AB=diameter of the circle O. OC=radius. Arc AXB is an arc of the circle with centre C. Prove areas of the shaded region are =
Answers
Draw a circle with center C And radius CA, as shown in the attached picture.
Let the lengths of radii AO, OB, OC be R. Triangle ABC is inscribed in the circle with center O and one of its sides is a diameter, this means that the angle ACB is a right angle.
|AO|=|OC|=R, by the Pythagorean theorem |AC|=[tex] \sqrt{2}R [/tex].
these are all shown in the picture.
2.
Area of triangle ABC is 1/2 * 2R * R= R^2
3.
Let the area between arc BXA and chord AB be Y. (the yellow region).
and let G be the shaded region between arcs AB and AXB.
G=1/2(Area circle with center O)-Y
=[tex] \frac{1}{2} \pi R^{2}-Y [/tex]
To find Y:
Notice that the area of the sector ACB is 1/4 of the area of circle with center C, since m(ACB) is 1/4 of 360 degrees.
So Area of sector ACB = [tex]\frac{1}{4} \pi (\sqrt{2} R)^{2}=\frac{1}{4} \pi*2 R^{2} =\frac{1}{2} \pi R^{2}[/tex]
Y =area of sector ABC-Area(triangle ABC)=[tex]\frac{1}{2} \pi R^{2}- \frac{1}{2}*2R*R=\frac{1}{2} \pi R^{2}- R^{2} [/tex]
4.
Finally,
[tex]G=\frac{1}{2} \pi R^{2}-Y=\frac{1}{2} \pi R^{2}-(\frac{1}{2} \pi R^{2}- R^{2})=R^{2}[/tex]
This proves that the 2 shaded regions have equal area.
Related Questions
Consider the equation 5/3v +4 +1/3v =8 What is the result of the equation after the first step in the solution
Answers
first step would be to simplify...
2v + 4 = 8 <==
Make a frequency distribution and find the relative frequencies for the following number set. Round the relative frequency to the nearest tenth of a percent. Some of the answers will be used more than once and some may not be used.
10 30 40 50 60 70
10 30 40 60 60 80
20 30 50 60 70 90
20 30 50 60 70 90
Number Frequency Relative Frequency
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
Answers
10 2 2/24 = 8.3%
20 2 2/24 = 8.3%
30 4 4/24 = 16.7%
40 2 2/24 = 8.3%
50 3 3/24 = 12.5%
60 5 5/24 = 20.8%
70 3 3/24 = 12.5%
80 1 1/24 = 4.2%
90 2 2/24 = 8.3%
total : 24
Say you want to buy x shirts which cost 2$ each and add tax which is $0.75. You have 13$ to make your purchase.
Answers
2x + 0.75 = 13
Add like terms
2x= 13-0.75
2x= 12.25
x= 12.25/2
x=6.125
You can buy 6 whole shirts with $0.25 left over
Hope this helps! A thanks/brainliest answer would be appreciated :)
Use the graph below to answer the question.
What is the slope of a line that is perpendicular to the line in the graph?
Answers
slope = 3/-3 = -1
slope of a line that is perpendicular to the line in the graph = 1
answer
1
Answer:
Im working on it right now and its 1
Step-by-step explanation:
Can someone help me figure this out: Factor 12y^2-27? I keep getting the steps confused.
Answers
3(4y^2-9)
The binomial inside is a perfect square so keep factoring.
3(2y+3)(2y-3)
The pair of binomials cannot be further factored so stop there.
two adjacent sides of a rhombus are represented by 5x + 7 and 6x -1. find the value of x
Answers
The value of x in equation 5x + 7 = 6x -1 is 8.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
5x + 7 and 6x -1
Now,
The equation is:
5x + 7 = 6x - 1
To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 5x from both sides and adding 1 to both sides. This gives us:
5x + 7 - 5x = 6x - 1 - 5x
7 + 1 = x - 1 + 1
8 = x
Therefore, by the given equations the answer will be x = 8.
Learn more about linear equations;
https://brainly.com/question/10413253
#SPJ2
If (x,y) are the coordinates of a point p in the xy-plane, then x is called the _______ of p and y is the _______ of p.
Answers
and the second coordinate of a point P is called the y-coordinate of P.
So
"x is called the ___x-coordinate____ of p and y is the ___y-coordinate____ of p."
Answer:
x-coordinate
y-coordinate
In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
Explanation:In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.
Together, the x and y coordinates specify the precise location of a point in the xy-plane.
Four times the complement increased by forty-six is the same as twice the supplement. find the measures of the angle, the complement, and the supplement
Answers
supplement: 180 - x
Four times the complement increased by forty-six = 4(90-x) + 46
twice the supplement: 2(180 - x)
so
Four times the complement increased by forty-six is the same as twice the supplement
4(90-x) + 46 = 2(180 - x)
360 - 4x + 46 = 360 - 2x
2x = 46
x = 23
answer
measure of angle x = 23
measure of complement = 90 - 23 = 67
measure of supplement = 180 - 23 = 157
Can some PLEASE help me with 8 and 9!!????
Answers
What is the rule for the sequence with the first four terms below? 0.5, 0.25, 0, –0.25
Answers
The rule for the given sequence (0.5, 0.25, 0, -0.25) is to subtract 0.25 from the previous term. Each consecutive term decreases by 0.25 to form the sequence.
The sequence given is 0.5, 0.25, 0, -0.25. To find the rule of this sequence, look at the differences between terms. Each term is subtracted by 0.25 to get to the next term.
Step-by-Step Explanation:
Start with the first term which is 0.5.Subtracting 0.25 from the first term gives the second term, 0.25.Continuing this pattern, subtracting 0.25 from the second term gives the third term, which is 0.Finally, subtracting 0.25 from the third term gives the fourth term, which is -0.25.Therefore, the rule for this sequence is subtracting 0.25 from the previous term to obtain the next term in the sequence.
A bat flies at an average speed of 32 kilometres an hour. At this speed, how far will it fly in 15 minutes?
Answers
Final answer:
To find out the distance a bat will fly in 15 minutes at an average speed of 32 kilometers per hour, you multiply the speed by the time in hours (15 minutes is 0.25 hours). The bat will fly 8 kilometers.
Explanation:
To calculate how far a bat flies in 15 minutes at an average speed of 32 kilometers per hour, we need to convert the time into hours since the speed is given in kilometers per hour (km/h). 15 minutes is equal to 0.25 hours (since there are 60 minutes in 1 hour, so 15 minutes divided by 60 minutes per hour equals 0.25 hours).
We can then use the formula for distance which is:
Distance = Speed × Time
The average speed of the bat is 32 km/h, and the time is 0.25 hours.
Distance = 32 km/h × 0.25 h = 8 km
So, the bat will fly 8 kilometers in 15 minutes.
what is the distance between the points (3,7) and (15,16) on a coordinate plane?
Answers
distance = Sqrt((x2-x1)^2 +(y2-y1)^2)
15-3 =12
16-7=9
12^2 = 144
9^2 = 81
144+81 = 225
square root of 225 = 15
the distance is 15
[tex]\sqrt{(15 - 3)^2 + (16 - 7)^2} \\ \\ \sqrt{12^2 + 9^2} \\ \\ \sqrt{144 + 81} \\ \\ \sqrt{225} \\ \\ 15[/tex]
So, 15 units is the answer.
In the diagram which angles are alternate interior angles with angle 14?
Answers
How do you subtract two negative numbers?
Answers
when you have 2 negative numbers you actually add the 2nd number to the first one
example:
-4 - -2 = becomes -4 + 2 = -2
At the beginning of the month a store had a balance of −$554. During the month the store lost another $600. What is the current balance?
Answers
So the stores current balance is $-1,154.
Please mark brainliest and have an amazing day.
