Answers
Answer:
area ≈ 12.505
perimeter ≈ 16.1684
Step-by-step explanation:
We are given
- the radius of the circle (and therefore area of the circle)
- the area of the triangle
We want to find
- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.
First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT
One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say
15 = AO * AT / 2
15 = 6 * AT / 2
15 = 3 * AT
divide both sides by 3 to isolate AT
AT = 5
Because OAT is a right triangle, we can say that the hypotenuse ² = the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that
OA² + AT² = OT²
5²+6² = OT²
25+36=61=OT²
square root both sides
OT = √61
Next, the Law of Sines states that
sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.
We want to find angle AOT, as stated earlier, so we have
sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT
We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is
sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have
sin(90)/√61 = sin(AOT) /5
plug in sin(90) = 1
1/√61 = sin(AOT)/5
multiply both sides by 5 to isolate sin(AOT)
5/√61 = sin(AOT)
we can thus say that
arcsin(5/√61) = AOT ≈39.80557
As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector
Related Questions
You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange).
If you randomly pick the piece of clothing and the color.
What is the probability that you'll end up with socks that aren't blue?
Answers
Answer:
¼ chance
Step-by-step explanation:
If there is 4 items and 1 blue die and its a ¼ chance if there was more blue then there would be a higher chance for having blue socks
All even numbers are
Answers
Answer:
2 4 6 8 10 12 14 16.....................................................
Answer:
even numbers are
Step-by-step explanation:
2,4,6,8,10,12,14,16,18,20,24,26 and so on
please mark me brainliest I will follow youI've provided a screenshot below. In the question, I don't understand why it can't be D. Like both C and D have the same slope, y= 2/3x. The only difference is what comes after for those two. So why is it y=2/3x -12 and not y= 2/3x +1 ???
Answers
Choice C is the only equation with slope 2/3, while choice D has slope -2/3. This subtle difference is enough that the two lines are not parallel. The positive slope line goes uphill when moving to the right. The negative slope line goes in the opposite direction: it goes downhill when moving to the left.
The graph is below comparing the original equation with choices C and D. I used GeoGebra to make the graph, but you could use any other tool you want (eg: Desmos).
Answer:
y = 2/3x - 12 is correct
Step-by-step explanation:
D is incorrect because the slope is -2/3
To have a parallel line, you have to have the some slope, but a different y- intercept
Ill graph y = -2/3x + 1 and y = 2/3x + 5/6 and show you:
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which of the following are good ideas to use when gathering your resources?
Check all that apply.
O A. Form an equation:
B. Draw a diagram.
C. List potential formulas.
D. Guess at the solution and see if you are close.
E. Organize into a table.
F. Write down the facts.
Answers
Answer:
Organize into a table for good gatherings.
Evaluate the expression
Answers
Answer:
answer is 5 this question
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
I believe its negative nonlinear association
Step-by-step explanation:
The line is going down so its definitely negative
And the line is not straight so its not linear
Therefore, its negative nonlinear association
Consider a triangle ABC like the one below. Suppose that a=51, b=16, and A=108. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or".
Answers
Answer:
B = 17.4°
C = 54.6°
c=43.7
Help Find the square root
Answers
Answer:
√121=11
√81=9
√4=2
√100=10
√144=12
√36=6
√16=4
√1=1
√49=7
√25=5
√9=3
√64=8
I hope this helps
Pleaseee i'm struggling so hard on this Geometry thing, show work please
Answers
Answer:
(12x+1)+(5x-3)=117
combine like terms 12x+5x=17x
1+-3= -2
17x-2=117
add 2 to both sides to isolate the variable
17x=119
divide both sides by 17 to further isolate the variable
x=119/17
x=7
answer is x=7
Step-by-step explanation:
add both angles to be the sum of the angle DEF and determine what x must be by the steps above
Answer:
x=7°
Step-by-step explanation:
Form an equation:
12x+1+5x-3=117°
Collect like terms:
Like terms are terms with the same variables and powers.
