Directions: Determine the area of the shaded region of each figure. The polygons in each problem are regular polygons. You must include your calculations.
Answers
Problem 1
Imagine placing the nonpencil part of your compass at the center of both hexagons. Extend the compass so the pencil reaches the right-most point on the larger hexagon. Then sweep a full 360 degrees to form a circle. This surrounds the larger hexagon to form what is called the circumcircle. The circumradius is 6+6 = 12 feet.
If we know the circumradius r = 12 and the number of sides n = 6, then we can find the area of the larger regular hexagon using this formula
[tex]A = 0.5n*r^2*\sin(360/n)[/tex]
Your calculator must be in degree mode. This formula only works for regular polygons.
Let's use that formula to calculate the area of the larger regular hexagon.
[tex]A = 0.5n*r^2*\sin(360/n)\\\\A = 0.5*6*12^2*\sin(360/6)\\\\A \approx 374.122974[/tex]
Then do the same for the smaller regular hexagon that has circumradius of r = 6 this time. We still have n = 6 sides.
[tex]A = 0.5n*r^2*\sin(360/n)\\\\A = 0.5*6*6^2*\sin(360/6)\\\\A \approx 93.530744[/tex]
Now subtract the areas
374.122974-93.530744 = 280.59223
The green region has an area of roughly 280.59223 square feet.=========================================================
Problem 2
The formula we use here is
[tex]A = 0.25n*s^2*\cot(180/n)[/tex]
where
n = number of sides = 5 in this case for both figuress = side length = will be different values depending on which figure you focus on"cot" refers to the cotangent function, which is the reciprocal of tangent. Your calculator should support cotangent. If not, then you'd have to do 1/tan of the value of 180/n. In this case, n = 5 so 180/n = 180/5 = 36. So you either calculate cot(36) or 1/tan(36)Your calculator must be in degree mode.This formula only works on regular polygons. These are polygons with the same side lengths and same angles.Let's use that formula to calculate the area of the larger regular pentagon. It has side lengths of s = 8
[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*5*8^2*\cot(180/5)\\\\A = 0.25*5*8^2*\cot(36)\\\\A = 0.25*5*8^2*\frac{1}{\tan(36)}\\\\A \approx 110.110554\\\\[/tex]
The larger regular pentagon has area of roughly 110.110554 square cm.
Repeat those steps for the smaller pentagon where each side is now s = 6. Keep n = 5 the same.
[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*5*6^2*\cot(180/5)\\\\A = 0.25*5*6^2*\cot(36)\\\\A = 0.25*5*6^2*\frac{1}{\tan(36)}\\\\A \approx 61.937186\\\\[/tex]
Now subtract the two areas to get the area of the shaded green region.
110.110554 - 61.937186 = 48.173368
The green region has area of roughly 48.173368 square cm.Related Questions
the radius of the bigger circle is 9cm and the area of the shaded region is twice that of the smaller circle then how long is the radius of the smaller circle ?
Answers
Answer:
the radius of the smaller circle = 3√3.Step-by-step explanation:
let C' be the bigger circle
and C be the smaller circle and r its radius.
Area(C') = π × (9² - r²)
Area(C) = π × r²
Area(shaded region) = area(C') - area(C)
= π × (9² - r²)
the statement “the area of the shaded region is twice that of the smaller circle ” means π × (9² - r²) = 2 × π × r²
Now, let’s solve the equation:
π × (9² - r²) = 2 × π × r²
⇔ π × (9² - r² - 2r²) = 0
⇔ π × (81 - 3r²) = 0
⇔ 81 - 3r² = 0
⇔ 81 = 3r²
⇔ r² = 27
⇔ r = √27
⇔ r = 3√3
Answer:
6.32
Step-by-step explanation:
Area of bigger circle = π(9)² = 81π cm²
Area of smaller circle = π(9)²/2 = 81π/2 = 40.5πcm²
Area scale factor = (Linear Scale factor)²
81π/40.5π = 9²/x² {cancel the π}
81/40.5 = 81/x² (cross multiplication)
81x² = 40.5 × 81
√x² = √40.5 (square root both sides)
x = 6.32
Drag the tiles to the correct boxes to complete the pairs.
Match each word problem to the equation that models it.
Answers
Matching each word problem to the equation that models it :
The sum of the squares of two positive integers is 394. if one integer is less than the other and the larger integer is x, find the integers. is modelled by : 2[tex]x^{2}[/tex] - 4[tex]x[/tex] - 390 = 0The sum of a positive integer x, and its inverse is [tex]\frac{4}{3}[/tex]. Find the integer models = 3[tex]x^{2}[/tex] - 4[tex]x[/tex] + 3 = 0The numerator of a fraction is 5 more than its denominator, if 3 is added to both the numerator and denominator, the fraction reduces to [tex]\frac{4}{3}[/tex]. Find the original fraction if x is its denominator models 3[tex]x[/tex] + 24 = 4[tex]x[/tex] + 12Meaning of word problemA word problem is a problem that is written in english format. the student is left with a task to unravel and transform it to a mathemtical equation.
in conclusion, the word problem has been matched to their individual equation they model.
