The accompanying diagram shows a revolving door
with three panels, each of which is 4 feet long.
What is the width, w, of the opening between x and
y, to the nearest tenth of a foot?
Answers
Answer:
7 ft.
Step-by-step explanation:
Please see the attached image.
I named the center Z btw
Because the circle is split into three congruent angles, each angle is 360/3=120°.
After dropping an altitude on the bottom triangle, the angle is bisected, so 120/2=60°.
By dropping the altitude, we also created a 30-60-90 triangle. By now you have probably learned the proportions for the sides of a 30-60-90 triangle, but if you haven't,
the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is the other leg multiplied by √3.
So ZW is 4/2=2, and WY is 2√3.
XW=WY, so XY=2√3*2=4√3
4√3 is approximately 7.
7 ft.
The three panels are divided into three equal parts. This mean that the central angle from each panel is 120 degrees. So, the side length of w and the length of curve xy is 7 feet and 8 feet
Let the center of the circle be O (see attachment).
So:
[tex]\angle XOY = \frac{360}{3} = 120^o[/tex] ---- because the circle is divided into 3 equal parts
Considering [tex]\triangle XOY[/tex]
[tex]\angle W O Y = \frac{\angle X O Y}{2}[/tex]
[tex]\angle WOY = \frac{120}{2} = 60[/tex]
Considering [tex]\triangle WOY[/tex]
[tex]\sin(60) = \frac{wy}{yo}[/tex]
Where:
[tex]yo= 4[/tex]
So, we have:
[tex]\sin(60) = \frac{wy}{4}[/tex]
[tex]0.8860 = \frac{wy}{4}[/tex]
Multiply through by 4
[tex]wy = 4 * 0.8660[/tex]
[tex]wy = 3.464[/tex]
Because w divides xy into w equal parts
[tex]wx = wy = 3.464[/tex]
The length of w is:
[tex]w =wx + wz[/tex]
[tex]w = 3.464+3.464[/tex]
[tex]w = 6.928[/tex]
Approximate
[tex]w = 7[/tex]
Next, is to calculate arc length xy
This is calculated as follows:
[tex]xy = \frac{\theta}{360} * 2\pi r[/tex]
Where:
[tex]\theta = \XOY = 120^o[/tex]--- central angle
So, we have:
[tex]xy = \frac{\theta}{360} * 2\pi r[/tex]
[tex]xy = \frac{120}{360} * 2 * 3.142 * 4[/tex]
[tex]xy = \frac{1}{3} * 25.136[/tex]
[tex]xy = 8.33[/tex]
Approximate
[tex]xy = 8[/tex]
Hence, the side length of w and the length of curve xy is 7 feet and 8 feet respectively.
Read more about solving triangles at:
https://brainly.com/question/23295201
Related Questions
HELPPPPPP ITS URGENT!!!!!!!!!!!!!!!!!
Thomas is going to deposit $840 in an account that earns 7.5% interest compounded annually. His wife Sheril will deposit $1,250 in an account that earns 6.9% simple interest each year. They deposit the money on the same day and make no additional deposits or withdrawals for the accounts. What statement is true concerning Thomas' and Sheril's account balance after 5 years?
a
Thomas' account will have about $475.32 less than Sheril's account.
b
Sheril's account will have about $431.25 less than Thomas' account.
c
Sheril's account will have about $475.32 less than Thomas' account.
d
Thomas' account will have about $431.25 less than Sheril's account.
Answers
Answer:
A
Step-by-step explanation:
trust
Answer:
The answer is A Thomas' account will have about $475.32 less than Sheril's account
Step-by-step explanation:
Its A because 840 Plus 7.5% Is 903 which means And 1,250 plus 6.9% is 1,336.25 so Sheril has $475.32
Use the drop-down menu to complete the following sentence.
Answers
Answer:
3/2 or 1 1/2
Step-by-step explanation:
6/8 ÷ 2/4 = x
6/8 x 4/2 = x
6/8 x 4/2 = 24/16
24/16 = 6/4 = 3/2
3/2 = 1 1/2
Answer:
[tex] \frac{3}{4} [/tex]
Step-by-step explanation:
[tex] \frac{6}{8} \div \frac{2}{4} = \frac{3}{4} [/tex]
or
[tex]1 \frac{1}{2} [/tex]
The function F is defined by F(x)= 12/x + 1/2
Use this formula to
find the following values of the function:
F(k)
F(a/2)
F(x-1)
F(2x+3)
F(x+h)
Answers
Answer:
F(2x+3) = 12/(2x+3) +1/2
Step-by-step explanation:
Put the argument of the function where the variable is. You can simplify if you want, but the original function definition is not simplified, so we assume it is not required.
F(x) = 12/x + 1/2
Put (2x+3) where x is:
F(2x+3) = 12/(2x+3) + 1/2
12/k+1/2
24/a+1/2
12/x-1+1/2
12/2x+3+1/2
Answers should be correct, respectively (to the order of ur questions)
A cell phone company advertises that their data plan costs "0.02 cents" for every kilobyte of data. Corinne used 1000 kilobytes of data. Using the advertised price, determine how much Corinne owes on the data plan.
Answers
In the circle above, LM = 2 and KL = 6.
What is the measure of MN?
A) 16
B) 10
C) 4
D) 8
Answers
Answer:
C. 4
Step-by-step explanation:
We can use power of a point to solve this problem. From this, we can set up the equation:
MN^2 = LM x MK
MK would be the sum of LM and KL because of segment addition postulate. Therefore, we can say MK = 2 + 6 = 8
Now, we can substitute the values we have in the equation above:
MN^2 = 2 x 8
MN^2 = 16
MN = 4
4*
Which property of real numbers is illustrated below?
12(x + 4) =12x + 48
A.
Distributive property of multiplication
B. Distributive property of addition
C. Associative property of multiplication
D. Associative property of addition
Answers
A: Distributive property of multiplication
Answer
Step-by-step explanation:
10. Geraldo Castro rented a car for 4 days at $45 per day, and drove the
car 600 miles at $0.22 per mile. He spent $30 for gasoline and purchased
a collision waiver for $12 per day. What is the total cost for renting the car?
(Section 9-7) *
A. $452
O B. $390
C. $45
O D. $30
Answers
Explanation:
$45 per day= $180
600 miles= 132 ($0.22x600)
Daily collision waiver=$48
As of now the cost is $360 + the $30 of gas= $390.
Solve the varible :
1: -5z + 8 = 33
2: -4b - 7 = 37
3: 8x + (-9) = 45
4: 6c + 7 = -29
Answers
Answer:
1: -5z + 8 = 33
-5z=33-8
z=-25/5
z=-5
2: -4b - 7 = 37
-4b=37+7
b=-42/4
b=21/7
3: 8x + (-9) = 45
8x=45+9
x=54/8
x=27/4
4: 6c + 7 = -29
6c=-29-7
c=-36/6
c=-6
A spinner has 17 equal-sized sections marked 1 through 17. Find the probability. Enter your answer as a simplified fraction.
You spin once and land on an odd number.
The probability that you land on an odd number is
Answers
A gardener has 3 pounds of compost. She will split the compost into 8 garden beds equally. How many pounds of compost will she put in each garden bed?
Answers
Answer:
3/8 pounds of compost
Step-by-step explanation:
Find how much compost she'll put in each garden bed by dividing the number of pounds of compost by the number of garden beds:
3/8
This fraction cannot be simplified further, so the answer is 3/8.
She will put 3/8 pounds of compost into each garden bed
Simone is designing a piece of artwork for a hotel. The artwork is in the shape of a square pyramid as shown. She wants to cover the pyramid with decorative glass. Use a net to find how many square feet of glass needs to cover the entire pyramid.
HELP ME!!!! I WILL GIVE YOU 50 POINTS!!!!!!!
Answers
Answer:
36.8 ft
Step-by-step explanation:
Answer:
63.21
Step-by-step explanation:
3×-3+5
please help me solve this mathematics questions
Answers
Answer:
-4
Step-by-step explanation:
3 x (-3) +5
-9 + 5=
-4
NEED HELP ITS A TEST!
Line n and point P are shown on the coordinate plane. What is the equation of the line parallel to line n that passes through point P?
A: y= 3x-6
B: y= 3x-6
C: y= 3x+12
D: y= -3x+3
Answers
Answer:
X = -2 - y/3
Step-by-step explanation:
First you need to know the current equation, for that:
Notice that when Y = 0, X = 2.
When Y = 6, X = 0
Therefore the equation is X = [tex]2-\frac{y}{3}[/tex]
To move that to the left of the X axis (negative direction) you just have to reduce the X number:
[tex]x=-2 - \frac{y}{3}[/tex]
Parallel lines have the same slope.
The required equation is: [tex]\mathbf{y = -3x - 6}[/tex]
The points on line n are:
[tex]\mathbf{(x,y) = (4,-6)(2,0)}[/tex]
So, the slope (m1) of line n is:
[tex]\mathbf{m_1 =\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
This gives
[tex]\mathbf{m_1 =\frac{0--6}{2 - 4}}[/tex]
[tex]\mathbf{m_1 =\frac{6}{-2 }}[/tex]
[tex]\mathbf{m_1 = -3}[/tex]
If the line is parallel to line n, then it has the same slope (m2) as line n.
So, we have:
[tex]\mathbf{m_2 = m_1 = -3}[/tex]
Point P is given as:
[tex]\mathbf{P = (-3,3)}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m_2(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = -3(x + 3) + 3}[/tex]
[tex]\mathbf{y = -3x - 9 + 3}[/tex]
[tex]\mathbf{y = -3x - 6}[/tex]
Hence, the required equation is: [tex]\mathbf{y = -3x - 6}[/tex]
Read more about linear equations at:
https://brainly.com/question/11897796
Marvin went fishing, and the difference in weight between the first two fish he caught was 0.00074 grams. Represent this in scientific notation.
Answers
Answer:
7.4 × 10^-4
Step-by-step explanation:
Answer:
7.4 * [tex]10^{-4}[/tex]
A 2-gallon bucket of paint costs $58.00. What is the price per quart? $
Answers
Answer:
7 dollars and 25 cents
Step-by-step explanation:
there is 8 quarts in 2 gallons then divide 58 dollars by 8 and you get 7 dollars 25 cents
Division is one of the four fundamental arithmetic operations. The price per quart is $7.25 per quart.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that A 2-gallon bucket of paint costs $58.00. Therefore, the price per gallon is,
Price per gallon = $58/2
Since a gallon is equal to 4 quarts. Therefore, the price per quart is,
Price per quart = $58/(4×2) = $7.25 per quart
Learn more about Division:
https://brainly.com/question/369266
#SPJ2
Help find the value of x pls I’ll give brainleist. No links or I’ll report you
Answers
Answer:
x = 12
Step-by-step explanation:
The angles are supplementary and add up to 180
(8x - 20) + (8x + 8) = 180
Combine like terms
16x - 12 = 180
add 12 to both sides
16x = 192
Divide both sides by16
x = 12
01:41:08
Dependent variable C depends on both independent variable A and independent variable B. Which statement is
correct?
Answers
Answer:
The correct answer is B. The relationship between independent variable A and dependent variable C, and the relationship between independent variable B and dependent variable C can both be analyzed, but they must be analyzed using separate scatter plots.Apr 30
Step-by-step explanation:
hope you get it right
Identify each table as exponential growth or decay.
Answers
An animal researcher randomly selected 98 dogs and cats and recorded if the napped between 2:00 p.m and 2:30 p.m. The two-way table displays the data.
Suppose an animal is randomly selected. let event c = cat and let event n = nap. what is the value of P(C|N)?
a. 38/98
b. 23/51
c. 47/98
d. 23/38
Answers
Answer: D 23/38
Step-by-step explanation:
Probability helps us to know the chances of an event occurring. The correct option is D, 23/38.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The value of P(C|N) is the ratio of the number of cats taking naps between 2:00 p.m and 2:30 p.m and the total number of cats.
Therefore, the value of P(C|N) is,
P(C|N) = P(C∩N)/P(C)
P(C|N) = 23/38
Learn more about Probability:
https://brainly.com/question/795909
#SPJ2
what is the answe to 5+5
Answers
Answer:
10
Step-by-step explanation:
Answer:10
it is 10 because if you had 5 dino nuggets and you got 5 more you would have 10 dino nuggets.
please helppp plesseee
Answers
Answer:
[tex]y = \sqrt{7^{2} + 3^{2} }[/tex]
D. 7.6
Step-by-step explanation:
y² = 7² + 3²
y² = 49 + 9
y² = 58
y = (58)^½
y = Rationalize(7.61577310586) ~ 7.6
2) A box contains 2 red
pencils, 4 blue pencils, and
6 green pencils. What is the
probability of picking a
green pencil, not replacing
it, and then picking a blue
pencil? Write your answer
as a fraction in simplest
form.
Answers
Answer:
2/11
Step-by-step explanation:
P(G,B) = 6/12 x 4/11
= 1/2 x 4/11
= 4/22 or 2/11 in simplest form
Someone help me pls
Answers
Answer:
x-¹⁰ is the correct answer dude
Answer:
= x^ 2 + x^ -12
= x^ 2 + (-12)
= x ^ -10
Which graph best represents the solution to the system of equations shown below?
y = -2x + 14
y = 2x + 2
Answers
Answer:
1st
Step-by-step explanation:
Solve for the h: V= 1/3 π r^2 h
Answers
Answer:
H = 3V/πr^2 V ∈ ℝ, r ∈ ℝ
Step-by-step explanation:
multiply both sides
swap the sides
and then write in parametric form
hope this helps!
If an exponential function grows by a factor of (2.5), what percent is being
added?
2.5%
250%
150%
25%
Answers
Answer:
Hello! answer: 250%
Hope that helps!
pls help!!!! ...!.!.!.!.!.!.!.!.!!.
Answers
Simplify: 8 + 14 – 5 - 7 + 3 - 7 - 4
Answers
Answer:
2
Step-by-step explanation:
Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex]8+14-5-7+3-7-4[/tex]
We'll Follow the PEMDAS order of operations:-
Add and subtract:-
8+14=22
[tex]22-5-7+3-7-4[/tex]
22-5=17
[tex]17-7+3-7-4[/tex]
17-7=10
[tex]10+3-7-4[/tex]
10+3=13
[tex]13-7-4[/tex]
13-7=6
[tex]6-4[/tex]
[tex]2[/tex]
OAmalOHopeO
In the diagram, LM is parallel to IK. Find the length of LM, to the nearest tenth of a metre.
Answers
Answer:
Step-by-step explanation:
Expression 9 x, if x=5
Answers
Answer:
45
Step-by-step explanation:
9x
Replace x with 5
9*5
45
Answer:
45
Step-by-step explanation:
9x5 equals 45