12x+5x=17x
1-3=-2
put I back into an equation:
17x-2=117°
As we want x, you would have to do inverse operations to 'undo the equation'.
117+2=119°
17x=119°
119÷17=7° (We divide by 17 because when a number is next to a letter, in algebra, it means you times so we have to do the opposite and divide)
So, x=7
Hope this helps :)
Topic: Simultaneous equations Class 9 ICSE
Answers
Denote the number by 10a + b, where both a and b are integers picked from {1, 2, 3, …, 9}.
"the difference of whose digits is 3" ==> |a - b| = 3
"4 times the number is equal to 7 times the number obtained by reversing the digits" ==> 4 (10a + b) = 7 (10b + a)
Simplifying the second equation, you get
40a + 4b = 70b + 7a
33a - 66b = 0
a - 2b = 0
Assume a > b, in which case we would have |a - b| = a - b, so
a - b = 3
Eliminate a to solve for b, then for a :
(a - b) - (a - 2b) = 3 - 0
b = 3 ==> a = 6
Then the original number is 63.
If instead we had assumed a < b, we would have had |a - b| = b - a = 3. Then
2 (b - a) + (a - 2b) = 2×3 + 0
-a = 6
But neither a nor b can be negative, so this case is moot.
F(x)=2x+1 and g(x)=x2-7, find (f+g)(x)
Answers
Answer:
x^2 +2x -6
Step-by-step explanation:
f(x)=2x+1
g(x)=x^2-7,
(f+g)(x) = 2x+1 + x^2 -7
Combine like terms
= x^2 +2x -6
f (x) = 2x + 1
g (x) = x² - 7
(f+g) (x) = 2x+1 + x² - 7
Adding like terms
⇛ x² + 2x - 6
Josh has an aquarium 30 inches deep it takes him 5 minutes to fill the bucket with 3 inches of water he estimates that it will take him under an hour to fill the entire bucket with water if you correct explain why or why not
Answers
I assume your question should be rephrased as "Josh has a bucket 30 inches deep..."
Josh is correct in estimating that it will take him under an hour to fill the entire bucket with water.
Given:
The bucket is 30 inches deepIt takes Josh 5 minutes to fill the bucket with 3 inches of waterTo find: If Josh is correct in estimating that it will take him under an hour to fill the entire bucket with water
It is given that, to fill the bucket with 3 inches of water, it takes Josh 5 minutes.
Using Unitary method, we can say that, to fill the bucket with 1 inch of water, it takes Josh [tex]\frac{5}{3}[/tex] minutes.
Then, to fill the bucket with 30 inches of water, it takes Josh [tex]\frac{5}{3} \times 30[/tex] minutes.
Solving, we can say that it takes Josh 50 minutes to fill the bucket with 30 inches of water.
Since the bucket is 30 inches deep, we can say that it takes Josh, 50 minutes to fill the entire bucket, which is just under an hour.
So, Josh is correct in assuming that it will take him under an hour to fill the entire bucket with water.
Learn more about Unitary method here:
https://brainly.com/question/12470900
In AFGH, mZF = (6x – 14), mZG = (4x – 8)°, and m_H = (x + 15)°.
Find mZF.
Answers
Answer:
Step-by-step explanation:
(6x - 14)° + (4x - 8)° + (x + 15)° = 180°
11x - 7 = 180
11x = 187
x = 17
m ∠ F = ( 6 × 17 - 14 )° = 88°
Mrs . Johnson has a total of 30 students in her class , The ratio of boys to girls is 2:3 , how many does Mrs. Johnson have in her class ?
Answers
Answer:
12 boys and 18 girls, 30 kids total
Answer:
12 boys and 18 girls
Step-by-step explanation:
If the ratio of boys to girls is 2:3, that means for every 5 students, 2 are girls and 3 are boys. That means 2/5 are girls and 3/5 are boys, so:
G is a transformation of f. What is the formula of g in terms of f?
A. [tex]-\frac{1}{2}f(x)[/tex]
B. -2f(x)
C. f ([tex]-\frac{1}{2}x[/tex])
D. f(-2x)
Answers
Answer:
C
Step-by-step explanation:
First, we can see that from f(x) to g(x), the change in x for each change in y is significantly increased. This represents a stretch in the x direction. A stretch/compression in the x direction is represented by
f(cx), with c > 1 representing a compression by c and 0 < c < 1 representing a stretch by a value of 1/c. From the vertex of each, when y changes by 1, in f(x) x changes by 2 (e.g. from x=2 to x=4), whereas in g(x) x changes by 4 (e.g. from x=-4 to x=0). Therefore, g(x) stretches x by 2, so c = 1/2, giving us
f(c(x))
= f(1/2(x))
Let's say f(a) = f(1/2(x))
Then, because the graph stretched by 2, the vertex goes from x=2 to x=4. Our vertex is at x=-4 in g(x), so to make the vertex equal to that, we can flip f(a) around the y axis. To flip this around the y axis, we can plug -a in for a, resulting in
f (-(a))
= f(-(1/2)(x))
= g(x)
Find f(-2) for f(x) = 2(4)^x
Answers
Answer:
2(4)^-2
=2/4^2
2/16
1/8
thanks
Answer:
f(- 2) = [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
To find f(- 2) substitute x = - 2 into f(x) , that is
f(- 2) = 2 [tex](4)^{-2}[/tex] = 2 × [tex]\frac{1}{4^2}[/tex] = 2 × [tex]\frac{1}{16}[/tex] = [tex]\frac{2}{16}[/tex] = [tex]\frac{1}{8}[/tex]
Please help! Giving brainiest!
The dot plots below show the test scores of some mathematics students and some science students: (View the attached image) Based on visual inspection of the dot plots, which group of students appears to have the larger average score?
a. The mathematics students
b.the science students
c. Both groups are similar
d. Not enough information is available to draw a conclusion.
Answers
Answer:
b. The science students
Step-by-step explanation:
If you count the dots, they are the same for both class (9 people) but the range of the science students' scores are higher than the range for the math students, which means that the sum of their scores will be larger than the math students' and since they have the same number of people, the number being divided for the average would be the same, so the science students' average would be greater than the math's.
I hope this helped! ;D
2x +4>- 6 and 5x -12<3
Answers
Step-by-step explanation:
bzbzbsbbsbsbsbsbsbsbsbbsbs indian
Find the multiplicative inverse (i.e., reciprocal) of 0/9
Answers
Answer:
undefined, you cannot divide by zero
Step-by-step explanation:
Can someone help me with this math work and please explain why the answer is what it is
Answers
Answer: 58unit²
Step-by-step explanation:
We will take 1 square as 1 unit
We will count the number of squares in in this figure.
Total squares = 58
Area = 58unit²
please click thanks and mark brainliest if you like :)
What is the radius of a hemisphere with a volume of 885 in^3, to the nearest tenth of
an inch?
Answers
Answer:
The desired radius is r = 7.5 inches
Step-by-step explanation:
The formula for the volume of a sphere of radius r is V = (4/3)πr³. A hemisphere is half a full sphere, so the formula for the volume of a hemisphere of radius r is (4/3)(1/2)πr³, or (2/3)πr³.
We know that the volume of the hemisphere is 885 in³:
885 in³ = (2/3)πr³ and need to solve this first for r³ and then for r.
This is equivalent to:
885 in³ = (2π/3)r³.
We can now isolate r³ by multiplying both sides of this equation by (3 / [2π]):
(3 / [2π])(885 in³) = (3 / [2π])(2π/3)r³ = r³
Then r³ = 422.556 in³
Finally, we find the desired hemisphere radius by taking the cube root of both sides of the above equation:
r = ∛(422.556 in³) = 7.5 in (which is to the nearest tenth of an inch)
The desired radius is r = 7.5 inches
[tex]x^{2} +5x+3[/tex]+2x^{2}+10x-15=0
Answers
please mark this answer as brainlist
Find the sum of all the numbers between 100 and 200 which are divisible by 7.
