In the figure above, point O is the center of the circle,
line segment BC is tangent to the circle at point B,
point A lies on the circle, and point O lies on line
segment AC. If the circumference of the circle is 50,
what is the length of minor arc AB ?
Answers
Answer:
16.67 or 16 2/3
Step-by-step explanation:
so, as BC is a tangent, it means the angle OBC is 90 degrees.
therefore, the angle BOC is 180 - 90 - 30 = 60 degrees.
that means the angle AOB is 180 - 60 = 120 degrees.
the triangle ABO must be an isosceles triangle, as the sides are both the radius of the circle. so, both remaining angles are the same : half of 180 - 120 = 60 = 30 degrees.
and so, we know that ABC is an isosceles triangle, because both "side angles" are equal = 30 degrees.
so, AB = BC.
and we know the circumference of the circle (50) and can calculate the radius
50 = 2×pi×r
25 = pi×r
r = 25/pi ≈ 7.96
now we have multiple ways to calculate AB.
AB = BC = tan(60) × r
or
AB = sqrt(r² + r² - 2×r×r×cos(120))
or ...
the first one might be easiest.
AB = tan(60) × 7.96 ≈ 13.78
oh, I just recognized, we need the arc AB (not the straight line).
even easier.
50 is the full "arc" of the circle for all 360 degrees.
but we only need the part of the angle AOB = 120 degrees.
so, this is then only the 120/360 part of the full circle circumference.
ABarc = 50 × 120/360 = 50 / 3 ≈ 16.67 or 16 2/3
Related Questions
look at the image below
Answers
Answer:
37.3m**3
Step-by-step explanation:
1/3*7*4*4 = 37.3m**3
Answer:
Pyramid Volume = (area of base * height) / 3
Pyramid Volume = (4 * 4 * 7) / 3
Pyramid Volume = 112 / 3
Pyramid Volume = 37.33333 cubic meters
http://www.1728.org/volpyrmd.htm
Step-by-step explanation:
Aakash, Bao Ying, Chris and Donna all live on the same street as their school, which
runs from east to west.
• Aakash lives 5 blocks to the west.
• Bao Ying lives 4 blocks to the east.
• Chris lives 2: blocks to the west. .
• Donna lives 61 blocks to the east.
a. Draw a picture that represents the positions of their houses along the street.
b. Find how far is each house from every other house?
c. Represent the relative position of the houses on a number line, with the school at
zero, points to the west represented by negative numbers, and points to the east
represented by positive numbers.
d. How can you see the answers to part (b) on the number line? Using the numbers
(some of which are positive and some negative) that label the positions of houses on
the number line, represent these distances using sums or differences.
ko
Answers
The distance between each of the students' houses are:
Aakash & Bao Ying live 9 blocks away from each other
Aakash & Chris live 3 blocks away from each other
Aakash & Donna live 66 blocks away from each other
Bao Ying & Chris live 6 blocks away from each other
Bao Ying & Donna live 57 blocks away from each other
Chris & Donna live 63 blocks away from each other
To solve this question, we represent each with the first letter of their names.
So, we have:
[tex]A= 5\ west[/tex] --- Aakash
[tex]B= 4\ east[/tex] ---- Bao Ying
[tex]C = 2\ west[/tex] --- Chris
[tex]D = 61\ east[/tex] ---- Donna
I've added the picture and the number line that represent the scenario as an attachment.
To calculate how far each lives from each other's, we start by representing west as negative and east as positive.
So, the representations become:
[tex]A = -5[/tex]
[tex]B = 4[/tex]
[tex]C = -2[/tex]
[tex]D = 61[/tex]
The absolute difference of each represents how far they live from one another.
Aakash & Bao Ying Aakash & Chris Aakash & Donna
[tex]AB = |-5 -4| =9[/tex] [tex]AC = |-5 --2| =3[/tex] [tex]AD = |-5 -61| =66[/tex]
Bao Ying & Chris Bao Ying & Donna
[tex]BC = |4 --2| =6[/tex] [tex]BD = |4 -61| =57[/tex]
Chris & Donna
[tex]CD = |-2 -61| =63[/tex]
This means that
Aakash & Bao Ying live 9 blocks away from each other
Aakash & Chris live 3 blocks away from each other
Aakash & Donna live 66 blocks away from each other
Bao Ying & Chris live 6 blocks away from each other
Bao Ying & Donna live 57 blocks away from each other
Chris & Donna live 63 blocks away from each other
To carry out the above computations from the number line, we simply count the numbers from one to the other.
