A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
accompanying figure. Write the area of the sector. A as a function of
Answers
Answer:
[tex]A(\theta)=\frac{162 \theta}{(\theta+2)^2}[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Let
r ---> the radius of the sector
s ---> the arc length of sector
Find the radius r
we know that
[tex]2r+s=18[/tex]
[tex]s=r \theta[/tex]
[tex]2r+r \theta=18[/tex]
solve for r
[tex]r=\frac{18}{2+\theta}[/tex]
step 2
Find the value of s
[tex]s=r \theta[/tex]
substitute the value of r
[tex]s=\frac{18}{2+\theta}\theta[/tex]
step 3
we know that
The area of complete circle is equal to
[tex]A=\pi r^{2}[/tex]
The complete circle subtends a central angle of 2π radians
so
using proportion find the area of the sector by a central angle of angle theta
Let
A ---> the area of sector with central angle theta
[tex]\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}[/tex]
substitute the value of r
[tex]A=\frac{(\frac{18}{2+\theta})^2\theta}{2}[/tex]
[tex]A=\frac{162 \theta}{(\theta+2)^2}[/tex]
Convert to function notation
[tex]A(\theta)=\frac{162 \theta}{(\theta+2)^2}[/tex]
Related Questions
9.8g of sugar is needed for every cake made. How much sugar is needed for 4 cakes?
Answers
Answer:
39.2g of sugar
Step-by-step explanation:
4×9.8=39.2
one cake needs 9.8g so four cakes would need 39.2
Answer:
39.2 g of sugar
Step-by-step explanation:
You just need to multiply the amount by 4.
there is 15 girls and 25 boys in a science club . what percent of the members are girls?
Answers
Answer:
Step-by-step explanation:
Total member = 25 + 15 = 40
[tex]girls percentage = \frac{15}{40}*100\\\\=\frac{15}{2}*5\\\\=\frac{75}{2}=37.5\\[/tex]
= 37.5%
1. The monthly rents for studio apartments in a certain city have a mean of $920 and a standard deviation of $190. Random samples of size 25 are drawn from the population and the mean of each sample is determined.
What is the mean of the indicated sampling distribution of sample means?
2. What is the standard error of the indicated sampling distribution of sample means?
3. Which one is more likely to take place?
a. Find one studio apartment that has a rent between $901 and $939.
b .Find a sample of 25 studio apartments with a mean rent between $901 and $939.
Answers
Answer:
1)Mean=920 $
2)Standard Error =S.E.=38
3)more likely to take place Event 25 studio apartments with a mean rent between $901 and $939
Step-by-step explanation:
Given:
True mean =920 $
S.D=190 $
No .of samples=25
To Find:
1)Mean of sample.
2)S.E
Solution:
Now , the mean for given sample distribution is given as 920 $
Hence Mean =920 $
Now calculating the Standard error
S.E.= S.D./Sqrt(n)
=190/Sqrt(25)
=190/5
=38
Therefore the Standard error is about 38 .
a) When n=1 then P(901≤X≤939)
So,
Z1=(901 -920)/190/Sqrt(1)]
Z1=-0.1
Z2=(939-920)/(190/Sqrt(1)]
Z2=0.1
So
Pr(-0.1≤Z≤0.1)=P(Z≤0.1)-P(Z≤-0.1)
=0.5398-0.4602
=0.0797 % chance of the sample distribution
b)n=25 then P(901≤X≤939)
Z1=(901-920)/S.E
Z1=-19/38=
Z1=-0.5
And Z2=0.5
So,
Pr(-0.5≤Z≤0.5)
=Pr(Z≤0.5)-Pr(Z≤-0.5)
=0.6915-0.3085
=0.3829
i.e 38.29 % chance of the sample distribution
Hence More likely to take place will be a sample of 25 studio apartments with a mean rent between $901 and $939.
0.3829>0.0797.
Because the probability of causing above event is more than the option A.