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if v1 = (3,7) and v2 = (2,4), then v1 v2 is equal to which of the following
Answers
Answer:
If it is dot product, then 32.
Step-by-step explanation:
3*2+7*4
6+28
32
I need help asap please
Answers
Answer:
52 seconds5833 feetStep-by-step explanation:
Each plane has a starting altitude and a fixed rate of climb. Its altitude at some time t will be the sum of the starting altitude and t times the rate of climb.
__
plane Aaltitude = starting altitude + t × rate of climb
a(t) = 4000 +35.25t
plane Bb(t) = 2427 +65.5t
same altitudeThe planes will be at the same altitude at the same time when ...
a(t) = b(t)
4000 +35.25t = 2427 +65.5t
1573 = 30.25t . . . . . . . . . . subtract 2427+35.25t
52 = t . . . . . . . . . . . . . divide by 30.25
That altitude is ...
a(52) = 4000 +35.25×52 = 4000 +1833 = 5833
summary52 seconds will pass before the planes are at the same altitude.
Their altitude then will be 5833 feet.
split 54 between 4 people
Answers
Answer:
your answer is 13.2
Step-by-step explanation:
If y varies directly with x and y = 87 when x = 3, find y when x = 5. Write and solve a direct variation equation to find the answer
Answers
Answer:
145
Step-by-step explanation:
y=kx
87=3k
k= 87/3
k= 29
y=29×5
y= 145
Nancy has 8 meters of rope. How many pieces of rope of length 1/2 meter can she cut from it
Answers
Answer:
16
Step-by-step explanation:
8 divided by 1/2 is
8 times 2
which is
16
Please help i will give brainliest
Answers
Answer:
See below
Step-by-step explanation:
The flat line portions of the graph are where Tim is not moving....the first flat area is where he had the puncture to fix....the second is tea-time
A/ 16:00 - 16:20 20 minutes
B/ 2000 meters in 10 minutes would be 12 000 m /hr = 12 km/hr
C/ No, he was slower ....on the way there it took him 20 minutes total cycling time
15:30 to 15:40 plus 15:50 to 16:00
Dylan has a total of 25 marbles. He gives ! marbles to his sister, Jane. What fraction
of marbles did Jane receive?
Answers
The Dylan sister Jane received 1/5 marbles, which is a part of 25 if the Dylan has a total of 25 marbles.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The total number of marbles Dylan has = 25
The total number of marbles Dylan gave to his sister = 5
If we choose one marble out of 25 = 1/25
If we choose 5 marbles = 5(1/25) = 1/5
Thus, the Dylan sister Jane received 1/5 marbles, which is a part of 25 if the Dylan has a total of 25 marbles.
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Part of the population of 7,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 3 of them are infected. How many elk are likely to be infected?
Answers
When the sample is given, the number of elk are likely to be infected is to be considered as the 450.
Calculation of the number of elk:Since the population is 7,500.
The random sample is 50.
So here be like
[tex]7500[/tex] ÷ [tex]50[/tex] × [tex]3[/tex]
= 450
hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 450.
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If dave decides to go scuba diving for the first time. If he descends at -2 1/3 feet every second, at what depth will he be at after 3 1/2 seconds.
Answers
Answer:
-8.66666667 feet because:
Step-by-step explanation:
-2 1/3 x 3 = 7
-2 1/3 ÷ 2 = 1.66666666667
7 + 1.6666666667 = 8.66666667
Probability & Sampling:Question 8
Mr. Evans wanted to compare the math grades of his 6th
grade students and 7th grade students. He displayed the
data on dot plots.
Answers
The conclusion that Mr. Evans can make is that On average, students in 6th Grade have lower grades than students in 7th Grade.
What is a dot plot?This is also known to be a dot chart. It is said to be a statistical chart that is made up of data points which are known to be plotted on a little and simple scale.
Note that based on the dotted plot of the student's grade, the conclusion that can be drawn or the one that Mr. Evans can make is that On average, students in 6th Grade have lower grades than students in 7th Grade.
See full question below
What conclusion can Mr. Evans make? Hint: Find the mean
answer choices
On average, students in 6th Grade have lower grades than students in 7th Grade.
On average, students in 6th Grade have higher grades than students in 7th Grade.
