INFO: The chairs are evenly spaced around
the wheel
Question: If the length of the cable from L to E is 80 feet, E to the ground is 35 feet, and F to the ground is 40
feet, what is the length of the cable from J to F?
Answers
Answer: About 72 feet
The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).
======================================================
Explanation:
Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.
M = center of the circleN = location where the cable is anchored to the groundWe're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.
The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.
-----------------
What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.
It turns out that the chord length c is connected to the radius r and central angle theta like so:
c = 2*r*sin(0.5*theta)
where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.
If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces
Those five spaces could be written as
The jump from L to AThe jump from A to BThe jump from B to CThe jump from C to DThe jump from D to EOr you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.
There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.
-----------------
Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.
c = 2*r*sin(0.5*theta)
80 = 2*r*sin(0.5*5pi/6)
80 = 2*r*sin(5pi/12)
80 = 2*r*0.9659258
80 = 2*0.9659258*r
80 = 1.9318516r
1.9318516r = 80
r = 80/1.931 8516
r = 41.4110483
The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.
-----------------
Now that we know the radius, we can determine how long chord JF is.
The central angle for chord JF is angle JMF
If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.
So,
c = 2*r*sin(0.5*theta)
c = 2*41.4110483*sin(0.5*2pi/3)
c = 71.7260397
Chord JF is roughly 71.7260397 feet long.
When rounding to the nearest foot, that's about 72 feet.
Related Questions
Select all values of x that make the inequality true: (x ≥ -1)
A. -4
B. -2
C. -1
D. 0
E. 1
F. 4
Answers
Answer:
c,d,e,f
Step-by-step explanation:
mark me brainliest
Select all values of x that make the inequality true: (x ≥ -1)
A. -4
B. -2
C. -1
D. 0
E. 1
F. 4
Answer:
C, D, E, F
Step-by-step explanation:
hope this helps! #HappyCheating
Help ASAP I’ll mark branliest
Answers
Answer:
C - 129
Step-by-step explanation:
180-51=129
Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 40 at one school and 13 of 30 at the other had this infection. Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other. Find the test statistic. [Suggestion: try to use a TI 83 or a similar calculator.]
Answers
Answer:
The test statistic is [tex]z = -0.28[/tex]
Step-by-step explanation:
First, before finding the test statistic, we need to understand the central limit theorem and difference between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A random sample of children in two different schools found that 16 of 40 at one school
This means that:
[tex]p_1 = \frac{16}{40} = 0.4, s_1 = \sqrt{\frac{0.4*0.6}{40}} = 0.0775[/tex]
13 of 30 at the other had this infection.
This means that:
[tex]p_2 = \frac{13}{30} = 0.4333, s_2 = \sqrt{\frac{0.4333*0.5667}{30}} = 0.0905[/tex]
Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other.
At the null hypothesis, we test if there is no difference, that is:
[tex]H_0: p_1 - p_2 = 0[/tex]
And at the alternate hypothesis, we test if there is difference, that is:
[tex]H_a: p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]p = p_1 - p_2 = 0.4 - 0.4333 = -0.0333[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0775^2+0.0905^2} = 0.1191[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0333 - 0}{0.1191}[/tex]
[tex]z = -0.28[/tex]
The test statistic is [tex]z = -0.28[/tex]
The question is in le picture below U-U
Answers
Answer:
30%
Also I LOVE THE EMMA PIC!!!!!!!!
Find the slope of the line parallel to the line graphed.
My Answer:
Answers
A box holds 30 tins How many boxes can be filled
with 810 tins
Answers
14. A cone has twice the base diameter and
three-fourths the height of a cylinder. Can
you tell what the relationship between the
volume of the cone and the volume of the
cylinder is? Explain your reasoning.
Answers
Answer:
1+1 is cannot be
Step-by-step explanation:
jajauajhwhahwwhhahwhauwu
Graph the following function on the axes provided.
Answers
Answer:
this may help you.look it once
Step-by-step explanation:
.
Paul is selling $2 raffle tickets for his baseball team. He needs to sell at least
$230 worth of tickets to earn a team jacket. If he has already sold $50 worth of tickets, how many more raffle tickets, x, does Paul need to sell to earn a team jacket?
Answers
Answer: 90 more tickets
Step-by-step explanation:
230 - 50 = 180
180 divided by 2 = 90 tickets
The new number 200 is 400 less than the original number what is the approximate per percent change
Answers
Answer:
200+400=600
400/600=2/3=66.6%
x > -3 For each statement list three numbers that would make a solution to the inequality true.
Answers
Answer:
x = -2
x = -1
x = 0
Step-by-step explanation:
Find three numbers to the left of -3 on the number line
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which expression has a value greater than 43 ?
PLEASEEE HELP!
Answers
Answer:
7^2
Step-by-step explanation:
7*7=49
4^3=43
49>43
Find the solution of the following equation whose argument is strictly between 90° and 180°.
