the shape alongside is one quarter of a circle with radius of 14 cm. find the length of arc AB ,perimeter of the figure , area , area of triangle AOB , area of shaded segment.
Answers
Answer:
1) The length of the arc AB is approximately 21.99 cm
2) The perimeter of the figure is approximately 49.99 cm
3) The area of the figure is approximately 153.938 cm²
4) The area of the right triangle ΔAOB is 98 cm²
5) The area of the shaded segment is approximately 55.938 cm²
Step-by-step explanation:
The given parameters are;
The radius of the circle from which we have the quarter circle, r = 14 cm
Therefore, we have;
The length of segment OA = The length of segment OB = r = 14 cm
1) The length of the arc AB = 1/4 × The circumference of the circle with radius 14 cm and center O
The length of the arc AB = 1/4 × 2 × π × r = 1/4 × 2 × π × 14 c m= 7·π cm ≈ 21.99 cm which is approximately 22 cm, to the nearest whole number
2) The perimeter of the figure = The length of the arc AB + The length of segment OA + The length of segment OB
∴ The perimeter of the figure = 7·π cm + 14 cm + 14 cm ≈ 49.99 cm which is approximately 50 cm, to the nearest whole number
3) The area of the figure (sector AOB) = The area of the quarter of a circle = π × r²/4 = π × (14 cm)²/4 = 49·π cm² ≈ 153.938 cm²
4) Whereby we have arc AB and segment OA and OB form a quarter (1/4) of a circle, we have;
∠AOB = 360°/4 = 90°
Therefore, ΔAOB is a right triangle
The base length of the right triangle ΔAOB (is taken as being) = Segment OA = 14 cm
The height of the right triangle ΔAOB (is taken as being) = Segment OA = 14 cm
The area of the right triangle ΔAOB = 1/2 × The base length × The height
∴ The area of the right triangle ΔAOB = 1/2 × 14 cm × 14 cm = 98 cm²
The area of the right triangle ΔAOB = 98 cm²
5) The area of the shaded segment = The area of the quarter of a circle (Sector OAB) - The area of the triangle ΔAOB
The area of the quarter of a circle = 49·π cm² ≈ 153.938 cm²
∴ The area of the shaded segment = 49·π cm² - 98 cm² ≈ 55.938 cm²
The area of the shaded segment ≈ 55.938 cm²
The area of the shaded segment is approximately 55.938 square centimeters.
The length of the arc AB is approximately 21.991 centimeters.
The perimeter of the figure is approximately 49.991 centimeters.
The area of triangle AOB is 98 square centimeters.
The area of the circle segment is approximately 153.938 square centimeters.
Procedure - Area of the shaded segmentThe area of the shaded segment ([tex]A[/tex]), in square centimeters, is obtained by subtracting the area of the triangle from the area of the circle quarter, that is:
Area of the shaded segment[tex]A = \frac{\pi\cdot r^{2}}{4}-\frac{1}{2}\cdot \left(\frac{\sqrt{2}}{2}\cdot r \right)\cdot \left(\sqrt{2}\cdot r\right)[/tex]
[tex]A = \frac{\pi\cdot r^{2}}{4}-\frac{1}{2}\cdot r^{2}[/tex]
[tex]A = \left(\frac{\pi}{4}-\frac{1}{2} \right)\cdot r^{2}[/tex] (1)
If we know that [tex]r = 14\,cm[/tex], then the area of the shaded segment is:
[tex]A = \left(\frac{\pi}{4}-\frac{1}{2} \right)\cdot (14\,cm)^{2}[/tex]
[tex]A \approx 55.938\,cm^{2}[/tex]
Where [tex]r[/tex] is the radius of the circle segment, in centimeters.
The area of the shaded segment is approximately 55.938 square centimeters. [tex]\blacksquare[/tex]
The length of the arc AB ([tex]s[/tex]) is determined by definition of circular arc:
Length of the arc AB[tex]s = \frac{\pi}{2} \cdot r[/tex] (2)
If we know that [tex]r = 14\,cm[/tex], then the length of the arc AB is:
[tex]s = \frac{\pi}{2} \cdot (14\,cm)[/tex]
[tex]s \approx 21.991\,cm[/tex]
The length of the arc AB is approximately 21.991 centimeters. [tex]\blacksquare[/tex]
The perimeter of the figure ([tex]p[/tex]), in centimeters, is the sum of the arc AB and the two legs of the right triangle, that is:
Perimeter of the figure[tex]p = \frac{\pi}{2}\cdot r + 2\cdot r[/tex]
[tex]p = \left(\frac{\pi}{2} + 2 \right)\cdot r[/tex] (3)
If we know that [tex]r = 14\,cm[/tex], then the perimeter of the figure is:
[tex]p = \left(\frac{\pi}{2} + 2 \right)\cdot (14\,cm)[/tex]
[tex]p \approx 49.991\,cm[/tex]
The perimeter of the figure is approximately 49.991 centimeters. [tex]\blacksquare[/tex]
The area of the triangle ([tex]A[/tex]) was used in the first part of this question and we proceed to extract it below:
Area of triangle AOB[tex]A = \frac{1}{2}\cdot r^{2}[/tex] (4)
If we know that [tex]r = 14\,cm[/tex], then the area of the triangle AOB is:
[tex]A = \frac{1}{2}\cdot (14\,cm)^{2}[/tex]
[tex]A = 98\,cm^{2}[/tex]
The area of triangle AOB is 98 square centimeters. [tex]\blacksquare[/tex]
The area of the circle segment ([tex]A[/tex]) was used in the first part of this question and we proceed to extract it below:
Area of circle segment[tex]A = \frac{\pi\cdot r^{2}}{4}[/tex] (5)
If we know that [tex]r = 14\,cm[/tex], then the area of the circle segment is:
[tex]A = \frac{\pi\cdot (14\,cm)^{2}}{4}[/tex]
[tex]A \approx 153.938\,cm^{2}[/tex]
The area of the circle segment is approximately 153.938 square centimeters. [tex]\blacksquare[/tex]
To learn more on circles, we kindly invite to check this verified question: https://brainly.com/question/11833983
Related Questions
Please help! It's an image.
The functionf(x)is shown in the graph.
What is the equation forf(x)?
Enter your answer in the box.
f(x)=
Answers
Answer:
y = 0.714 x -5
Step-by-step explanation:
at x =0, y = -5, means the constant is -5
at x= -7 y= -8,
-8= -7a -5
a=0.714
y = 0.714 x -5
Write an equation of the line passing through the point (2, 10) that is perpendicular to the line 2x+y=17.
Answers
Answer:
y = 0.5x + 9
Step-by-step explanation:
What we know:
An equation with the point (2,10) passing through it is perpendicular to the equation 2x+y=17.
The root of 2x+y=17 is (8.5, 0).
The two equations intersect at (3.2, 10.6)
Let's check if 3.2 and 10.6 work for 2x+y=17.
2(3.2) + 10.6 = 17
6.4 + 10.6 = 17, which is true.
Let's try y = 0.5x + 9, to see if we get the same output as the earlier equation.
y = 0.5(3.2) + 9
y = 1.6 + 9
y = 10.6, so 3.2 as x does work.
As a result, the perpendicular equation is y = 0.5x + 9.
The average human fingernail grows at a rate of 3.47 millimeters per month. One millimeters = 0.1 centimeters. How much in centimeter, would the average human fingernail grown in one year?
Answers
Answer:
4.164 cm
Step-by-step explanation:
Given that:
Growth of an average human fingernail = 3.47 mm per month
One mm (millimeter) = 0.1 cm (centimeter)
To find:
Growth of an average human fingernail in one year = ?
Solution:
Here, we are given the growth for one month.
There are 12 months in an year, so growth over an year can be found by adding the growth of one month for 12 times.
Growth in one year = 3.47 mm + 3.47 mm+ ..... 12 times
Growth in one year = 12 \times 3.47 mm = 41.64 mm
In millimeters, the growth of an average human fingernail = 41.64 mm
Let us convert it into centimeters by multiplying it with 0.1.
Therefore growth in centimeters = 41.64 mm [tex]\times[/tex] 0.1 = 4.164 cm
please help its the last one i need ! Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
Answers
Answer:
See explanation
Step-by-step explanation:
The first option (4t - 8/5)... equals 16/3 t -23/5 (the fourth option in the first row)
The second option 7t - 22 (still in the first row) equals 3(3t-4)...(the third option in the second row)
The third option (still in the first row) 5(2t+1)... equals 3t + 33 (the final option in the second row)
The two options in the second row to the left equal each other
-11/4 t + 36 = (-9/2t + 3)+(7/4t + 33)
How do you write a slope parallel to a line?
Answers
Answer:
slope is m. Parallel means it has the same slope as the line it's parallel to. Let's say the slope of line 1 is 3, and your y intercept is 12. The equation would then be y = 3x + b and b would be 12 bc x would be 0 at y intercept making the equation become y = (0)x+b and for y to be 12, b has to be 12 in this case. So y = 3x + 12
Josh runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Answers
Answer:
6 / 55 = x / 44
44*6/55= x
x = 4.8 miles
Step-by-step explanation:
Laila is setting up a conical tent in the backyard. The height of the tallest part of the tent is 7 feet. The inside of the tent has a volume of 56 cubic feet. How many square feet are covered by the base of the tent?
