the answer is 17,000
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here is an image for an explanation
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find the area and perimeter please
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Answer:
the area is 740 cm and the perimeter is 148
6. If gallon A has 8L of water and gallon B has 800 ml of water, calculate the total volume of water in both the gallons.
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Answer:
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What is the value of g(-4)?
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Answer:
A
Step-by-step explanation:
(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)
[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]
Find the missing side lengths leave your answer as a racials simplest form
Answers
Answer:
y=3 and x=3*sqrt(3)
Step-by-step explanation:
sin(30)=y/6
1/2=y/6, y=3. As it's a right angled triangle, 6^2-3^2=x^2, x=3*sqrt(3)
Answer:
x = 3 sqrt(3)
y = 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 30 = y /6
6 sin 30 = y
6 (1/2) = y
3 = y
cos theta = adj / hyp
cos 30 = x /6
6 cos 30 =x
6 ( sqrt(3)/2) =x
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In the figure above, AABC is an equilateral
triangle and each circle is tangent to the other
two circles. If each circle has diameter 10, what
is the distance h?
(A) 103
(B) 1513
(C) 15+513
(D) 10+1013
(E) 10+5/5
Answers
Answer:
B
Step-by-step explanation:
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Answer:
[tex] \cos(z) = \frac{30}{34} [/tex]
What is the key difference between simple interest and compound interest, and how does this difference affect the effectiveness of each? PLSSS HELP I HAVE ONE DAY LEFT
Answers
Answer:
The key difference between simple interest and compound interest is that in simple interest, the interest is calculated based on the principal amount of the loan.
The formula is principal multiplied by time by rate divided by 100.
Compound interest on the other hand, has to do with the principal amount and accumulated interest on previous periods.
The difference affects the effectiveness of each because in SI, interest is calculated once, while in CI, there's accumulated interest.
help i need help with math help if u can
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6x2 + 6y + 12
What is the expected value of the two investments? Type the correct answer in each box. Round your answers to the nearest whole dollar value. The expected value of the Computer Co. stock is $ 5,040 0], and the expected value of the US Treasury bond is $ 5,085
THE AWNSER IS IN THE QUESTION
Answers
Answer: $5,040 & $5,085
Step-by-step explanation:
The expected value of the Computer Co. stock is $5,040, and the expected value of the US Treasury bond is $5,085
The expected value of both the stocks Computer Co. and US Treasury bond is $5,062.5.
What is the weighted average?When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.
To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.
The expected value is the weighted average also known as the mean.
Given, The expected value of the Computer Co. stock is $ 5,040, and the expected value of the US Treasury bond is $ 5,085.
Therefore the expected value of both stocks is,
= (5040 + 5085)/2.
= $5,062.5
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The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1,2851,1871,2221,1941,2681,3161,2751,3171,275
Required:
a. Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviations.
b. Find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site. (Round your answers to the nearest whole number.)
Answers
Answer:
a) The sample mean is 1260 and the standard deviation is 48.
b) The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
Step-by-step explanation:
Question a:
Mean is the sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{1285 + 1187 + 1222 + 1194 + 1268 + 1316 + 1275 + 1317 + 1275}{9} = 1260[/tex]
Standard deviation is the square root of the sum of the differences squared between each value and the mean, divided by the one less than the sample size. So
[tex]s = \sqrt{\frac{(1285-1260)^2 + (1187-1260)^2 + (1222-1260)^2 + (1194-1260)^2 + (1268-1260)^2 + ...}{8}} = 48[/tex]
The sample mean is 1260 and the standard deviation is 48.
Question b:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8595\frac{48}{\sqrt{9}} = 30[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1260 - 30 = 1230
The upper end of the interval is the sample mean added to M. So it is 1260 + 30 = 1290
The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
Viết các số 1,2,..,100 theo một thứ tự nào đó, được dãy a1, a2,..,a100. CMR: Tổng S= |a1 - 1| + |a2 -2| + .. +|a100 -100|. Hãy tổng quát hóa bài toán
Answers
Question 2 of 10
Which pair of functions are inverses of each other?
O A. f(x) = i +15 and g(x) = 12x - 15
O B. f(x) = - 10 and g(x) = 2410
O C. f(x) = y3x and g(x) = (3) 3
O D. f(x) = 11x- 4 and g(x) = 4
SUBMIT
Answers
Answer:
option c f(x)=-10and g(x)=2410
help me with this questions please!
Answers
9514 1404 393
Answer:
r = 18
Step-by-step explanation:
Let d represent the number of districts. The given information lets us write two equations:
3d = 27 . . . . . the number of state senators
d +r = 27 . . . . the number of representatives
The first equation tells us ...
d = 27/3 = 9
The the second equation tells us ...
r = 27 -d = 27 -9 = 18
The number of at-large representatives is r = 18.
Which equation represents an exponential function that passes through the point (2, 36)?