Answers
Answer:
180degreesStep-by-step explanation:
Given the complex value
z² = -81i
z = (-81i)^1/2
Get the argument of -81i
theta = arctan(y/x)
theta = arctan(-81/0)
theta = -90degrees
theta = -π/2
Since tan is negative in the secind quadrant
theta = π - π/2
theta = π/2
According to demoivres theorem
theta = 1/2 * π/2
theta = π
theta = 180degrees
9 mi
12 mi
What is the length of the hypotenuse?
miles
Answers
Two trains leave New York at the same time. One travels south 50 miles per hour and the other traveled east at 40 miles per hour. How far apart are they at the end of THREE HOURS?
Answers
Answer:
192 miles
Step-by-step explanation:
This is a right triangle problem
One leg of the triangle is
50 * 3 = 150
The other leg is
40 * 3 = 120
the distance is the hypotenuse
c^2 = 150^2 + 120^2
c^2 = 22500 + 14400
c^2 = 36900
Take the square root of both sides
c = 192.093727123
c ≈ 192 miles
Answer:
30 miles apart
Step-by-step explanation:
Im not sure if this is the corect answer to this but this is what i think what i did was get 50 x 3 and 40 x 3 since they starded at the same times and finished after 3 hours so multiply your numbers by 3 so...
50 x 3=150
40 x 3=120
150-120=30 miles apart
30 POINTS, NO LINKS, AND ANSWER RIGHT.
-15 = 8z + 7. what is the value of z
Answers
Rationalize the denominator and simplify
Answers
In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?
Answers
Answer:
its A
Step-by-step explanation:
its A ️ ♀️ ️ ♂️ ️
2.52343454 + -34355343.99
NEED HELP PLZZZZZZ ASAP
Answers
Answer:
5555555555555555555555555555555555555 trust
Step-by-step explanation:
Find the radius of the curcle
Answers
Answer:
radius=diameter/2
=9/2
=4.5 in.
diameter=radius*2
=3m*2
=6m
Step-by-step explanation:
Step-by-step explanation:
1) r=d/2
r=9in/2
r=4.5in
2) d= r×2
d=3m×2
d=6m
Construct a histogram for the following data set: 11, 17, 13, 2, 22, 18, 16, 14, 16, 21, 17, 9, 9, 7, 3
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Guys help me with this quick pls
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Answer:
[tex]117 = 66 + \beta \\ \beta = 51[/tex]
Helppppppppppp!!!!! Please
Answers
Answer:
The answer is C.
Step-by-step explanation:
angle 5 and 4 makes a line which is 180 and since angle 5 equals 57 , 180-57=123.
find m
135°
125°
55°
100°
Answers
Answer:
answer: m = 125
Step-by-step explanation:
parellograms add up to a total of 360 so m = 125 because 125 + 125 + 55 + 55 = 360 Hope this helps!
Step-by-step explanation:
here's your solution
==> sum of corresponding angles of parallelogram = 180°
==> angle J + angle k = 180°
==> 55° + k = 180°
==> k = 180° - 55°
==> k = 125°
[tex]hope \: it \: helps[/tex]
giving out brainliest answer please help me out asap !! it’s due today
Answers
Answer:
180=3x+7x+10
simplify
180=10x+10
subtract 10 from both sides
170=10x
divide both sides by 10
x=17
Please help me this is for a test. Thank you so much whoever answers this.
Answers
Answer: Pretty sure the answer is 3.
Step-by-step explanation:
[tex]\frac{2(4+7)-7}{5}[/tex]
[tex]\frac{2(11)-7}{5}[/tex]
[tex]\frac{22-7}{5}[/tex]
[tex]\frac{15}{5}[/tex]
Jerry has $90 in his savings account. The interest rate is 10%, compounded annually. To the nearest cent, how much interest will he earn in 3 years
Answers
Answer:
27 cents
Step-by-step explanation:
10% of 90= 9
9x3=27
Answer:
p x t x r / 100
90 x 10 x 3 / 100
=27
a)Solve for x:
y = 130 − 4x
b) What is the value of x when y = 120
Answers
Answer:
[tex]x = \frac{5}{2}[/tex]
Step-by-step explanation:
y = 130 - 4x
======================
120 = 130 - 4x
-10 = -4x
x = [tex]\frac{-10}{-4} =\frac{5}{2}[/tex]
are these two triangles congruent? if so state, how you know.
Answers
Answer:
by SSS axiom
hope it helps.
Answer:
Step-by-step explanation:
Yes
the two sides that are marked make 2/3 of the sides needed for SSS
The line shared by both triangles make the third side.
Answer: SSS
Each triangular face of the following solid figure is congruent. If the area of each face is 12 square inches, what is the
surface area of the entire figure?
Answers
Answer:
the surface area is 48in^2 because there are 4 faces and you have to find the surface are in which you must multiply 12 by 4.
Step-by-step explanation: