please help i need this done by the next hour and i’m failing and struggling
3. The sector of a circle is shown below. It has a radius of 10 centimeters and a central
angle of 51 degrees. Find to the nearest tenth in both cases:
(a) the length of AB in centimeters(b) the area of the sector in square centimeters
1. An arc has a central angle of 1.8 radians and a radius of 20 inches. a. Determine the length of AB in inches
b. to the nearest degree what is the measure of
Answers
Answer:
Question 3)
[tex]\stackrel{\frown}{AC}=36\text{ inches}[/tex]
[tex]\angle BCA\approx103^\circ[/tex]
Question 1)
[tex]\stackrel{\frown}{AB}\approx 8.9\text{ cm}\\[/tex]
[tex]A\approx44.5\text{ cm}^2[/tex]
Step-by-step explanation:
Question 3)
We are given that the central angle is 1.8 radians and has a radius of 20 inches.
Part A)
The formula for arc length in terms of radians is given by:
[tex]s=r\theta[/tex]
Where s is the arc length, r is the radius, and θ is the angle in radians.
In this case, r is 20 and θ is 1.8. Hence, the arc length is:
[tex]\stackrel{\frown}{AC}=(20)(1.8)=36\text{ inches}[/tex]
Part B)
∠BCA is the central angle that measures 1.8 radians.
We can convert radians to degrees using the following formula:
[tex]\displaystyle d=\theta\cdot\frac{180^\circ}{\pi}[/tex]
Where d is the measure in degrees, and θ is the measure in radians.
Therefore:
[tex]\displaystyle d=1.8\cdot\frac{180^\circ}{\pi}\approx103.1324\approx103^\circ[/tex]
Question 1)*
Part A)
We will use the arc length formula in degrees given by:
[tex]\displaystyle s=2\pi r\cdot \frac{\theta^\circ}{360}[/tex]
Where r is the radius and θ is the angle measured in degrees.
We have a radius of 10 centimeters and a central angle of 51°. Therefore, our arc length is:
[tex]\displaystyle \stackrel{\frown}{AB}=2\pi(10)\cdot\frac{51}{360}=20\pi\cdot\frac{51}{360}\approx8.9\text{ cm}[/tex]
Part B)
We will use the formula for the area of a sector in degrees given by:
[tex]\displaystyle A=\pi r^2\cdot\frac{\theta^\circ}{360}[/tex]
So, we will substitute 10 for r and 51 for θ. Hence, the area of the sector is:
[tex]\displaystyle A=\pi (10)^2\cdot \frac{51}{360}=100\pi\cdot\frac{51}{360}\approx44.5\text{ cm}^2[/tex]
*Notes:
For this question, it is possible and completely fine for us to convert 51° to radians and then use the formulas in terms of radians.
Answer:
(1). 36 inch. , 103° ; (2). 8.9 cm , 44.5 cm² ;
Step-by-step explanation:
1).
(b). m∠BCA = 1.8 rad. × [tex]\frac{180}{\pi }[/tex] ≈ 103° ( π ≈ [tex]\frac{22}{7}[/tex] )
(a). C = 2 π r , the length of arc AB = ( 2 × [tex]\frac{22}{7}[/tex] × 20 ) ÷ 360° × 103.132° ≈ 36 inches
3).
(a). The length of arc AB = ( 2 × [tex]\frac{22}{7}[/tex] × 10 ) ÷ 360° × 51° ≈ 8.9 cm
(b). A = π r² , the area of the sector = ( [tex]\frac{22}{7}[/tex] × 10² ) ÷ 360° × 51° ≈ 44.5 cm²
Related Questions
What is the least positive integer divisible by each of 1, 3, 5, and 7?
Answers
Answer:
105
Step-by-step explanation:
You need the least common multiple of the 4 numbers. Since 3, 5, and 7 are prime numbers, the answer is their product.
LCM = 3 * 5 * 7 = 105
The least positive integer that is divisible by each of 1, 3, 5, and 7 is 105.
In order to solve the question, we simply have to find the lowest common multiple that is applicable to all the numbers that are given on the question.
In this case, the lowest common multiple can be gotten by multiplying the numbers be high will be:
= 1 × 3 × 5 × 7 = 105
Therefore, the number is 105.
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Consider a function f(x) such that f(5x) =x-5/5x-1. Find f(x) and hence write down the domain of f(x).
Answers
Answer:
[tex]f(x) = \frac{x - 25}{5x - 5}[/tex]
Domain: [tex]x \ne 1[/tex]
Step-by-step explanation:
Given
[tex]f(5x) = \frac{x - 5}{5x - 1}[/tex]
Required
Determine f(x) and its domain
To determine f(x), we replace 5x with x in f(5x)
So, we have:
[tex]f(5x) = \frac{\frac{5x}{5} - 5}{5x - 1}[/tex]
[tex]f(x) = \frac{\frac{x}{5} - 5}{x - 1}[/tex]
Take LCM
[tex]f(x) = \frac{\frac{x - 25}{5}}{x - 1}[/tex]
[tex]f(x) = \frac{x - 25}{5} * \frac{1}{x-1}[/tex]
[tex]f(x) = \frac{x - 25}{5x - 5}[/tex]
To get the domain, we set the denominator as
[tex]5x - 5 \ne 0[/tex]
[tex]5x \ne 5[/tex]
[tex]x \ne 1[/tex]
What is the value of x^2 - 3y + 5x + 2 whenx = 7 and y = 4?
Answers
Answer:
74
Step-by-step explanation:
[tex]x^2 - 3y + 5x + 2 \\ \\ = {7}^{2} - 3(4) + 5(7) + 2 \\ \\ = 49 - 12 + 35 + 2 \\ \\ = 74[/tex]
Plz someone help I beggggg
Answers
Answer:
25100 i believe would be the answer
Step-by-step explanation:
A sweater is $43. It is on sale for 20% off. What is the final price? $34.40 $47 $8.60
Answers
43 - 8.6 = 34.40
Solution: $34.40
Answer:
34.40
Step-by-step explanation:
43×0.2 = 8.60
43-8.60= 34.40
PLS ANSWER FAST!!!
a rate is a ratio that compares
A) a part to a part
B) a part to a whole
C) quantites with different units
D) quantities with the same units
Answers
Answer:
c
Step-by-step explanation:
A rate is a ratio that compares quantites with different units.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
A rate is a comparison of two quantities that have different units, such as miles per hour, dollars per gallon, or meters per second.
A rate can be expressed as a fraction or a ratio, with the numerator representing the quantity being measured and the denominator representing the unit of measurement.
Hence, a rate is a ratio that compares quantites with different units.
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A car is traveling 60 miles per hour. How long will it take to travel 240 miles?
Answers
Answer:
4 hours
Step-by-step explanation:
240 / 60 = 4
Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 27 miles at a speed of 9 mph, while Bob's
motorboat traveled 36 miles at a speed of 12 mph. For how long were Niles and Bob traveling?
OA
2 hours
ОВ.
6 hours
OC.
5 hours
OD. 3 hour please help me with this
Answers
Answer:
D- 3 hours long they were traveling
Step-by-step explanation:
27÷ 9= 3
36÷ 12= 3
The sum of two numbers is 125. Their difference is 47. The two numbers are:
39 and 86.
40 and 85.
47 and 78.
None of these choices are correct.
Answers
Answer:
39 and 86.
Step-by-step explanation:
39 and 86 equal 125 when added. When 47 is subtracted from 86 you get 39.
Calculator Item 2 is unpinned. Click to pin. Mrs. Pitts wrote the volume formula as "V=1/3 Bh. What does "B" represent? A: The radius of the base B: The circumference of the base C: The diameter of the base. D: The area of the base.