Answers
Answer: 24
Step-by-step explanation:
I got it right on edge
Answer:
Answer is 24
Step-by-step explanation:
ywwww :)
#DJPP
In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle PNO = (x+14)^{\circ}m∠PNO=(x+14) ∘ , \text{m}\angle OPQ = (5x-2)^{\circ}m∠OPQ=(5x−2) ∘ , and \text{m}\angle NOP = (x-1)^{\circ}m∠NOP=(x−1) ∘ . Find \text{m}\angle OPQ.M∠OPQ.
Answers
Answer:
<OPQ = 23 degrees
Step-by-step explanation:
Given
Interior angles m∠PNO=(x+14) and m∠NOP=(x−1)
Exterior angle = m<OPQ = (5x-2)
The sum of interior angles is equal to the exterior angle, that is;
m∠PNO+m∠NOP = m<OPQ
x+14 + x-1 = 5x-2
2x + 13 = 5x-2
Collect like terms;
2x-5x = -2-13
-3x = -15
x = 15/3
x = 5
Get <OPQ
<OPQ = 5x - 2
<OPQ = 5(5)- 2
<OPQ = 25-2
<OPQ = 23 degrees
In a new necklace, the ratio of star-shaped beads to moon-shaped beads is 5 to 2. If the necklace has 20 star shaped beads, how many total beads are on the necklace? Explain.
Answers
Answer:
28
Step-by-step explanation:
In the ratio:
star-shaped beads = 5
moon-shaped beads = 2
total number of beads = 5 + 2 = 7
ratio of star-shaped beads to total number of beads = 5:7
star-shaped beads = 20
Let x = total number of beads.
20/x = 5/7
Cross multiply.
5x = 20 * 7
Divide both sides by 5.
x = 4 * 7
x = 28
Answer: 28
Answer the Point-slope equation with line for given point and have the slope given
(4,-3),m=-1
Answers
Answer:
y + 3 = - (x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 1 and (a, b) = (4, - 3) , then
y - (- 3) = - 1 (x - 4) , that is
y + 3 = - (x - 4)
Isolate k
C= 8+g∙k
How do you Isolate K by itself
Answers
k=(C-8)/g
Explanation:
Since our goal is to isolate k, we would have k on one side of the equal sign and everything else we move to the other. We do this by performing inverse operations to both sides (ex. The inverse of adding is subtracting and the inverse of multiplying is dividing).
C=8+gk
Subtract both sides by 8
C-8=8+gk-8
C-8=gk
Divide both sides by g
(C-8)/g=gk/g
(C-8)/g=k
k=(C-8)/g
I hope this helps!
What is the simplified form of the expressions?
a. −6a2b−1
b. 5/y−3
Answers
Not sure if the answer is correct
y=-x Identify the slope and y-intercept
Answers
Answer:
57
Step-by-step explanation:
the number with the equation
Answer:
Slope: m = -1 y-intercept: b = 0Step-by-step explanation:
slope-intercept form of equation: y = mx + b
wherae m is the slope and b is the y-intercept
So:
y = -x
y = -1x + 0 ⇒ m = -1 b = 0
the pta wants to cover the wet areas of the trail with wood chips. they find that one bag of wood chips covers 3 1/2-yard section of the trail. if there is a wet section of the trail that is approximately 50 1/4 yards long, how many bags of wood chips are needed to cover the wet section of the trail?
PLEASE THIS IS DUE IN 1 HOUR
Answers
please help me on this
Answers
9514 1404 393
Answer:
y = 25, 17, 13, 5 . . . . (top-down order)
Step-by-step explanation:
Put the values of x in the expression for y and do the arithmetic.
y = 29 - 4×1 = 25
y = 29 - 4×3 = 17
y = 29 - 4×4 = 13
y = 29 - 4×6 = 5
5x + 10y > 40
Need help with this it says to graph but I know how to graph I just need help on simplifying the equation.
Answers
Answer:
x > -2y + 8
Step-by-step explanation:
In order for the parallelogram to be a rectangle x=
Answers
Answer:
x = 2
Step-by-step explanation:
Set the two equations 13x+34 and 10x+10 together to add up to 90 on the right which should look like this 13x + 34 + 10x + 10 = 90. Combine the two x-values to get 23x and the two other numbers to get 44. Your equation should now be 23x + 44 = 90. Subtract 44 on both sides to get this equation 23x = 46. Divide 23 on both sides to get your x value which is 2.
Answer:
X is equal to 2
Step-by-step explanation:
90 = 13x + 34 + 10x + 10
Combine Like Terms:
90 = 23x + 44
Subtraction Property of Equality:
90 - 44 = 23x + 44 - 44 ---> 46 = 23x
Division Property of Equality:
46 ÷ 23 = 23x ÷ 23 ---> 2 = x
Check Your Work:90 = 13x + 34 + 10x + 10
Fill In Variables:
90 = 13(2) + 34 + 10(2) + 10
90= 26 + 34 + 20 + 10
90 = 60 + 30
90 = 90
I need help with this .please help me
Answers
Answer:
Step-by-step explanation:
Upper left
On the number line below, P represents a number. What is the value of the opposite of that number?
Answers
The physical education teacher assigns each student a number from 1 to 100 and uses a
computer to randomly generate a list of 30 numbers to select the students for the
sample. What type of sampling is being used?
Answers
Answer:
Simple random sampling
Step-by-step explanation:
The type of sampling used here is simple random sampling(SRS) because SRS is defined as the sampling technique where a group of subjects known as sample are selected for study from a larger group known as population. Thereafter, each individual will be entirely chosen by chance and then each member of the population will have an equal opportunity of being included in the sample.
Thus question given corresponds to this definition.
The graph below displays the relative frequency distribution for X, the total number of dogs and cats owned per household, for the households in a large suburban area. For instance, 14 percent of the households own 2 of these pets.
Number of dog/ Relative Frequency
0- 0.36
1- 0.24
2- 0.14
3-0.09
4- 0.07
5- 0.04
6-0.04
7- 0.02
(a) According to a local law, each household in this area is prohibited from owning more than 2 of these pets. If a household in this area is selected at
random, what is the probability that the selected household will be in violation of this law? Show your work.
(b) If 12 households in this area are selected at random, what is the probability that exactly 3 of them will be in violation of this law? Show your
work.
(c) The mean and standard deviation of X are 1.65 and 1.851, respectively. Suppose 100 households in this area are to be selected at random and X , the
mean number of dogs and cats per household, is to be computed. Describe the sampling distribution of X , including its shape, center, and spread.
Answers
Answer:
maybe 7 divided by 2 or o.o2 divided by 7
Step-by-step explanation:
Duke and Mary collect stamps. Duke has 1,364 stamps, and Mary has 1,808 stamps. How many stamps do they have in all?
A.
3,152
B.
3,162
C.
3,172
D.
3,272
Answers
Answer:
Mary and Duke have 3,172 stamps altogether
1,364 + 1,808 = 3,172
An animal park has lions tigers and zebras.20% of the animals are lions and half the animals are zebras.If there are 120 animals at the park , how many tigers are there?
Answers
Answer:
40
Step-by-step explanation:
20% of 120 which is 24 are lions
half of the animals which is 120 ÷ 2 is 60 for the zebra
therefore, 60+24 is 84
120 - 84 is 36
what is the value of f(5) in f(x)=-2(x+1)
Answers
Answer:
-12
Step-by-step explanation:
simplify:
4 x - -5х + 3x- x+2х - 7х
Answers
Answer:
6x
Step-by-step explanation:
4 x - -5х + 3x- x+2х - 7х
Combine like terms so, so since all are the same you just do the operation they want u to do..
4x + 5x= 9x
9x + 3x = 12x
12x - x = 11x
11x + 2x= 13x
13x - 7x = 6x
Hint: 2 negatives make a postitive
Hint: in there is just an "x" there is always an invisible one in it... 1x
Hope this helped!
Tim has 80 coins in his piggy bank. Of these coins, 28 are nickels and the rest are quarters. What percent of the coins in the bank are quarters?
Answers
Answer:
65%
Step-by-step explanation:
Regina's father has 3 1/2 cups of pudding to divide equally among Regina and her 3 friends. How many cups of pudding does each person receive?
Answers
Answer:
The answer is .875 cups of pudding for each person
Step-by-step explanation:
To solve this problem you will have to divide 3 1/2 among 4 people.
3 1/2 divided by 4 is equal to .875
someone please help me with this !
Answers
Step-by-step explanation:
The coordinates of Point S(1,2)
The coordinates of point T(7,5)
length of ST=√(7-1)²+(5-2)²
|ST|=√36+9
|ST|=√45=3√5
Answer:
a) S(1,2) T(7,5)
b)3√5 = 6.7 ( approximately)
Step-by-step explanation:
Look at the picture below.
Hope you find this helpful
a) 34y=15=
b) -58y=20=
c) -x=23=
d) -51=-y=
Answers
a) 34y=15
=> y= 34-15
=> y = 19
b) -58y=20
=> y= -58-20
=> y = -78
c) -x=23
=> -1x=23
=> x= 23+1
=> x= 24
d) -51= -y
=> -51= -1y
=> y= -51+1
=> y= -50
Hope it helps!
If Rachel can reach 91 inches high, AC = 2x, and BC= 5x+7, how tall is the object she's
reaching for (AC)?
a) 24 inches
b) 13 inches
c) 67 inches
d) 91 inches
Answers
Answer:
d 91
Step-by-step explanation:
she is reaching it perfectly at this height in the problem, its super easy