Answers
Answer:
a) 220.17 cm
b) 2127.12 cm²
Step-by-step explanation:
perimeter = circumference
it is the sum of the inner and the outer arc and the 2 side lines of 25.
we know a full circle has 360 degrees. but we only look at a segment of a circle of 150 out of the total of 360 degrees.
the circumference of a circle is
C = 2×pi×r
the 150 degree part is then
C = 2×pi×r×150/360 = 2×pi×r×15/36 = pi×r×15/18 =
= pi×r×5/6
the radius of the inner circle is 20.
=>
Ci = pi×20×5/6 = pi×50/3
the radius of the outer circle is 20 + 25 = 45
Co = pi×45×5/6 = pi×75/2
so, the total perimeter/ circumference is
C = Ci + Co + 25 + 25 = pi×50/3 + pi×75/2 + 50
= pi×100/6 + pi×225/6 + 50 = pi×325/6 + 50 =
= 220.17 cm
the area of the shaded shape is the area of the large circle segment minus the area of the small circle segment.
the area of a circle is
A = pi×r²
the 150 degree part is then
A = pi×r²×150/360 = pi×r²×5/12
so, for the inner circle that is
Ai = pi×20²×5/12 = pi×400×5/12 = pi×100×5/3 = pi×500/3
for the outer circle that is
Ao = pi×45²×5/12 = pi×2025×5/12 = pi×10125/12 =
= pi×3375/4
so, the total area of the shaded shape is
A = Ao - Ai = pi×3375/4 - pi×500/3 = pi×(10125-2000)/12 =
= pi×8125/12 = 2127.12 cm²
Related Questions
this is the easiest question
Answers
Answer: [tex]3\dfrac{2}{6}\ h[/tex]
Step-by-step explanation:
Given
Rami practices his saxophone for [tex]\frac{5}{6}[/tex] hour on 4 day each week
So, for a week she practices around
[tex]\Rightarrow \dfrac{5}{6}\times 4\\\\\Rightarrow \dfrac{20}{6}[/tex]
Converting it into mixed fraction
[tex]\Rightarrow \dfrac{20}{6}=\dfrac{18+2}{6}\\\\\Rightarrow 3\dfrac{2}{6}\ h[/tex]
Answer:
33/100
Step-by-step explanation:
Which expression is equivalent to
Answers
Answer:
8x^12 y^3
Step-by-step explanation:
8x^12 y^3
The three planes given meet at a point. The planes are 3x+y-2z = 11, 4x-2y+z = -5, x+5y-4z = 33. The intersection is at what point? (Please explain.)
Answers
Answer:
(2, 7, 1)
Step-by-step explanation:
We have three equations, and using Gauss-Jordan Elimination, we can solve for x, y, and z
3x + y - 2z = 11
4x - 2y + z = -5
x + 5y - 4z = 33
We can start by taking out the z from all rows except one. To do this, we can work with the second row. I chose the second row because -5 is small and easy to add up with other numbers, and z has no coefficient in this row.
We can add 2 times the second row to the first row and 4 times the second row to the third row to get
11x - 3y = 1
4x - 2y + z = -5
17x -3y = 13
We then have the first and third rows having two variables. Since the y coefficients are the same, we can eliminate the y by adding the negative of the first row to the third row. Our result is then
11x - 3y = 1
4x - 2y + z = -5
6x = 12
From the third row, we can gather that x= 2. We can then plug that into the first row to get
22 -3y = 1
subtract 22 from both sides
-3y = -21
divide both sides by -3
y = 7
We can then plug our x and y values into the second row to get
4(2) - 2(7) + z = -5
8 - 14 + z = -5
-6 + z = -5
add 6 to both sides
z = 1
Our answer is thus (2, 7, 1)
An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles. To the nearest tenth of a degree, what was the angle of elevation?
Answers
Answer:
11.5 degrees
Step-by-step explanation:
For future reference trianglecalculator.net is very helpful
The angle of elevation to the nearest tenth of a degree is 11.54°.
What is an angle of elevation?An angle of elevation is defined as the angle between the slant horizontal line of an eye and the object in relation to the baseline called the adjacent.
In trigonometry, the angle of elevation can be determined by using the sine rule.
[tex]\mathbf{sin \ \theta = \dfrac{opp}{hyp} }[/tex]
[tex]\mathbf{sin \ \theta = \dfrac{5}{25} }[/tex]
[tex]\mathbf{ \theta =sin^{-1} (0.2)}[/tex]
[tex]\mathbf{ \theta =11.54^0}[/tex]
Learn more about the angle of elevation here:
https://brainly.com/question/88158
The tength of a picture frame is 12 cm more than twice the width. If the perimeter is 204cm, find the
dimensions (length and width) of the frame.
Answers
Answer:
30cm x 72 cm
Step-by-step explanation:
The perimeter is the measurements of all sides added together. Let's start by dividing the perimeter by 2, so we have the sum of the length and width. This gives us 102cm. Let's call the width x, and the length y. We know y is x times 2 plus 12. (2x + 12) So, we know [x + y = x + (2x + 12)]. So let's solve.
x + y = x + (2x + 12)
102 = x + (2x + 12)
102 = 3x + 12
102 - 12 = 3x + 12 - 12
90 = 3x
90/3 = 3x/3
30 = x
The width is 30cm.
John has 8 cards that spell the word H O M E W O R K. He shuffles them and then places them face down. Assume he returns the card on each occasion.
a) What is the probability that he will choose the letter O?
Answers
Answer:
1/4
Step-by-step explanation:
......................
Answers
Answer:
Value of opposite ∠2 = 120°
Step-by-step explanation:
Given question:
Quadrilateral inscribed in a circle
Value of ∠1 = 60°
Find:
Value of opposite ∠2
Computation:
In Quadrilateral inscribed in a circle, sum of opposite angle is 180
So,
Value of ∠1 + Value of ∠2 = 180°
60 + Value of ∠2 = 180
Value of ∠2 = 180 - 60
Value of ∠2 = 120
Value of opposite ∠2 = 120°
which of the following is equal square root of 9 x 4
Answers
Answer:
You didn't list any "of the following"
Here are some possible answers
√( 9 x 4) = 3 * 2
√( 9 x 4) = 6
Help me please thank u
Answers
Answer:
your answer to this question is C.
plsplspls help it's due today and is needed for reports. I'll brainlist you! just do the questions u know and leave the ones u don't idm I'll do it myself but at least do a few. it'll make my day:)
Answers
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
For all right triangles, the Pythagorean Theorem states:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the right triangle.
Therefore, we have (starting from the blanks):
[tex]x^2+576=676,\\x^2+576-676=676-676,\\x^2=100,\\x=\boxed{10}[/tex]
The train departs from Paris at 2028 and the journey takes 9 hours 10 minutes. Find the the train arrives in Milan
Answers
05:28 plus 10 minutes = 05:38
Answer= 05:38
Find the value of x.
Answers
Answer:
x = 29
Step-by-step explanation:
The three angles add to 90 degrees
x+3 + x-1 + x+1 = 90
Combine like terms
3x +3 = 90
Subtract 3 from each side
3x+3-3 = 90-3
3x = 87
Divide by 3
3x/3 = 87-3
x = 29
Answer:
x = 29
Step-by-step explanation:
The 3 angles sum to 90° , that is
x + 3 + x - 1 + x + 1 = 90
3x + 3 = 90 (subtract 3 from both sides )
3x = 87 ( divide both sides by 3 )
x = 29
(−7,−6)y(9,10)(-7,-6)y(9,10)
Answers
Answer:
i need more information to answer this question
Step-by-step explanation:
find the equation of a circle with a point at ( 10 , - 4 ) and a point at ( -2 , - 4 )
Answers
Answer:
Solution given:
letA=(10,-4)
B=(-2,-4)
centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]
radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units
we have
Equation of a circle is;
(x-h)²+(y-k)²=r²
(x-4)²+(y+4)²=36
or.
x²-8x+16+y²+8y+16=36
x²-8x+8y+y²=36-32
x²-8x+8y+y²=4
The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.
Answer:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
Step-by-step explanation:
the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter
since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle
remember midpoint formula,
[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]
let,
[tex] \displaystyle x _{1} = 10[/tex][tex] \displaystyle x _{2} = - 2[/tex][tex] \displaystyle y _{1} = - 4[/tex][tex] \displaystyle y _{2} = -4[/tex]thus substitute:
[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]
simplify addition:
[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]
simplify division:
[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]
so the centre of the circle is (4,-4)
since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is
[tex] \displaystyle r = 4 - ( - 2)[/tex]
simplify which yields:
[tex] \displaystyle\boxed{ r =6}[/tex]
recall the equation of circle
[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
we acquire that,
h=4k=-4r=6therefore substitute:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]
simplify:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
and we are done!
also refer the attachment
(the graph is web resource of desmos)
Pls I need help with this
Answers
Answer:
third side = 4
Step-by-step explanation:
third side is hypoenuse as it is opposite to 90 degree.
using pythagoras theorem
(perpendicular)^2 + (base)^2 = (hypotenuse)^2
2^2 + (2[tex]\sqrt{3[/tex] )^2 = hypotenuse^2
4 + 4*3 = hypotenuse^2
16 = hypotenuse^2
[tex]\sqrt{16}[/tex] = hypotenuse
4 = hypotensue
ONI
Write the following ratios in their simplest form:
100 minutes: 1-hours
2
15m: 1050cm
9min : 600seconds
125
(iv)
1000
efine the following terms
Common fraction
Answers
Answer:
1. 5 min : 3 min
2. 10 cm : 7 cm
3. 9 sec : 10 sec
Step-by-step explanation:
1. Since 60 minutes = 1 hour
Thus;
100 minutes : 60 minutes
10 minutes : 6 minutes
5 minutes : 3 minutes
The simplest form = (5:3) minutes
2. 100 cm = 1 m,
⇒ 15 m = 15 x 100 cm = 1500 cm
Thus;
1500 cm : 1050 cm
150 cm : 105 cm
30 cm : 21 cm
10 cm : 7 cm
The simplest form = (10:7) cm
3. 60 seconds = 1 minute
⇒ 9 minutes = 9 x 60
= 540 seconds
Thus;
540 seconds : 600 seconds
54 seconds : 60 seconds
9 seconds : 10 seconds
The simplest form = (9:10) seconds
4. A common fraction is one that has the same value on each side of an expression or equation.
Part A: Drag the factors of 45 and 75 into the correct boxes.