Students will always have a lower math grade in 6th Grade than 7th Grade.
On average, students in 6th Grade and 7th Grade have about the same grade
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James read 4 pages in a book in 6 minutes. How
long would you expect him to take to read 6
pages?
Answers
Answer:
We can solve by using a proportion
4 pages/6 minutes = 6 pages/x minutes .... cross-multiply.....
4x = 36 divide by 9 on each side
x = 9 minutes
Step-by-step explanation:
Which statement is true about the circumference of a circle?
A: The circumference is the measurement around the circle.
B: The circumference is the measurement of the radius.
C: The circumference is the measurement of the diameter.
D: The circumference is double the radius.
Answers
Answer:
[tex]\large\boxed{\textsf{A: The circumference is the measurement around the circle.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked what's true about the Circumference.}[/tex]
[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is the sum of all the arcs of a circle.}[/tex]
[tex]\textsf{Arcs are the curved edges of a circle that make up the \underline{Perimeter}.}[/tex]
[tex]\textsf{Because the Circumference makes up all of the Arcs in a circle, which is the perimeter;}[/tex]
[tex]\textsf{Option A is the most reasonable choice, as the circumference is the perimeter of}[/tex]
[tex]\textsf{a circle.}[/tex]
Find the slope of the tangent line to the curve y = 3x2
- 2x at the point (1,2)
Studying for final pls help
Answers
Answer:
slope is 4
Step-by-step explanation:
since your trying to find the slope of the tangent line, you have to find the first derivative, once you do plug in your x to give your slope at the designated spot,
Which function best models the data in the graph? y = 10.1x 101 y = x2 101 y = 101(2x) y = 1.01x2 101
Answers
Based on the calculations, the function which best models the data in the graph is y = 10.1x + 101.
How to determine the function?Mathematically, the equation of a line in standard form is given by this formula:
y - y₁ = m(x - x₁)
Where:
m is the slope.y is the point on the horizontal axis.x is the point on the vertical axis.In order to determine the function which best models the data in the graph shown in the image attached below, we would calculate the slope of the data by using this formula:
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\\\\Slope = \frac{202\;-\;101}{10\;-\;0}\\\\Slope = \frac{101}{10}[/tex]
Slope = 10.1.
For the function, we have:
y - y₁ = m(x - x₁)
y = 10.1(x - 0) + 101
y = 10.1x + 101.
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The next part is D then C
Step-by-step explanation:
For an end of the year party, Ms. Dean purchased 96
stickers, 80 lollipops, and 40 cookies. Each student will
receive an equal number of each. There will be no stickers,
lollipops, or cookies left over. What is the greatest number
of students Ms. Dean can have in her class?
Answers
Answer: 15
Step-by-step explanation:
Whats the area of this shape?
Answers
The area of the shape shown in the image which is in the shape of kite figure is 168 squared centimeters.
What is the area of the kite figure?The area of the kite figure is half of the product of its diagonals. Area of kite figure can be find out using the following formula.
[tex]A=\dfrac{pq}{2}[/tex]
Here, p and q are the diagonals of the kite.
The length of the first diagonal of the kite figure is,
p=6+15
p=21 cm
The length of the second diagonal of the kite figure is,
q=8+8
q=16 cm
Thus, the area of kite figure is:
[tex]A=\dfrac{21\times16}{2}\\A=\dfrac{21\times16}{2}\\A=168\rm\; cm^2[/tex]
Thus, the area of the shape shown in the image which is in the shape of kite figure is 168 squared centimeters.
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What does X= and what is the angle
A. Corresponding
B.same side interior
C. Alternate interior
D.Alternate exterior
Answers
Determine the sum of the terms in the series 25 + 30 + 35 + ⋯ + 245. Show your work.
Answers
Answer:
6075
Step-by-step explanation:
Given series is: 25 + 30 + 35 + ⋯ + 245.Here, first term (a) = 25Common difference (d) = 5Last term [tex](a_n) = 245[/tex]First we find the number of terms that this series has by the following formula:[tex]a_n = a+(n-1)d[/tex]Plugging the values of a, d and [tex]a_n[/tex], we find.[tex]245 = 25+(n-1)5[/tex][tex]\implies 245 - 25=(n-1)5[/tex][tex]\implies 220=(n-1)5[/tex][tex]\implies \frac{220}{5}=n-1[/tex][tex]\implies 44=n-1[/tex][tex]\implies 44+1=n[/tex][tex]\implies\red{\bold{ n=45}}[/tex]Thus, the given series contains 45 terms.Next, we find the sum of the given series using the formula given below.[tex]S_n = \frac{n}{2}(a+a_n)[/tex][tex]\implies S_{45}= \frac{45}{2}(25+245)[/tex][tex]\implies S_{45}= \frac{45}{2}(270)[/tex][tex]\implies S_{45}=45*135[/tex][tex]\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}[/tex]Simplify: 39x+21x-4. Round to the nearest ten
Answers
Answer:
60x-4
Step-by-step explanation:
39x+21x=60x
Therefore, you are left with 60x-4, which is in its simplest form.
billy has 2.4m of ribbon for crafts. he wants to share it evenly with 12 friends. how many centimeters of ribbon would 7 friends get
Answers
You would have to do 2.4 divided by 12 to get 0.2. Then multiply 0.2 by 7 to get 1.4.
Answer:
140cm
Step-by-step explanation:
We first have to change 2.4 meters into centimeters. And the formula for that is (x)m = (x)cm x 100.
So 2.4 x 100 = (x)m. We can solve this by moving the "." two times to the right and we will get 2.4m = 240cm.
The next step is to divide it by twelve because Billy wants to share it with 12 friends. 240cm/12 = 20cm per person.
Then we have to multiply 20 with 7 to see how many centimeters 7 friends would get.
20*7 = 140. So the answer is 140cm.
Please help fghgbvnghgbvhgghg
Answers
Answer:
x=326
Step-by-step explanation:
0.3x - 34 + 0.2x -39 = 90.
Simplify this equation.
0.5x = 163
x = 326
So confused! Anyone good at this?
Answers
Answer:
x = 90 degrees.
Step-by-step explanation:
These are all regular octagons and the value of x = 2 * external angle of an octagon.
The sum of external angles of a polygon sum to 360 degrees and in the case of an octagon each external angle = 360/8 = 45 dgrees,
So angle x = 2*45 = 90 degrees.
F is directly proportional to A. If F=36 when A=9 find, F when A=4
Answers
Answer:
16
Step-by-step explanation:
f=ka
36=9k
k=4
f=4×4
f=16
Can't figure out the other ones. There are two inages for this. Use the square to answer the following questions. DC=8.5 and DW=6
Answers
Answer:
6; 12; 8.5; 90°; 90°; 45°; 45°
Step-by-step explanation:
A square has all sides the same length, and diagonals the same length. The diagonals bisect the right angles in the corners, and they cross at right angles.
__
As you have already observed, ...
BW = DW = 6
AC = BD = 2(DW) = 2(6) = 12
Further, ...
DA = DC = 8.5 . . . . sides of a square are the same length
∠DWA = 90° . . . . . diagonals cross at right angles
∠ABC = 90° . . . . . corner angles are right angles
∠ABD = 45° . . . . . the diagonal cuts the corner angle in half
∠DCA = 45° . . . . . all of the acute angles are congruent
_____
Additional comment
A square is a rhombus that is also a rectangle. The relevant characteristics are ...
all sides of a rhombus are congruentthe diagonals of a rhombus cross at right angles. Each bisects the vertex angles at either end, which are congruent.the corner (vertex) angles of a rectangle are right angles1/3 + 1/4 + ? = 1
? = the answer
Answers
Answer:
5/12 (corrected)
Convert with lowest common denominator, 12(find by multiplying)
1/3 = 4/12
1/4 = 3/12
Add the fraction's numerators
4 + 3 = 7
Subtract by 1 whole
7/12 - 12/12 = 5/12
Thus, your answer is 5/12
Answer:
5/12
Step-by-step explanation:
to give the fractions the same denominator, find their gcm
3 * 4 = 12
therefore multiply 1/3 by 4/4 to get 4/12
multiply 1/4 by 3/3 to get 3/12
3/12 + 4/12 = 7/12
to find the remainder subtract
12/12 - 7/12 = 5/12
your answer is 5/12
hope this helps:)
can someone help me with this?
Answers
240 cm³
volume of rectangular prism:
Length * Width * Height
4 cm * 20 cm * 3 cm
240 cm³
Answer
20x4x3= 240
Step-by-step explanation:
Length x Width x Height
The table shows the ratio of people who ate a certain type of lunch to the total number of people who ate lunch. A total of 840 people ate lunch. What statement is true?
Answers
The sum of the individual lunch ate by people is equal to the total number of people who ate lunch.
What is an equation?An equationi is an expression that shows the relationship between two or more variables and number.
Given that the total number of people who ate lunch is 840, hence:
The sum of the individual lunch ate by people is equal to the total number of people who ate lunch.
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find the sum of the arithmetic series shown below 10+9+8… +(-255)
Answers
Answer:
−228
Step-by-step explanation:
10+9+8+−255
Add 10 and 9 to get 19.
19+8−255
Add 19 and 8 to get 27.
27−255
Subtract 255 from 27 to get −228.
−228