Answers
Answer:
2107
Step-by-step explanation:
In this type of question we have to follow these steps
1) Find the biggest number in interval which is divisible by seven
For this question it is 196
2)Find the smallest number in interval which is divisible by seven
For this question it is 105
3) Then subtract 105 from 196
196-105=91
4) Divide 91 by seven
91:7=13
5)Lastly we have to add 1 to the 13
13+1=14
So we found that we have 14 different numbers that divisible by seven in this interval. So next steps will be about sum of them
To find them sum we have a formula:
(biggest number + smaller number) x number of terms / 2
(196+105) x 14 /2 = 2107
raise irrational number to rational power and get a rational number
Answers
9514 1404 393
Answer:
(√2)² = 2
Step-by-step explanation:
You can do this for any rational root of a rational number. Simple examples are squares and cubes:
(√5)^2 = 5 . . . . . . √5 is irrational
(∛6)^3 = 6 . . . . . . . ∛6 is irrational
__
You can also do it with other rational roots:
x = 83^(2/3) is irrational
x^(3/2) = 83 is rational
Can someone help me on this ASAP it’s very tricky
Answers
Well the two equations are in y=mx+b form, also known as slope-intercept form.
The slope for the first equation is 5/6. The slope for the second is -4/3. Its very simple. We say that x is 0 for example...
When X = 0...
First equation: Y=7
Second Equation: Y=-6
On the graph you plot (x,y) (0,7) on the graph. so on the Y axis, put a dot at 7. This is for the first equation. We can say x is 6 also, and then the answer is -1.
So the second point is (6,-1).
FIRST EQUATION ONLY: Plot (0,7), (6,-1)
For the second I wont be elaborate as much but its (0,-6), (3,-10)
Brainiest/Heart if helpful!
Answer:
(-6, 2)
Step-by-step explanation:
When you graph [tex]y=\frac{5}{6} x+7[/tex], you get the red line.
When you graph [tex]y=-\frac{4}{3} x-6[/tex], you get the blue line.
The answer is the point they intersect, or cross. That would be (-6, 2).
I hope this helps!
pls ❤ and mark brainliest pls!
given m||n, find the value of x
Answers
Answer:
x=16
Step-by-step explanation:
The angles indicated are alternate exterior angles and alternate exterior angles are equal when the lines are parallel
5x+28 = 7x-4
Subtract 5x from each side
5x+28 -5x = 7x-4-5x
28 = 2x-4
Add 4 to each side
28+4 = 2x-4+4
32 = 2x
Divide by 2
32/2 = 2x/2
16 =x
Step-by-step explanation:
(5x+28)=(7x-4)
2x=32
x=16
Which of the following is a rational number?
square root 97
square root 98
square root 99
square root 100
Answers
Answer:
[tex]\sqrt{100}[/tex] is a rational number
Step-by-step explanation:
[tex]\sqrt{97}=9.848857.....\\\\\sqrt{98}=\sqrt{2*7*2}=2\sqrt{7}\\\\\sqrt{99}=\sqrt{3*3*11}=3\sqrt{11}[/tex]
Square root of all prime numbers are irrational numbers
12 flowers are planted in a squared garden.How many garden are needed for this purpose?
Answers
answer:
tell us why the other gardens are needed
4.32/3.6=
please help soon!!
Answers
Answer:
if this is division it's 1.2.
Step-by-step explanation:
just divide it of its division if not sorry
Answer:
1.2
Step-by-step explanation:
a wall of a building is 36 inches wide. sixteen inches is concrete, 14 inches is brick, and 6 inches is limestone. what fraction of the wall is brick?
Answers
Answer:
878
Step-by-step explanation:
that is because i know what i am doing.