For instance:
There are 3 numbers from Akash to Chris.
This means that: Aakash & Chris live 3 blocks away from each other
Learn more about number line at:
https://brainly.com/question/13189025
Please help!
The quantities x and y are proportional.
x: 4 5 10
y: 10 12.5 25
Find the constant of proportionality (r) in the equation y=rx.
Answers
9514 1404 393
Answer:
r = 2.5
Step-by-step explanation:
The constant of proportionality can be found by solving the equation for r:
r = y/x
Then any corresponding values of x and y can be used to find r:
r = 25/10 = 2.5
The constant of proportionality is 2.5.
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answers
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
-3(y-5)+6y-2 simplify using distributive property and then combine like terms ANOTHER ONE PLEASE
Answers
Answer:
3y+13
Step-by-step explanation:
-3(y-5)+6y-2
Distribute
-3y +15 +6y-2
Combine like terms
-3y+6y +15-2
3y +13
[tex]\bf \large{\purple{ \implies}} \tt \: - 3(y - 5) \: + \: 6y \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 15 \: + \: 6y \: - 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 6y \: + \: 15 \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: 3y \: + \: 13[/tex]
To make a stemplot of these rainfall amounts, round the data to the nearest 10, so that stems are hundreds of millimeters and leaves are tens of millimeters. Make two stemplots, with and without splitting the stems. Which plot do you prefer
Answers
The two stem plots (with and without splitting the leaves) are plotted below using the data given in the attached picture :
The stem and leaf plots are given below:
Rounding the data to the nearest 10;
The values obtained are :
630, 670, 740, 650, 710, 740, 720, 700, 650, 600, 780, 780, 790, 810, 830, 860, 860, 900, 810, 790, 790, 960, 870
Ordering the data allows for easier generation of the plot.
Ordered data : 600, 630, 650, 650, 670, 700, 710, 720, 740, 740, 780, 780, 790, 790, 790, 810, 810, 830, 860, 860, 870, 900, 960
The stem plot without splitting :
STEM __ LEAF
6 ___ 00, 30, 50, 50, 70
7 ___ 00, 10, 20, 40, 40, 80, 80, 90, 90, 90
8 ___ 10, 10, 30, 60, 60, 70
9 ___ 00, 60
KEY : 6 | 00 = 600
The stem plot WITH splitting :
STEM __ LEAF
6 ___ 00, 30
6 ___ 50, 50, 70
7 ___ 00, 10, 20, 40, 40
7 ___ 80, 80, 90, 90, 90
8 ___ 10, 10, 30
8 ___ 60, 60, 70
9 ___ 00
9 ___ 60
KEY : 6 | 00 = 600
The stem plot with splitting gives a cleaner and more arranged output of the data as the values aren't congested on a single line.
Learn more on stem and leaf plot : https://brainly.com/question/12857419?
look at the image for the answer below?
Answers
Answer:
Does the answer help you?
base:10 height:2.5 what is the slope of the ramp
Answers
Answer:
Slope is B. ¼
Step-by-step explanation:
Slope: is hypotenuse
[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]
which means slope = 1/4
Write The Greatest 8digit Number using three different digits
Answers
Answer:
99999987
Step-by-step explanation:
Solve four and two fifths plus two and two thirds
Answers
The answer is 7 1/15
if a bicycle is 2.5 feet in diameter and races for 345 feet how many time does the wheel turn
Answers
A rotation or turn always moves clockwise and never counterclockwise.
True
False
Answers
Answer:
False
Step-by-step explanation:
It can go in any direction
Answer:
False
Step-by-step explanation:
Rotations can be either clockwise or counterclockwise
Follow the instructions on the image
Answers
Answer:
k=3
Step-by-step explanation:
Assuming the centre of dilation is 0,0, we can use the formula (kx,ky) to determine it.
Here,
The co-ordinates of pre-image=(0,1),(-1,-1) & (1,-1)
The co-ordinates of image=(0,3),(-3,-3) & (3,-3)
Now,
(kx,ky)=(0,3)
(k*0,k*1)=(0,3)
Equating,
k=3
You can use the other coordinates to further solidify your answer.