O f(x) = 4(3)
O fx) = 4(x)
O f(x) = 6(3)
O f(x) = 6(x)
Answers
Answer: It would be the first equation because:
Step-by-step explanation:
In order to be an exponential function, the X
variable has to be in the exponent, that eliminates
the second and fourth answers
f(X) = 4(3)X
using the point (2,36)
f(2) = 4 (3)2
= 4 (9 )
= 36
The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Let the point on the graph be P ( 2 , 36 )
So , when x = 2 , the value of y = 36
f ( x ) = 4 ( 3 )ˣ be equation (1)
when x = 2
f ( 2 ) = 4 ( 3 )²
f ( 2 ) = 4 x 9
f ( 2 ) = 36
Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ
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Please send only answer
Want to bring a metal rod to assemble a toy frame. All long metal rods must be used at least. How much to assemble the frame as shown in the picture
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Answer:
how many times should u use the metal rod ??
a parking lot charges $2 per hour for the first 4 hours
Answers
Answer:
8
Step-by-step explanation:
Complete the equation
[tex] \sqrt{20} = \: \: \sqrt{5} [/tex]
Answers
Step-by-step explanation:
I'm not sure about it
Try it find examples
Step-by-step explanation:
so at the end 2=1
not sure but hopefully you get the idea :)
can anybody help with this ?
Answers
Answer:(
fx).(gx)=D. -40x^3+25x^2+45
Step-by-step explanation:
What will the height of the firework be 3 seconds after the launch? How many seconds after the launch will it take for the firework to fall to the same height again?
Answers
Answer:
524m
Step-by-step explanation:
In a standardized normal distribution the mean is ____ while the standard deviation is ____.
A. 0; 1
B. 1; 0
C. 0; 0
D. 1; 1
Answers
Answer:
A. 0; 1
Step-by-step explanation:
Required
Mean and standard deviation of a standardized normal distribution
A standardized normal distribution is represented as:
[tex](\mu,\sigma) = (0,1)[/tex]
This implies that:
[tex]\mu = 0[/tex] -- mean
[tex]\sigma = 1[/tex] --- standard deviation
Hence, (a) is true
An automobile owner has 40% chance of having exactly one accident in a year and 60% chance of having no accidents in a year. There is no chance that the automobile owner incurs more than one accident in a year.
If there is an accident, the loss amount has the following distribution:
Loss Amount Probability
30 0.30
60 0.15
100 0.45
180 0.10
Suppose there is an ordinary deductible of $40 and the maximum payment by the insurer is $130.
Determine the standard deviation of the payment made by the insurer to the automobile owner.
A: 32.44
B: 33.60
C: 34.77
D: 26.78
E: 27.43
Answers
Answer:
A. 32.44
Step-by-step explanation:
Automobile owner has 40% chance for one accident in a year and 60% of zero accident in a year.
Let x is the loss of accident and y is the payment by insurer.
Y = 0 if X < 40,
x - 40 if 40 < x < 130
130 if x [tex]\geq[/tex] 170
Then, Var [y] = E y^2
Var [y] = 1052.16
E = 32.437.
What is the value of p?
A. 125°
B. 45°
C. 35°
D. 550
Answers
Answer:
C- 35 °
Step-by-step explanation:
Interior angle adjacent to 90° angle = 90° (supplementary angles of a line segment).
Interior angle adjacent to 125° angle = 55° (supplementary angles of a line segment).
Sum of two interior angles of the triangle = 55+90 = 145°
∠p = 180° - 145° = 35°
PLEASE ANSWER
The distance from the vertex of the curve to the focus is equal to _____.
Here’s the options
the distance from the vertex to the directrix
the distance from the vertex to the y-axis
the distance from the vertex to the origin
a constant
Answers
Answer:
The distance from the vertex to the directrix.
Step-by-step explanation:
According to this question, we are speaking about a parabola, which has the characteristic that the distance from the vertex to the focus is equal to the least distance from the vertex to the directrix.
Hence, the right answer is: The distance from the vertex to the directrix.
Find the lengths of the other two sides of the isosceles right triangle
Answers
Answer:
[tex]x=5[/tex]
[tex]h=\sqrt{(5)^{2}+x^{2} } =\sqrt{(5)^{2}+(5)^{2} }[/tex]
[tex]h=\sqrt{25+25} =\sqrt{50}[/tex]
[tex]h=5\sqrt{2}[/tex]
OAmalOHopeO
Round 5,821 to the nearest thousands place:
Answers
Answer:
6000 hope this helps
if the question is 5,422 then the round figure is 5000
but the question is 5,821 its above 5500 will be 6000
Multiply (2x-5)(x+3)
Answers
Answer:
2x^2+x-15
Step-by-step explanation:
foil
Answer:
2x^2 + x - 15
Step-by-step explanation:
using FOIL
(2x - 5)(x + 3)
[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]
[2x^2 + 6x - 5x - 15]
2x^2 + x - 15
The surface areas of two similar solids are 16m2 and 100 m2. The volume of the larger one is 750m3. What is the volume of the smaller one?
Answers
Answer:
48 m^3
Step-by-step explanation:
If the scale factor of linear dimensions between two solids is k, then the scale factor for areas is k^2, and the scale factor of volumes is k^3.
Let's call the solid with 16 m^2 of area solid A, and the other one solid B.
The scale factor of areas from, A to B is (100 m^2)/(16 m^2) = 25/4
In other words, multiply the area of the solid A by 25/4 to get the area of solid B.
Let's check: 16 m^2 * 25/4 = 16 * 25/4 m^2 = 4 * 25 m^2 = 100 m^2
We do get 100 m^2 for solid B, so the area scale factor of 25/4 is correct.
The area scale factor is k^2, so we have:
k^2 = 25/4
We solve for k:
k = 5/2
Now we cube both sides to get k^3, the scale factor of volumes.
k^3 = 5^3/2^3
k^3 = 125/8
Let V = volume of smaller solid, solid A.
V * 125/8 = 750 m^3
V = 750 * 8/125 m^3
V = 48 m^3
