The diagram shows the entrance to a tunnel.
The circular arc has a radius of 3m and center O.
AB is horizontal and angle AOB = 120°.
During a storm the tunnel filled with water, to the level shown by the shaded area in the diagram.
Calculate the shaded area.
Answers
Step-by-step explanation:
it filled up half the circle (up to the center point) - if we had a full circle. but a little bit is cut off (below AB).
what we see is that the shaded area is the sum of the area of the triangle AOB and 2 equally sized circle segment areas left and right of AOB.
since we are dealing with a half-circle, we have 180° in total. 120° are taken by AOB, so, that leaves us with 180-120 = 60° for both circle segments (so, one has an angle of 30°).
and 2×30° = 1×60°, so we can calculate the area of one 60° segment instead of two 30° segments.
AOB is an isoceles triangle (the legs are equally long, and therefore also the 2 side angles are equal).
the area of this triangle AOB is
1/2 × a × b × sin(C) = 1/2 × 3 × 3 × sin(120) =
= 3.897114317... m²
a circle segment area of 60° is 60/360 = 1/6 of the full circle area (as a full circle = 360°).
so, it's area is
pi×r² × 1/6 = pi×3²/6 = pi×3/2 = 4.71238898... m²
so, the total area of the shaded area is
3.897114317... m² + 4.71238898... m² =
= 8.609503297... m²
The area of the shaded portion of the circle is A = 8.61 m²
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the area of the shaded region be A
Let the radius of the circle be r = 3 m
The triangle ΔAOB is an isosceles triangle with side lengths = 3m
The area of the triangle ΔAOB = ( 1/2 ) x 3 x 3 x sin (120)
On simplifying the equation , we get
The area of the triangle ΔAOB = 3.897 m²
Now ,
There are 2 sectors , with sector angle = 30°
The area of the two sectors = 2 x ( 30/360 ) x π x 3²
On simplifying the equation , we get
The area of the two sectors = 2 x 2.357
The area of the two sectors = 4.714 m²
Now ,
The area of the shaded region of circle A = area of the two sectors + area of the triangle ΔAOB
Substituting the values in the equation , we get
The area of the shaded region A = 4.714 + 3.897
The area of the shaded region A = 8.611 m²
Therefore , the value of A is 8.611 m²
Hence , the area is 8.611 m²
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Related Questions
4x + y = 10
7x + 2y = 17
Answers
Answer:
x = 3, y = - 2
Step-by-step explanation:
By substitution method,
4x + y = 10 -------> equation 1.
7x + 2y = 17 -------> equation 2.
From equation 1,
y = 10 - 4x ------> equation 3.
Substitute equation 3 in 2,
7x + 2 ( 10 - 4x ) = 17
7x + 20 - 8x = 17
7x - 8x = 17 - 20
- x = - 3
x = 3
Substitute x = 3 in equation 1,
4 ( 3 ) + y = 10
12 + y = 10
y = 10 - 12
y = - 2
Hence,
x = 3
y = - 2
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pa brainliest kung ayaw, edi wag** char
i got the first part but cant figure out the second, help would be appreciated
Answers
Answer:
see explanation
Step-by-step explanation:
look at the explanation& answer photo
Ali graphs the function f(x) = –(x + 2)2 – 1 as shown.
On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 2, negative 1), and goes through (negative 1, 0). A vertical dashed line at (negative 2, 0) is parallel to the y-axis.
Which best describes the error in the graph?
The axis of symmetry should be x = –1.
The axis of symmetry should be x = 2.
The vertex should be a maximum.
The vertex should be (–2, 1).
Answers
Answer:
The axis of symmetry should be x = 2.
Step-by-step explanation:
I got it right on Edge.
Answer:
The axis of symmetry should be x = 2.
Step-by-step explanation it took the test
Please help simplify fractions
Answers
Answer:
this is easy the a sewer is 12
Find the missing length of the triangle.
Answers
Answer:
11 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] (Pythagorean Theorem)
[tex]a^{2}[/tex] + [tex]4^{2}[/tex] = [tex](12\frac{1}{3})^{2}[/tex] (square numbers)
[tex]a^{2}[/tex] + 16 = 152 [tex]\frac{1}{9}[/tex] (subtract 16, both sides
[tex]a^{2}[/tex] = 136 [tex]\frac{1}{9}[/tex] (square root both sides)
a = 11 [tex]\frac{2}{3}[/tex] or 11.66 repeating
How do you recognize if a binomial is a difference of perfect squares and how is the pattern used to factor the binomial?
Answers
Answer:
A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Step-by-step explanation:
A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.
A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Answer:
Step-by-step explanation:
An example is a^2 - b^2.
Also 64 - 49 (as 64 are both perfect squares).
The way to factor is by using the identity:
a^2 - b^2 = (a - b)(a + b) ( a + in one parentheses and - in the other)
Examples:
x^2 - 4y^2 = (x - 2y)(x + 2y) [ x is the square root of x^2 and 2y is square root of 4y^2)
144 - 16 = (12 - 4)(12 + 4)
9x^2 - 36y^2 = (3x - 6y)(3x + 6y)
PLEASE I NEED HELP!!! BRAINLIEST FOR THE FASTEST ANSWER
Answers
Hello!
[(4πr³)/3]/2
r = 7,5yd
[4 *3,14*7,5³/3]/2
=> 883, 125yds ³
Evaluate the expression if r = 1/6 r times r and then you multiply the answer by 3
Answers
Answer:
r = ⅙
⅙ × ⅙ = 0.03
0.03 × 3 = 0.09
Using your answer from #7, find the perimeter of the triangle.
Answer From #7: 9
Answers
Answer:
58
Step-by-step explanation:
x=9
3(9) + 1 + 4(9) -8 + (9) - 7 = 58
Please help i am confused
Answers
Answer: (4)
Step-by-step explanation:
The parts listed in the congruence statements don't correspond, so they aren't necessarily congruent.
Please Help I'm Confused.
Answers
Answer:
The last one
Step-by-step explanation:
Look at A and A'
It moved 4 units to the right and 1 unit down
The same with B, B' and C, C'
Each glass mug below has a radius of 2 inches and a height of 3.75 inches. If the mugs are
sold in sets of 4, find the total surface area of the mugs, not including
the handles.
Answers
Total surface area includes the area of the 2 bases and the area of the curve surface area this was found to be 289.064 square inches for all four mugs
Mensuration of SolidsGiven Data
Radius r = 2 inchesHeight h = 3.75 inchesNumber of mugs = 4Total surface area of cylinder = 2πr(r + h)
TSA of 1 mug = 2*3.142*2(2+3.75)
TSA of 1 mug = 12.568(5.75)
TSA of 1 mug = 72.266 square inches
if the total surface area of one mug is 72.266 square inches
hence the total surface area of 4 mugs will be
= 72.266*4
= 289.064 square inches
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Jake has 900 cm³ of material. He uses 14. 5 cm³ to make a right triangular prism. He wants to make a second prism that is a dilation of the first prism with a scale factor of 4. How much more material does Jake need in order to make the second prism? Select from the drop-down menu to correctly complete the statement. Jake needs an additional Choose. Cm³ of material to make the second prism.
Answers
A ratio shows the relation between two numbers. The amount of more material that is needed by Jake is 42.5 cm³.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the volume of the first prism is 14.5cm³, while the scale factor is 4. Since the scale factor is applicable to dimension, and volume is always the cube of three-dimension.
Therefore, the volume of the scaled prism will be the cube the of the volume of the first prism, which can be written as,
[tex]\rm \text{Volume of the Scaled prism}= (Scale\ factor)^3 \times \text{Volume of the first prism}[/tex]
Substitute the values,
[tex]\rm \text{Volume of the Scaled prism}= 4^3 \times 14.5 = 928\ cm^3[/tex]
Since, the volume of material with Jake is 900 cm³, while the material he has already used is 14.5 cm³, thus the volume of the material that is left with Jake is 885.5 cm³(900cm³-14.5cm³).
Now, since the material needed to make the scaled prism is 928 cm³, the amount of material that is with Jake is 885.5 cm³, therefore, the amount of the material that is needed by Jake to complete the scaled prism can be written as,
The Amount of more material Needed by Jake = Amount of material needed to make the scaled prism - Amount of material left with Jake
The Amount of more material Needed by Jake = 928 cm³ - 885.5 cm³
= 42.5 cm³
Hence, the amount of more material that is needed by Jake is 42.5 cm³.
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PLEASE HELP!!! will give brainlisest
Answers
Answer:
[tex]\sf \dfrac{x}{8}-22[/tex]
Explanation:
[tex]\rightarrow \sf \left(\dfrac{7}{8}x-4\right)-3\left(\dfrac{1}{4}x+6\right)[/tex]
remove parenthesis
[tex]\sf \rightarrow \dfrac{7}{8}x-4-\dfrac{3x}{4}-18[/tex]
expand
[tex]\rightarrow \sf \dfrac{7x}{8}-\dfrac{3x}{4}-22[/tex]
simplify
[tex]\rightarrow \sf \dfrac{x}{8}-22[/tex]
Answer:
[tex]\frac18x-22[/tex]
Step-by-step explanation:
Given expression:
[tex](\frac78x-4)-3(\frac14x+6)[/tex]
Expand:
[tex]\implies \frac78x-4-\frac34x-18[/tex]
Gather like terms:
[tex]\implies \frac78x-\frac34x-4-18[/tex]
Change 3/4 into eighths:
[tex]\implies \frac78x-\frac68x-4-18[/tex]
Combine like terms:
[tex]\implies \frac18x-22[/tex]
Use the function below to find f(-4).
fx) = 2^x
Answers
Answer:
1/16
Step-by-step explanation:
plug in -4 instead of the x.
if the exponent is negative it can be written as 1/2^4
so the answer is 1/16
please guys help me if u answer it correctly I will brainlist u
Answers
Answer:
1= 40, 25, 10
2= 9,375, 46,875, 234,375
3= 234, 729, 2,187
4= 192, 384, 768
Find the solution to the equation:
f(x)=x^2-4x+3
Please show work!
Answers
Answer:
UM make a graph if you want so yea
Step-by-step explanation:
[tex]\\ \rm\rightarrowtail x^2-4x+3[/tex]
Use quadratic formula
[tex]\\ \rm\rightarrowtail x=\dfrac{4\pm\sqrt{16-12}}{2}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{4\pm 2}{2}[/tex]
[tex]\\ \rm\rightarrowtail x=2\pm 1[/tex]
[tex]\\ \rm\rightarrowtail x=3,1[/tex]
Taylor's family took a road trip to Mount Rushmore. Taylor slept through the last 21% of the trip. If Taylor fell asleep after they had travelled 711 miles, what was the total length of the trip?
Answers
711=79%
711/1=79/100
711/79=9
9x100=900
the trip was 900 miles all together. you can check if your answer is right by multiplying 900 by 0.79. If it comes out to 711, you are right.
What is the measure of
Answers
Answer:
25
if j 25 L is going to be 25
i need help with this
Answers
Answer:
if c=1
then,
28-1×1×1+6=33
if c=2
then,
28-2×2×2+6=26
if c=3
then,
28-3×3×3+6=7
Expression: 28 - c^3 + 6
If c = 1...
28 - (1)^3 + 6
28 - 1 + 6
27 + 6
33
If c = 2...
28 - (2)^3 + 6
28 - 8 + 6
20 + 6
26
If c = 3...
28 - (3)^3 + 6
28 - 27 + 6
1 + 6
7
Hope this helps!
The roberts family is getting an inground circular pool with a radius of nine feet. The company needs to dig out an extra three feet all the way around the pool to have room for plumbing. What is the area of the grass that will be removed?
Answers
Answer:
197.92
Step-by-step explanation:
radius of bigger circle is 12 (9 + 3). Area of cirlce is Pi(R²)
12² is 144 so 144Pi
9² is 81 (for the inner circle) so 81Pi
144 - 8 is 63Pi which in decimal form is 197.92.
What is the volume of this cone? Use 3.14 for π and round your answer to the nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.
Answers
V = 1/3•pi•2•2•8
V = 33.49333333333333
V = 33.5 inches squared
Please Help Will GIve Brainlest! Locks in 1 Hour!