What is the measure of MBT?
Answers
[tex]\\ \sf\longmapsto 17x-6=5x+18[/tex]
[tex]\\ \sf\longmapsto 17x-5x=18+6[/tex]
[tex]\\ \sf\longmapsto 12x=24[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{24}{12}[/tex]
[tex]\\ \sf\longmapsto x=2[/tex]
Now
[tex]\\ \sf\longmapsto \angle{MBT}[/tex]
[tex]\\ \sf\longmapsto 5x+18[/tex]
[tex]\\ \sf\longmapsto 5(2)+18[/tex]
[tex]\\ \sf\longmapsto 10+18[/tex]
[tex]\\ \sf\longmapsto 28[/tex]
Answer:
m∠MBT = 28°
Step-by-step explanation:
BN is an angle bisector. This makes ∠NBM and ∠MBT equal.
[tex]17x-6=5x+18\\12x-6=18\\12x=24\\x=2[/tex]
Finally, substitute the value for the variable.
[tex]5(2)+18\\10+18\\28[/tex]
Therefore, m∠MBT = 28°.
trigonometric identities
Answers
Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.
4 sin²(θ) - 1 = 0
==> sin²(θ) = 1/4
==> sin(θ) = ±1/√2
==> θ = π/4, 3π/4, 5π/4, 7π/4
I ONLY need 8c
Please show ALL STEPS
Answers
Answer:
8c
f(g(x)) = x^4 + 2x^3 - x
g(f(x)) = x^4 + 2x^3 + 2x^2 - x
Step-by-step explanation:
f(x) = x^2 - x ; g(x) = x^2 + x
f(g(x)) = (x^2 + x)^2 - (x^2 + x)
f(g(x)) = (x^2 + x)^2 - x^2 - x
f(g(x)) = (x^2 + x)(x^2 + x) - x^2 - x
f(g(x)) = x^4 + x^3 + x^3 + x^2 - x^2 - x
f(g(x)) = x^4 + 2x^3 - x
g(f(x)) = (x^2 - x)^2 + x^2 - x
g(f(x)) = (x^2 + x)(x^2 + x) + x^2 - x
g(f(x)) = x^4 + x^3 + x^3 + x^2 + x^2 - x
g(f(x)) = x^4 + 2x^3 + 2x^2 - x
Plz help me solve need help
Answers
Answer:
t=1, u=-2, w=-2
Step-by-step explanation:
A hot air balloon descends 200 feet per
minute from an altitude of 1000 feet. Write a expression
Answers
y=90x+2,000
Step-by-step explanation:
90 is the rate of change because the hot air balloon descends 90 feet per minute.
And 2,000 is the starting point because the hot air balloon started the descent at 2,000 feet.
Use the vertex
(h, k)
and a point on the graph
(x, y)
to find the general form of the equation of the quadratic function.
(h, k) = (−4, −1), (x, y) = (−7, 8)
Answers
Answer:
Step-by-step explanation:
Let the quadratic function be
y=a(x+4)²-1
∵(-7,8) lies on it.
8=a(-7+4)²-1
8+1=a(-3)²
9a=9
a=9/9=1
so quadratic function is
f(x)=1(x+4)²-1
or
f(x)=x²+8x+16-1
so quadratic function is
f(x)=x²+8x+15
Use AABC shown below to answer the question that follows:
Which of the following is a step towards proving the similarity of triangle so AABC and ADBA? (5 points)
Segment BC is a hypotenuse.
Angle B is congruent to itself.
Segment BA is shorter than segment BC.
Segment BC is intersected by segment AD.
Answers
Answer:
Bc is intersected by segment AD
Answer:
Bc is intersected by segment AD
Step-by-step explanation:
the mode of some data is 20 if each value is increased by 2 what will be the mode of the data
what is the answer
Answers
Answer:
40
Explanations
Have to multiple 20 by 2 then your answer would be 40
The mode of the increased data will be 22.
What is the mode?The mode is that specific value that is found several times in a certain observation of a set of values.
How to calculate the mode of increased value?Here, mode of some data is 20.
Therefore, 20 is the most repeated value of that data observation.
Now, the each of value is increased by 2.
Then, the mode will be (20+2)=22
Learn more about mode here :
https://brainly.ph/question/12346912
#SPJ2
Question is in the picture.
Answers
Answer:
I dont know sorry
Step-by-step explanation:
Jaha ia yaiw ja
A football is kicked with a speed of 18.0 m/s at an angle of 36.9° to the horizontal.
7. What are the respective vertical and horizontal components of the initial velocity of the football?
A) 10.8 m/s, 14.4 m/s
B) 12.9 m/s, 7.61 m/s
C) 7.61 m/s, 12.9 m/s
D) 14.4 m/s, 10.8 m/s
E) 9 m/s, 9 m/s
Answers
Answer:
A
Step-by-step explanation:
horizontal component=18cos 36.9°≈14.39 m/s≈14.4 m/s
Vertical component=18 sin 36.9°≈10.81 m/s≈10.8 m/s
Write an inequality, in slope-intercept form, for the graph below. If necessary,
use *<=' for sor">=' for .
(0,4)
(2.0)
Answers
Answer:
y<=(-2x+4)
Step-by-step explanation:
The equation of line is y=-2x+4. For the region left of it, y<=(-2x+4)
The 7-digit numbers in a given area code have the form ABC-XXXX. Given ABC is 972, how many
possible phone numbers are there? (The form is 972-XXXX and the numbers 0-9 can be used)
Answers
Total number of possibilities is 10,000.
Step-by-step explanation:
Given:
Total number between (0-9) = 10 number
Frequency of unknown number = 4 times
Find:
Total number of possibilities
Computation:
Total number of possibilities when repetition is allowed;
Total number of possibilities when repetition is allowed = 10 × 10 × 10 × 10
Total number of possibilities when repetition is allowed = 10,000
Total number of possibilities when repetition is allowed = 10,000 times
Learn more:
https://brainly.com/question/10716370?referrer=searchResults
Given:
Overall number [tex]\bold{(0-9) = 10}[/tex]
Unknown source frequency [tex]= \bold{4\ times}[/tex]
Find:
The overall amount of opportunities=?
Calculation:
The total possible number for repeaters [tex]=\bold{ 10 \times 10 \times 10 \times 10}[/tex]
The total amount of repeat possibilities [tex]=\bold{ 10,000}[/tex]
Total amount of repeating options [tex]=\bold{ 10,000\ times}[/tex]
So, the "total number of possibilities is [tex]\bold{ 10,000}[/tex]"
Learn more:
brainly.com/question/17539761
consider the functions f(x)=-2x+4 and g(x)=8x-2 calculate the coordinates of the x and y interceptes of f(x)
Answers
Answer:
It more complex .Try to take help toggely
Which graph represents the solution set of the inequality 11 ≤ 2x + 5 ≤ 15
Answers
Answer:
D.
Step-by-step explanation:
First, simply the inequality.
[tex]11\leq 2x+5\leq 15\\6\leq 2x\leq 10\\3\leq x\leq 5[/tex]
Based on the simplified inequality, you are looking for a line with closed points on 3 and 5. Therefore, the answer is D.
Locate the points of discontinuity in the piecewise function shown below.
Answers
Answer:
Step-by-step explanation:
The given piecewise function i
From the given function it is clear that function is divided at x=-1 and x=2. It means we check the discontinuity at x=-1 and x=2.
For x=-1,
LHL:
Since LHL ≠ f(-1), therefore the given function is discontinuous at x=-1.
For x=2,
LHL:
Since LHL ≠ f(2), therefore the given function is discontinuous at x=2.
Therefore, the correct option is A.
THE DISTANCE OF A PARTICLE FROM
IT'S STARTING POINT AT TIME T
SECONDS IS GIVEN BY S= 80T - 1672.
WHAT IS THE VELOCITY OF THE
PARTICLE AFTER 2 SECONDS?
Answers
Answer:
the answer will be 3.........
the triangular side wall of the flower has been used of advertisement the side of a wall or 122m 12 and 120m the advertisement yeild an earning of rupees 5000 per metre square square A company hired one of its wall for 3 months how much rent did it pay
Answers
refer the attached image for the answer
HOPE SO IT HELPS YOU