Part B: What is the greatest common factor of 45 and 75? Enter your answer in the box.
Answers
Answer:
3 x 5 is the gcf of 45 and 75. gcf(45,75) = 15.
Step-by-step explanation:
hope this helped! yw :}
find the slope of the line that contains 2,2 and -3, 4
Answers
Answer:
-2/5
Step-by-step explanation:
your answer is -2/5 because whenever you have two points you can go ahead and just do rise over run and the formula is y1-y2/x1-y1 now you can go ahead and label them so y1 is 2, y2 is 4, x1 is 2 and x2 is -3 and now plug everything in
2-4/2-(-3)
-2/5
Help me please help me please help me please !!!!!!!!!!!!!
Answers
Answer: y = 1/4x - 1.
Step-by-step explanation: This line has a slope (rise over run) of 1/4, and a y-intercept of -1. Plugging those values into slope-intercept form (y = mx + b) gives you the answer.
simplify
x2 + 6 − (3x2 − 2x − 5)
Answers
Answer:
- 2x² + 2x + 11
Step-by-step explanation:
Given
x² + 6 - (3x² - 2x - 5) ← distribute parenthesis by - 1
= x² + 6 - 3x² + 2x + 5 ← collect like terms
= - 2x² + 2x + 11
Answer:
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
x = 39°
Step-by-step explanation:
51° + 90° = 141°
180° - 141° = x
x = 39°
They often don't label the 90° angle, so watch out for that in the future
180 - 144 = 36
36°
Tom and friends went to the movie the show started at 2:30pm and ended at 4:15 how long did the movie last Well the movie lasted 1 hour and 45 mins hope this help
Answers
Answer:
You are correct, it is 1 hr 45 minutes since 2:30+30 = 3:00 and 1:15 + 3:00 = 4:15. 1:15+30 = 1:45.
Step-by-step explanation:
Do the surface area plzzz and u get 25 points and if u Dk don’t answer and no links
Answers
Answer:
184
Step-by-step explanation:
A = 2(wl+hl+hw) = 2 · (6 · 2 + 10 · 2 + 10 · 6) = 184
Answer:
SA = 184 m²
Step-by-step explanation:
The opposite faces of the cuboid are congruent , then surface area (SA) is
SA = 2(2 × 6) + 2(6 × 10) + 2(2 × 10)
= 2(12) + 2(60) + 2(20)
= 24 + 120 + 40
= 184 m²
The algebraic expression 6x² + 9x + 3 represents the area of a rectangle. What is the area of the
rectangle when x = 3 feet?
a. 51 square feet
b. 60 square feet
c. 66 square feet
d. 84 square feet
Answers
Which linear equation best fits the data ?
Answers
Answer:
[tex]{ \tt{slope = \frac{2 - 1.5}{40 - 60} }} \\ = - 0.025 \\ \\ { \tt{y = mx + c}} \\ 2 = ( - 0.025 \times 40) + c \\ c = 3 \\ { \bf{ y = - 0.025x + 3}}[/tex]
A rectangular field has perimeter 600 m and area 21600 m squared. Find the dimensions of the field.
Answers
Answer:
Let length be x and width be y
[tex]perimeter = 2(l + w) \\ 600 = 2(x + y) \\ x + y = 300 - - - (a) \\ \\ area = l \times w \\ 21600 = xy - - - (b) \\ from \: (a) : \\ y = 300 - x \\ \therefore21600 = x(300 - x) \\ 21600 = 300x - {x}^{2} \\ {x}^{2} - 300x + 21600 = 0 \\ (x - 180)(x - 120) = 0 \\ x = 180 \: \: or \: \: 120 \: m \\ \\ y = 120 \: \: or \: \: 180 \: m \\ \\ { \boxed{ length = 180 \: m}} \\ { \boxed{width = 120 \: m}}[/tex]
what is 5 pi over three raidans in degrees
Answers
Answer:
300 degrees
Step-by-step explanation:
5 pi/3
To change radians to degrees, multiply by 180/pi
5 pi/3 * 180/pi
5/3 * 180
5 * 60
300 degrees
the expanded form of 6,398 is
Answers
Answer:
The expanded form of 6,398 is 6000 + 300 + 90 + 8
the histogram on the left shows the number of hours students in an art class practiced drawing during one week.
Answers
Step-by-step explanation:
mmm Next no se...........
what additional information is needed to prove the triangles congruent by AAS
Answers
Answer:
pq=su
Step-by-step explanation:
its the only one that makes sense