Answers
Answer:
-3.274
Step-by-step explanation:
attached
Hopes this helps
{please mark me brainiest}
You place some money in a savings account the savings account earns 2% simple interest. explain how you can find the interest earns after x years.
Answers
Because of this, you can plug in what you know to find your total amount in your account.
Convert the interest rate to a decimal. 2%=0.02
Answer:
A=P*0.02*x
where
A=Total amount of money in account ($)
P=Amount of money invested ($)
x=Time (yrs)
Question is in the picture:
Answers
Answer:
its a cause you divide 6 on both sides and 48 divided by 6 is 8 and since its a greater than symbol and the numbers werent negative its gonna be a
Step-by-step explanation:
Answer:
A ) the Value of t is greater than 8
Step-by-step explanation:
6t>48
t>48/6
t>8
I need help!!!!
The square below has the given side lengths. x is positive
Answers
Answer:
Value of X: X=2
Length of One Side: 31
Area: 961u^2
Perimeter: perimeter = 124
Step-by-step explanation:
Set the sides equal to each other, simplify and then use quadratic equation. One result is positive and the other is negative, shape's sides have to be positive so use the positive value for X.
Answer:
See below, please
Step-by-step explanation:
This square
[tex]3 {x}^{2} + 6x + 7 = 2 {x}^{2} - 2x + 27[/tex]
[tex](3 {x}^{2} - 2 {x}^{2} ) + (6x + 2x) + (7 - 27) = 0[/tex]
[tex] {x}^{2} + 8x - 20 = 0[/tex]
[tex](x + 10) \times (x - 2) = 0[/tex]
Hence,
[tex]x1 = 2[/tex]
[tex]x2 = - 10[/tex]
Because x is positive, So,
[tex]x = 2[/tex]
Then we know
The length of one of the sides
[tex] = 3 {x}^{2} + 6x + 7 = (3 \times {2}^{2}) + (6 \times 2) + 7 = (3 \times 4) + 12 + 7 = 31[/tex]
The area of the square
[tex] = {31}^{2} = 961[/tex]
The perimeter of the square
[tex] = 31 \times 4 = 124[/tex]
Evaluate the expression 2bc for b = 1.5 and c = 5.
Answers
Answer:
15
Step-by-step explanation:
To answer this, simply input your values into the equation:
Since b is given as 1.5, and c is given as 5, you put it into the calculation 2bc
so, you would do 2x1.5x5
which is equal to 15
Answer: 15
Step-by-step explanation: Multiply it. You have 2bc, b=1.5, c=5 plug those values into 2bc. You should get 2(1.5)(5) and that'll be 15.
Unit 4: Congruent Triangles Homework 2: Angles of Triangles
Answers
The value of the third angle that can be found in the information given about the congruent triangles will be 45°.
How to solve the triangle?From the complete information, the angles that are given in the triangle are 76° and 59°.
It should be noted that the value of the total angles that are in a triangle is 180°. Therefore, the value of the last angle will be:
= 180° - (76° + 59°)
= 180° - 135°
= 45°
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how many different 3 digit numbers can be formed using the digits 9,3,4,7 and 6? assume no number can be used more than once
Answers
Answer:
57
Step-by-step explanation:
976/974/973/967/964/963/947/946/943/937/936/934/796/794/793/769/764/763/749/746/743/739/736/734/697/694/693/679/674/673/649/647/643/639/637/634/497/496/493/479/476/473/439/437/436/397/396/394/379/376/374/369/367/364/349/347/346
Which expression is equivalent to cosine (startfraction pi over 2 endfraction r) for all values of r?
Answers
The trigonometric expression cos (π/2 + r) is equivalent to the negative of sin r. Then the correct option is C.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
The trigonometric expression is given below.
[tex]\cos (\dfrac{\pi}{2} + r)[/tex]
We know that the formula
[tex]\cos (\dfrac{\pi}{2} + r) = -\sin r[/tex]
Thus, the cos (π/2 + r) is equivalent to the negative of sin r.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Answer:
C?
Step-by-step explanation:
, someone confirm