Which expression is equivalent to -3 -3x-1 + x?
2x-4
-2x +4
-2x-42
4- 2x
Answers
Answer:
the answer is -2x-4
Step-by-step explanation
Answer:
the answer is -2x-4
Step-by-step explanation:
Answer of this time table
Answers
Answer:
1st box= 5
2nd box= 3
3rd box= 8
4th box=5
Answer:
Step-by-step explanation:
1st box= 5
2nd box= 3
3rd box= 8
4th box=5
What is the area of the following circle? Either enter an exact answer in terms of pie or use 3.14 for pie and enter your answer a decimal
Answers
The area of a circle with a radius of 1.2 meters is 4.5 m², rounded to two significant figures to match the precision of the given radius.
Explanation:The area of a circle is given by the formula A = πr², where π (pi) represents a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. When calculating the area with a radius of 1.2 meters, we get the precise calculation as A = π(1.2 m)² = 4.5238934 m². However, as the radius is given with only two significant figures, the area should also be rounded to two significant figures, resulting in A=4.5 m².
What common side do AGDE and AHED share?
Answers
Answer:
The common side shared is ED.
Step-by-step explanation:
Answer:
The common side shared is ED , it is their common base
Mr. Z constructs a cube with 512 magnetic blocks. Students in his two classes will each make an identical cube. There are 28 students in one class and 25 students in the other class. How many blocks does he need for all his students?
Need help and steps
Answers
Answer asap A box plot is shown below: A box and whisker plot is shown using a number line from 20 to 45 with primary markings and labels at 20, 25, 30, 35, 40, 45. In between two primary markings are 4 secondary markings. The box extends from 26 to 38 on the number line. A line in the box is at 31. The whiskers end at 20 and 43. The title of the art is Visitors at the Exhibition, and below the line is written Number of Visitors. What is the median and Q1 of the data set represented on the plot? Median = 31; Q1 = 26 Median = 30; Q1 = 26 Median = 31; Q1 = 20 Median = 30; Q1 = 20
Answers
Answer:
The Answer Is B. Median = 30; Q1 = 26
Step-by-step explanation:
Answer: Median 31 and Q1 is 26 its 100% verified
Step-by-step explanation:
A cylinder has a volume of 315x cubic meters and a height of 21 meters. What is the area of the base?
15x square meters
18x square meters
294x square meters
o 6,615x square meters
Answers
15x quare meters.
V = π r2 h
2.1857 as r
21 Goves about 315 x cubic meters.
Area of a circle with 2.1857 as radius is around 15.
Which gives you 15x square meters.
find the area of a circle with a circumference of 11 feet
Answers
Answer:
94.985 feet
Step-by-step explanation:
the formula for area of a circle is pi×r²
if you are using 3.14, it is 94.985
if you are using pi, then it is 95.03317777
what's the answer to this ?
Answers
Answer:
x = 13.1°
A is correct answer
Step-by-step explanation:
Given Data:
Angle = ∅ = 24°
Base = b = 12
To find out:
Hypotenuses = x = ?
Formula:
Cos∅ = Base/Hypotenuses
Cos∅ = b/x
x = b/Cos∅
Solution:
x = b/Cos∅
x = 12/Cos(24°)
x = 12/0.91
x = 13.1°
Factor the trinomial:
5x^2 + 12x + 7
Answers
What is the area of this composite figure?
12.56 in. sq
10.28 in. sq
7.14 in. sq
16.56 in. sq
Answers
Answer:
7.14 in. sq
Step-by-step explanation:
First find the area of the square; 2x2=4
Now find the area of the semi-circle; radius = 1.
1 squared= 1 Now multiply by 3.14 which equals 3.14
Now divide by 2 because it's a semi-circle, you get 1.57.