A student must choose to participate in two different events during field day. There are four track events, two academic events, and six team sports events. What is the approximate probability that the student will choose to participate in two team sports?
0.114
0.227
0.273
0.545
Answers
Answer:
.227
Step-by-step explanation:
Answer:
0.227
Step-by-step explanation:
An urn holds 5 white and 3 black marbles. if 2 marbles are to be drawn at random without replacement and x denotes the number of white marbles, find the probability distribution for x
Answers
i = [tex]p(0) = \frac {3} {8} x \frac {2} {7} = \frac {3} {28} ; p (1) = \frac {3} {8} x \frac {5} {7} + \frac {5} {8} x \frac {3} {7} = \frac {15} {28}; p (2) = \frac {5} {8} x \frac {4} {7} = \frac {5} {14} [/tex]
(a) i. The probability mass function of X is 5 / 14
Hypergeometric Distribution is the probability distribution of a hypergeometric random variable.
The hypergeometric distribution is used to calculate the statistical importance of having drawn a specific k successes (out of n total draws) from the aforementioned population in the hypergeometric test uses.
ii. Please see attached image for the answer.
To find the probability distribution for x, consider the possible values of x and calculate the probability of each value. When 2 marbles are drawn without replacement, there are two possible outcomes. The probability distribution for x is P(x = 0) = 3/28, P(x = 1) = 15/56, and P(x = 2) = 5/14.
Explanation:To find the probability distribution for x, we need to consider the possible values of x and calculate the probability of each value.
Since there are 5 white marbles and 3 black marbles in the urn, the total number of marbles is 8.
When 2 marbles are drawn without replacement, there are two possible outcomes: (1) both marbles are white and (2) one marble is white and one marble is black.
Let's calculate the probabilities:
P(x = 0) = P(both marbles are black) = (3/8) * (2/7) = 6/56 = 3/28
P(x = 1) = P(one marble is white and one marble is black) = (5/8) * (3/7) = 15/56
P(x = 2) = P(both marbles are white) = (5/8) * (4/7) = 20/56 = 5/14
Therefore, the probability distribution for x is:
P(x = 0) = 3/28
P(x = 1) = 15/56
P(x = 2) = 5/14
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2 , and a vertical shift up 3 units.
Answers
y = A sin(Bx + C) + D
where
A = amplitude
B = frequency
C = shift on starting angle
D = shift of wave on the y-axis
From the given problem, A = 1 and D = 3. There is no value for C because there is no mention of any shift in angle. About the frequency, you can obtain this by getting the reciprocal of the period. Thus, B = 2/π. The complete equation is
y = sin(2x/π) + 3
Answer:
y = sin(4x) + 3
Step-by-step explanation:
y = Asin(Bx + C) + D
A is amplitude = 1
B = 2pi/period = 2pi / (pi/2) = 4
C does not mention.
D: shift up or down = 3
=> y = sin(4x) + 3
round 0.9144 to the nearest tenth of a yard
Answers
hope this helps:)
PLEASE HELP IM RUNNING OUT OF TIME!!!!!
Which of the following radical expressions has an absolute value symbol in its simplified form?
I hope i wrote these right
MY CHOICES ARE:
a. 16x^4−−−−√4
b. 81x−−−√4
c. −125x^3−−−−−−√3
d. 64x^3−−−−√3
Answers
(16x^4)^(1/4) = 2*abs(x)
A parachutist's speed during a free fall reaches
207
kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 5 seconds of free fall?
Answers
207km/h = 57.5m/s
2) Use the rate from question 1.
Make an equation and cross multiply to solve for x.
57.5/1 = x/5
x = 57.5(5)
x = 287.5
So he fell 287 meters in just 5 seconds
A panel containing four on-off switches in a row is to be set. assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.
Answers
_ _ _ _, where you can put one of two marks (off or on) on any _.
So, the number of different ways will be 2 * 2 * 2 * 2 = 16
Answer: 16 possible settings.
In the formula that gives the circumference of a circle, which quantity is multiplied by 2Ï€ ?
A. Diameter
B. Radius
C. Area
D. Circumference
Answers
The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:
C = 2 π r
We can see that in the formula, what is multiplied by 2 π is the radius (r).
Therefore the answer to this is
B. Radius
A rope 10 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.
Answers
(10-x)/(2π)=r
A=π(100-20x+x^2)/(4π^2)
A=(x^2-20x+100)/(4π)
...
x/4=s, x=4s using this in the area of a circle we get:
A=(16s^2-80s+100)/(4π)
A=(4s^2-20s+25)/π
And of course the area of a square is s^2
A=(4s^2+πs^2-20s+25)/π
The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.
Let's denote:
- [tex]\( x \)[/tex] as the length of one side of the square (in feet).
- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.
1. Area of the Square [tex](\( A_s \))[/tex]:
The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].
2. Area of the Circle [tex](\( A_c \))[/tex]:
The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:
[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]
Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]
The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].
Substituting the value of [tex]\( r \)[/tex], we get:
[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]
[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]
3/8 of people at a fun fair were children 3/4 of the remaining people were men there were 140 more children than women how many people went to the fun fair
Answers
The remaining fraction was 1-3/8=5/8
the fraction of men was 3/4*5/8=15/32
the fraction of women=1/4*5/8=5/32
given that the there were 140 more children than women, the fraction represented by this is:
3/8-5/32
=7/32
thus the total number of people who were there was:
1/(7/32)*140
=640
The answer is 640
Color of car. a. Qualitative/Ordinal b. Qualitative/Nominal c. Quantitative/Discrete d. Quantitative/Continuous
Answers
$1,100 at 8%, for 15 years, compounded annually. Total Amount = $ Interest Amount = $
Answers
A=p (1+r)^t
A future value?
P present value 1100
R interest rate 0.08
T time 15 years
A=1,100×(1+0.08)^(15)
A=3,489.39
To find the interest amount the formula is
I=A-p
I=3,489.39−1,100
I=2,389.39
Final answer:
Compound interest plays a crucial role in determining the final amount of an investment over time, showcasing the power of compounding. In this scenario, with an initial amount of $1,000, an interest rate of 10.1%, and 47 years of compounding annually, the total interest earned would be $91,045.80.
Explanation:
Compound interest is calculated on the principal amount plus the interest earned over time. In this case, with an initial amount of $1,000, an interest rate of 10.1% compounded annually, and an end amount of $92,045.80 after 47 years, compound interest plays a significant role in determining the final amount.
To calculate the total interest earned over the 47 years, you subtract the initial principal amount of $1,000 from the end amount of $92,045.80. This gives you the total interest earned. In this scenario, the total interest earned would be $92,045.80 - $1,000 = $91,045.80.
Compound interest is crucial in understanding how investments grow over time, and it showcases the power of compounding when money is invested wisely and for a long period.
What is the length of the hypotenuse of a right triangle if each of the two legs is 4 units? square root of 8 units 4 units square root of 32 units 8 unit?
Answers
Answer:
Well if you still need the answer around 4 years later LOL its √32
Step-by-step explanation:
Answer:
√32
Step-by-step explanation:
Because this is totally helpful 4 years later
Solve each system:
80x+60y=85
100x-40y=20
Answers
x= 1/2 (fraction)
At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
Answers
x + y = 2400/5 = 480 - flying with the wind
adding the 2 equations
2x = 880
x = 440
Speed of the plane with no wind = 440 mph
Answer: The speed of the plane with no wind is 440 miles per hour.
Step-by-step explanation:
Let the maximum speed of the plane be 'x'.
Let the maximum speed of the wind be 'y'.
Since we have given that an airplane travels 2400 miles against the wind in 6 hours.
As we know that
Downstream is given by
[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]
Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.
As we know tha t
Upstream is given by
[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]
We just need to find the speed of the plane with no wind.
Using the elimination method,
[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]
Hence, the speed of the plane with no wind is 440 miles per hour.