Answers
Answer:
D: The area of the base.
Step-by-step explanation:
The volume of a triangular based pyramid is represented by the formula given that the question as:
V = 1/3BH
where B = Base area of the triangular based pyramid
H = Height of the triangular based pyramid.
Hence, option D is correct
B = The area of the base.
Solve the following equation for I. A = 2nr + nrl. Explain each step please
Answers
question: How many unites down would triangle RST need to be translated in order for the coordinates of R to be (-3, 0)
Answers
please help. i’ll give brainliest
Answers
Answer: What is the question?
Step-by-step explanation:
What is the question?
Calculate the area of the shaded region
Answers
Area of the rectangle = (18 m) (12 m) = 216 m²
Area of the triangle cutout = 1/2 (7 m) (9 m) = 63/2 m²
Area of the shaded region = 216 m² - 63/2 m² = 369/2 m² = 184.5 m²
Which of the following statements can be used to show that today's high temperature, 12°F, is warmer than yesterday's high temperature, which was -15°F?
-15°F = 12°F
-15°F ≥ 12°F
-15°F 72°F
Answers
Answer:
-15°F < 12°F
Step-by-step explanation:
Hope it helps you in your learning process.
she has 3 bags of flour and 2 smaller bags with 0.75 kg and a bigger bag that ha 1.14 how much flower does she have in total
Answers
Answer:
3(1.14) + 2(0.75)
3.42 + 1.5
4.92 kg of flour
I need explanation + answer.
Do not write the answer without explanation, please.
thanks in advance!
Answers
Answer:
C. 22,400.
Step-by-step explanation:
62.9% = 0.629 as a decimal fraction.
Total number of employees in small businesses in the county
= 270 * 132.
So the estimated number with less than $1000 savings
= 270 * 132 * 0.629
= 22,417.
Find the values of X and Y
Answers
Answer:
x=90, angle bisector theorem
y=43,
90+47+y=180
=137+y=180
y=43
The difference of two numbers is 308. The smaller of the numbers is 730. What is
the other number?
Answers
Answer:
1038
Step-by-step explanation:
730+308= the big number
Answer:
1038
Step-by-step explanation:
Write down the solution to these simultaneous equations.
y = 2x + 1
y=0.5x – 2
Answers
Step-by-step explanation:
2x +1= 0.5x - 2
X = - 2
y = 0.5x (- 2) - 2
y = - 3
( x, y ) = ( -2 , -3 )
hope it helps!
A bag contains only red, blue and green counters.
There are 120 counters in the bag.
The probability of choosing a red counter is ¼ and the probability of choosing a blue
counter is 0.2
How many green counters are in the bag?
Answers
Answer:
Step-by-step explanation:
Answer:
66
Step-by-step explanation:
Red counters: 120/4=30
Blue counters:120/5=24
Green counters:30+24=54, 120-54=66
Which of the scatterplots have no correlation? Check all that apply.
On a graph, points curve up and down.
On a graph, points are grouped together to form a horizontal cluster.
On a graph, points are grouped together to form a vertical cluster.
On a graph, points are grouped together and decrease.
On a graph, points are scattered over the graph.
Answers
Answer:
2, 3, and 5
Step-by-step explanation:
got it right on test.
The scatterplots (B), (C), and (E) have no correlation. which is the correct answer would be options (B), (C), and (E)
What is the Scatter plot?The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis.
When analyzing data with more than two variables, a scatter plot is used, which has a separate vertical axis for each variable.
According to the given option,
The second has no slope, therefore there is no correlation.
The third has a zero average slope with no upward or descending trend; no correlation.
The fifth has a general increasing tendency and will have a non-zero correlation.
Thus, the scatterplots (B), (C), and (E) have no correlation.
Hence, the correct answer would be options (B), (C), and (E),
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What is the value of x?
Answers
70+30=100
so x has to equal 80
(mark brainliest if correct pls)
Sum of three angles in the triangle equals to 180.
70+30+x=180
100+x=180
x=180-100
x=80
Therefore, the answer is 80.
help meh please i need hell
Answers
Answer:
1 3/8
Step-by-step explanation:
please help!
the answer is in the picture because i can’t type it out :D
Answers
Answer:
x is 20 and y is 23
Step-by-step explanation:
Answer:
x = 15
y = 4
Step-by-step explanation:
In a triangle a line parallel to any of the sides of the triangle divides the remaining two sides in the proportion. Therefore,
[tex] \frac{12}{y} = \frac{x}{5} = \frac{18}{6} \\ \\ \frac{12}{y} = \frac{x}{5} = \frac{3}{1} \\ \\ \implies \:\frac{x}{5} = \frac{3}{1} \\ \\ x = 5 \times 3 \\ \\ x = 15 \\ \\ \\ \frac{12}{y} = \frac{3}{1} \\ \\ 3y = 12 \\ \\ y = \frac{12}{3} \\ \\ y = 4[/tex]
if lines intersect, does that make it, one solution, no solution, or infinite solution?
Answers
Answer:
one solution
Step-by-step explanation:
No solution is when they don't intersect at all. Infinite solutions is if the two lines are on top of each other.
Answer:
one solution
Step-by-step explanation:
if they intersect, they become one solution, if they don't intersect, than there are no solutions. If the graphs of the equations are the same, there are infinite solutions.
brooke plays on her schools softball team. Last season she was at bat 500 times and made a safe hit 28% of the time. How is 28% expressed as a fraction
PLEASE HELP please?
Answers
Answer:
28/100
Step-by-step explanation:
Find the area of the irregular figure.
2 in.
3 in.
5 in.
A = [ ? ]in.2
3 in.
2 in.
4 in.
4 in.
Answers
Answer:
area = 35 in²
Step-by-step explanation:
(multiple choice) How is e-mail different from other types of communication?
can't save messages
can't hear tone of voice
can't get clues from body language
can't access sent messages
Answers
Answer: You can't hear the tone of voice or get clues from body language.
Step-by-step explanation:
When sending emails, the sender and the recipient communicate through a screen, thus each person is unable to see the other when conversing or hear the inflections or emphasis of voice in the message, although we can always attempt to interpret tone. Email allows you to store emails in the inbox or archive and access sent messages, but email lacks the ability to intimately understand specifics such as tone of voice or body language.
Answer:
cant get clues from body language, cant hear tone of voice
Step-by-step explanation:
Exercise 21
Let x represents a length in cm where x > 1.5.
AB = 2x - 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Si.
. CBFG is a rectangle of area S2.
. ADEB is a right trapezoid of area S3.
1) Express S1 and S2 and S3 in terms of x
Plzzz I need help
Answers
Answer:
see explanation
Step-by-step explanation:
area of Δ ABC is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 4x - 6 and h = 2x - 3 , then
A = [tex]\frac{1}{2}[/tex] (4x - 6)(2x - 3) ← expand using FOIL
= [tex]\frac{1}{2}[/tex](8x² - 24x + 18) ← distribute
= 4x² - 12x + 9
----------------------------------------------------------
Area of rectangle CBFG is calculated as
A = lb ( l is length, b is breadth )
Here l = 4x - 6 and b = 3x - 2, then
A = (4x - 6)(3x - 2) ← expand using FOIL
= 12x² - 26x + 12
----------------------------------------------------------
Area of trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases
Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then
A = [tex]\frac{1}{2}[/tex] (2x - 3)(4x + 1 + 2x + 3)
= [tex]\frac{1}{2}[/tex] (2x - 3)(6x + 4) ← expand using FOIL
= [tex]\frac{1}{2}[/tex] (12x² - 10x - 12) ← distribute
= 6x² - 5x - 6