Multiply 1.57 by 2 because you have 2 semi-circles, the would equal 3.14
Add 4+3.14 and you get 7.14
The area of the composite figure is 7.14 in. sq
Answer:
Step-by-step explanation:
A certain company's main source of income is selling cloth bracelets.
The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by:
P(x)=-2x^2+16x-24P(x)=−2x
2
+16x−24P, left parenthesis, x, right parenthesis, equals, minus, 2, x, squared, plus, 16, x, minus, 24
What bracelet price should the company set to earn this maximum profit?
Answers
Answer:8
Step-by-step explanation:
.
Answer:
2 or 6, you can type in either one.
Step-by-step explanation:
Michelle earns $5 for each lawn she mows. Last week she earned $30 mowing lawns. This week she earned $20 mowing lawns. Which statement correctly explains how many more lawns Michelle mowed last week than this week? A) Michelle mowed 2 more lawns because 30 ÷ 5 is 2 more than 20 ÷ 5. B) Michelle mowed 10 more lawns because 30 + 5 is 5 more than 20 + 5. C) Michelle mowed 10 more lawns because 30 – 5 is 10 more than 20 – 5. D) Michelle mowed 50 more lawns because 30 × 5 is 50 more than 20 × 5.
Answers
Answer: A
Step-by-step explanation:
Answer:
A is correct because it is the only one to make sense
an arc subtends a central angle measuring 2pi/3 radians. what fraction of the circumference is this arc?
Answers
Answer:
1/3
Step-by-step explanation:
The fraction of the circumference that the arc subtends is 1/3.
Explanation:An arc that subtends a central angle measuring 2π/3 radians is a fraction of the circumference. To find the fraction, we can use the formula:
Fraction of circumference = (angle/2π) x 1
Substituting the given angle into the formula, we have:
Fraction of circumference = (2π/3 /2π) x 1
Simplifying the expression, we get:
#SPJ11
Can anyone help this is due TODAY!!
Answers
Answer:
$1.67
Step-by-step explanation:
Let x be the no. of gums
96.6 + 0.79x》100
0.79x 》 3.4
x》4.3037974684
So x = 5
15% discount: she pays 0.85(96.6)
= 82.11
20% discount (after gums)
She pays 0.8[96.6 + 5(0.79)]
= 0.8(100.55)
= 80.44
Less:
82.11 - 80.44
= 1.67
Dose anyone know what to do I don’t know how
Answers
Answer:
a=7b+27/2
Step-by-step explanation:
1: Add 7/3b to both sides.
2 /3 a+ −7 /3b + 7/3b = 9+ 7/3b
2/3a=7/3b+9
2: Divide both sides by 2/3.
2/3a= 7/3b + 92
/ 2/3a / 2/3a
a=7b+27/2
Percy and Caren are having a debate. Percy contends that the headquarters of the United States Department of Defense (also known as the Pentagon) has a longer perimeter than the United States Capitol. Caren contends the opposite. To settle their debate, they find satellite images of both buildings online and juxtapose them on a single coordinate grid (shown below). Assume the Pentagon is a regular pentagon with side length 300. The perimeter of the Pentagon is
Answers
Answer:
1500 units.
Step-by-step explanation:
-A pentagon is a a regular pentagon with 5 equal sides.
-Since the side length's are equal, the perimeter is simply the product of one side length by the number of sides of the polygon.
-Given its sides measures 300 each, its perimeter can be calculated as:
[tex]P=5s\\\\=5\times 300\\\\=1500 \ units[/tex]
Hence, the Pentagon's permimeter is 1500 units.
Answer:
The perimeter of the Pentagon is 1500
The perimeter of the Capitol is 1131
Percy would win the debate
Step-by-step explanation:
the nth term of a sequence is n+7
work out the first three terms
Answers
Answer:
Term 1
Substitute 1 into N
(1) + 7 =8
Term 2
Substitute 2 into N
(2) + 7 =9
Term 3
Substitute 3 into N
(3) + 7 = 10
Answer:
Step-by-step explanation:
hello : put this values n=1 , n=2 ;n=3
A planet follows an elliptical path described by 256 x squared plus 16 y squared equals 4096.256x2+16y2=4096. A comet follows the parabolic path y equals x squared minus 16.y=x2−16. Where might the comet intersect the orbiting planet?
Answers
Final answer:
To find the intersection points of the comet and the planet's orbits, we need to solve the system of equations formed by their respective path equations.
Explanation:
To find where the comet might intersect the orbiting planet, we need to find the common points between the equation of the planet's elliptical path and the equation of the comet's parabolic path.
By substituting the expression for y in the equation of the planet into the equation of the comet, we get 256x^2 + 16(x^2 - 16) = 4096.
Simplifying this equation and solving for x will give us the x-coordinates where the comet may intersect the planet's orbit. Substituting these x-values back into either the planet's or comet's equation will give us the corresponding y-coordinates.
FOR 30 POINTS WILL GIVE BRAINLIEST
The annual salaries of the sales team at Pat’s company are listed in the table below.
$42,000
$80,000
$50,000
$56,000
$45,000
$63,000
$42,000
$70,000
What is the mean salary of a salesperson at the company?
$38,000
$53,000
$56,000
$58,000
Answers
Answer:
C
Step-by-step explanation:
Answer:
$56,000
Step-by-step explanation:
Fiona is making a box to hold firewood cut to 20-inch lengths. The box has to be 2 feet wide to accommodate the length of the wood pieces. Fiona wants the length to be 7 feet longer than the height. The graph models the possible volume (y) of Fiona’s box determined by its length (x). Which value of x makes sense for the length of Fiona’s box? x < 7 x > 0 x > 3.5 x > 7
Answers
Answer:
c
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
triangle fgh is a right triangle? true or false
Answers
Answer:true
Step-by-step explanation:
Answer:
on ilearn i answered true and it was wrong. so the answer is false!
Step-by-step explanation:
ilearn
Can anyone help me i was not a school and I need help
Answers
so the right answer is of option A.
Hope this will help u...
Answer:
A. 12375
Step-by-step explanation:
Simple Interest Formula:
[tex]A = P(1+rt)\\[/tex]
A = 37375 in this case. This is the amount of money you'll have after 9 years. However, the question asks for how much interest you'll gain, meaning you have to subtract the principle from it. 37375 - 25000 = 12375
i have four numbers that are 5, 6, 8, 10 which three of these numbers form a right triangle
Answers
Answer:
6, 8, 10
Step-by-step explanation:
Pythagorean theorem:
To form a right triangle we need to have 3 numbers where when we take the sum of the squares of the first two it equals the square of the third number.
If we take 6, 8, and 10 then if makes this true.
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100 (This means it's correct)
What is the converse of the following conditional statement? If x = 12, then 2x – 5 = 19.
Answers
Answer:
If 2x - 5 = 19, then x = 12
Step-by-step explanation:
What is the median for the given set of data?
{40, 54, 22, 30, 55, 13, 33}
A) 32
B) 33
C) 40
D) 42
Answers
Step-by-step explanation:
Arranging in ascending order, we get
13 , 22 , 30 , 33 , 40 , 54 , 55
no of data (N) = 7
Now Position of Median
= {(N +1 ) / 2}th item
= {(7+1) / 2 } that item
= 4 that item
So now exact median = 33
Answer:
The answer is 33
Step-by-step explanation:
By arranging the numbers in order of smallest to largest you get: ----------------> 13, 22, 30, 33, 40, 54, 55. Cross off a number from each side until you get one or two left in the middle. Cross out 13 and 55 then 22 and 54 then 30 and 40. Now you have 33 left in the middle, that is your median
Evaluate the expression 8 7/3
Answers
Answer: 31 / 3 exact form
10.3 decimal form
10 1 / 3 mixed number form
Step-by-step explanation: