Answers
(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3
(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1
(iii) h(0) = 1/7
The value of λ must be 7, for h(x) to be continuous at x = 0.
The given function is,
h(x) = 1/7, when x = 0
= 1 - 2 cos 2x, when x < π/2
= 1 + 2 cos 2x, when x > π/2
= x cos x/sin λx, when x < 0
Now,
(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3
(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1
(iii) h(0) = 1/7
Since the function is continuous at x = 0, so
[tex]\lim_{x \to 0}[/tex] h(x) = h(0)
[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7
[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7
1/λ = 1/7
λ = 7
Hence the value of λ must be 7.
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Related Questions
6
Professor Snozz wrote a new book, Pi to
Ten Million Places. He earns 8% of total
sales dollars as a royalty. If 300 copies
of his book are sold at $29.50 each, how
much does Professor Snozz make?
Answers
If professor Snozz earns 8% of "total-sales", then the amount that the professor make on selling of 300 copies is $708.
In order to find out how much Professor Snozz makes, we first calculate the "total-sales" revenue of the 300 copies of the book;
⇒ Total sales revenue = (number of copies sold) × (price per copy),
⇒ Total sales revenue = 300 × $29.50,
⇒ Total sales revenue = $8850;
Next, we calculate amount of royalty that Professor Snozz earns, which is 8% of the total sales revenue;
So, Royalty = 8% of "Total sales revenue";
⇒ Royalty = 0.08 × $8850,
⇒ Royalty = $708;
Therefore, Professor Snozz earns $708 as a royalty for selling 300 copies of his book.
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6. The following are the costing records for the year 2020 of a manufacturer: Production 1,000 units, Cost of raw materials Rs,20,000, Labour cost Rs.12,000, Factory overheads Rs.8,000, Office overheads Rs.4,000, Selling expenses Rs.1,000, Rate of profit 25% on the selling price. The manufacturer decided to produce 1,500 units in 2021. It is estimated that the cost of raw materials will increase by 20%, the labour cost will increase by 10%, 50% of the overhead charges are fixed and the other 50% are variable. The selling expenses per unit will be reduced by 20%. The rate of profit will remain the same. Prepare a cost statement for the year 2021 showing the total profit and selling price per unit.
Answers
Answer:
Here's a cost statement for the year 2021:
Production of 1,500 units
Cost of raw materials = Rs. (20,000 x 1.2) = Rs. 24,000
Labour cost = Rs. (12,000 x 1.1) = Rs. 13,200
Fixed overheads = Rs. (8,000/2) = Rs. 4,000
Variable overheads = Rs. (8,000/2 x 1.5) = Rs. 6,000
Office overheads = Rs. 4,000
Selling expenses per unit = Rs. (1,000 x 0.8 / 1,500) = Rs. 0.53
Total cost per unit = Rs. (24,000 + 13,200 + 4,000 + 6,000 + 4,000) / 1,500 = Rs. 28.80
Profit = 25% of selling price
Selling price per unit = (28.80 / (1 - 0.25)) = Rs. 38.40
Total profit = (1,500 x 38.40 x 0.25) = Rs. 14,400
Therefore, the cost statement for the year 2021 shows a total profit of Rs. 14,400 and a selling price per unit of Rs. 38.40.
What is the circumference of a circle (to the nearest whole number) whose diameter is 12?
Answers
Answer: 3.14 is all ways the circumference
Step-by-step explanation:
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answers
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
What is the domain of the function shown on the graph?
Answers
Answer:
A
Step-by-step explanation:
the domain is the values of x covered by the graph
on the left the graph → - ∞
on the right the graph tends to + ∞
there are no excluded values of x on the domain , so
domain is - ∞ < x < ∞
The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:
thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth
According to this data, what is the experimental probability that a team will consist entirely of boys?
0.2
0.04
0.33
0.02
Answers
The required experimental probability that a team will consist entirely of boys is 0.04. Option B is correct.
To find the experimental probability that a team will consist entirely of boys, we need to count the number of trials in which all three coin tosses resulted in tails (which represents a team consisting entirely of boys), and divide by the total number of trials (which is 50).
From the data, we can see that there are only 2 trials where all three coin tosses resulted in tails, so the experimental probability of a team consisting entirely of boys is:
2/50 = 0.04
Therefore, the experimental probability that a team will consist entirely of boys is 0.04.
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For which distribution is the mode the best measure of center?
A. Skewed
B. Normal
C. Biomodal
Answers
Answer:
The mode is the best measure of center for a distribution that is bimodal, meaning that it has two peaks. In such a distribution, the mean and median may not be representative of the center of the data, but the mode is a good measure of center because it reflects the most common value(s) in the data.
For skewed distributions, the mode may not be a good measure of center because the peak of the distribution is not necessarily at the center of the data. In a normal distribution, the mean, median, and mode are all equal and are good measures of center.
I put the question in the photo but it’s basically a contingency table I just can’t find which like formula to us
Answers
a) The probability that exactly one of them will be a girl = 0.3407
b) The probability that at least one of them will like the football = 0.7672
a) If we select three students then the probability that exactly one of them will be a girl
From the attached two way table we can observe that the total number of girls = 22
the total number of boys = 18
and the total number of students = 40
The possible outcomes for selecting 3 students from 40 would be,
⁴⁰C₃
Using combination formula,
⁴⁰C₃ = 40! / (3! × (40 - 3)!)
= 9880
If there is exactly one girl then other two must be boys in the set of 3 selected students.
So, the required probability would be,
P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃
P = (22 × 153)/9880
P = 0.3407
b) The number of students like the football = 15
and the number of students who don't like the football are 40 - 15 = 25
The probability that at least one of them will like the football would be,
P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃
P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880
P = 0.7672
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Find a function of the form
or whose graph matches this one:
Answers
The function whose graph matches this one y= 4 sin (π/7 x) - 2
As, The general form of a sine function is
y= A sin (kx) + C........(1)
From the given graph the maximum value of the function is 2 and minimum value of the function is -6.
So, Amplitude= (Max- Min)/2
A = (2- (-6))/2
A= 8/2
Amplitude= 4
Now, The function complete a cycle in 14 units, so period of the function is 14.
2π/k= 14
k = π/7
and, Midline= (Min + Max)/2 = (2-6)/2 = -2
So, the function is
y= A sin (kx) + C.
y= 4 sin (π/7 x) - 2
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Please help me I am stuck at this thanks so much
Answers
Answer:
34.83/.9 = 38.7 g mass (after one hour)
38.7/.9 = 43 g (starting mass)
The starting mass of the ice cube was 43 grams.
x = 16 and y = 2, given that x is directly related to the square of y. If x = 100, what is one possible value of y?
Answers
Answer: 5
Step-by-step explanation:
Since x is directly related to the square of y, we can write the equation:
x = ky^2
where k is a constant of proportionality. We can solve for k using the given values of x and y:
16 = k(2^2) -> 16 = 4k -> k = 4
Now that we know k, we can use it to find y when x = 100:
100 = 4y^2 -> 25 = y^2 -> y = ±5
Since y cannot be negative, the only possible value of y is 5. Therefore, when x = 100, y could be 5.
Answer:
One possible value of y when x = 100 is y = 5.
Step-by-step explanation:
Using the direct variation formula, we know that x = ky^2, where k is a constant. Given that x = 16 and y = 2, we can solve for k:
16 = k(2)^2
k = 4
Now we can use this value of k to find y when x = 100:
100 = 4y^2
y^2 = 25
y = 5 or -5 (since the question only asks for one possible value, we can choose either solution)
Therefore, one possible value of y when x = 100 is y = 5.
Convert the rectangular coordinates (5,−5√3) to polar form. Let r>0 and 0≤θ<2π.
Enter your answer by filling in the boxes. Enter coordinates as simplifed fractions or radicals in simplest form.
( , )
Answers
Answer:
(10, 5π/3)
Step-by-step explanation:
To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Substituting the given values, we get:
r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10
θ = arctan((-5√3)/5) = arctan(-√3) = -π/3
Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:
θ = -π/3 + 2π = (5π/3)
Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).
Help is appreciated!
Answers
Answer:
Snacks: $75
Alcohol: $200
Dairy: $300
Average delivery charge per week: $63.89 (rounded to two decimal places)
Step-by-step explanation:
To find the average delivery charge the store pays each week, first calculate the total delivery cost for each category and then find the total cost for all deliveries. Finally, divide the total cost by the total number of deliveries.
Snacks:
3 deliveries * $25 per delivery = $75
Alcohol:
2 deliveries * $100 per delivery = $200
Dairy:
4 deliveries * $75 per delivery = $300
Total cost for all deliveries:
$75 (Snacks) + $200 (Alcohol) + $300 (Dairy) = $575
Total number of deliveries:
3 (Snacks) + 2 (Alcohol) + 4 (Dairy) = 9
Average delivery charge per week:
$575 (total cost) / 9 (total number of deliveries) = $63.89 (rounded to two decimal places)
what is the answer to 7/8 x 6
Answers
Answer:
5.25
Step-by-step explanation:
7 divide 8 = 0.875
0.875 × 6 = 5.25
Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 24, 32, and 40 and a second triangle labeled D prime with side lengths of 6, 8, and 10 Determine the scale factor used. Scale factor of one half Scale factor of 4 Scale factor of 2 Scale factor of one fourth
Answers
The scale factor used is 1/4.
We have,
Length of sides of triangle D 24, 32, and 40.
Length of sides of triangle D' 6, 8, and 10.
So, scale factor
= length of corresponding side in D' / length of corresponding side in D
= 6/24
= 1/4
Thus, the scale factor used is 1/4.
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The cost of 2 footballs and 3 tennis balls is £21.73.
The cost of 5 footballs and 7 tennis balls is £53.20.
Work out the cost of
a) a football.
b) a tennis ball.
Answers
Answer: A) £7.49
B) £2.25
Step-by-step explanation:
Step 1:
Let the cost of a football be [tex]f[/tex]and the cost of a tennis ball be [tex]t[/tex].
Step 2:
Write the 2 equations we have from the given information:
[tex]2f + 3t = 21.73[/tex] [tex] \textsf{(from the cost of 2 footballs and 3 tennis balls)} [/tex]
[tex]5f + 7t = 53.20[/tex] [tex] \textsf{(from the cost of 5 footballs and 7 tennis balls)} [/tex]
Step 3:
Solve for one variable in one of the equations. For example, we can solve for [tex]f[/tex]in the first equation:
[tex]2f + 3t = 21.73[/tex][tex]2f = 21.73 - 3t[/tex][tex]f = \frac{(21.73 - 3t)}{2}[/tex]Step 4:
Substitute this expression for [tex]f[/tex] into the second equation and solve for [tex]t[/tex]:
[tex]5f + 7t = 53.20[/tex][tex]5[\frac{(21.73 - 3t)}{2}] + 7t = 53.20[/tex][tex]54.325 - 7.5t + 7t = 53.20[/tex][tex]0.5t = 1.125[/tex][tex]t = 2.25[/tex]So, the cost of a tennis ball is £2.25.
Step 5:
Substitute this value of [tex]t[/tex] into the expression for [tex]f[/tex] and solve for [tex]f[/tex]:
[tex]f = \frac{(21.73 - 3t)}{2}[/tex][tex]f = \frac{(21.73 - 3(2.25))}{2}[/tex][tex]f = 7.49[/tex]So, the cost of a football is £7.49
Step 6:
Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.
The equation x2 + y² - 6x + 2y = b describes a circle.
If the radius of the circle is 4 units, what is the value of b in the equation above?
Answers
Answer:
Step-by-step explanation:
given equation of a circle : x^2+y^2-6x+2y=b.
BY comparing it with x^2+y^2+2gx+2fy+c=0, we get
centre as (-g,-f)=(3,-1)
Since we know that radius r=sqrt(g^2+f^2-c)
Here radius is given as 4 units.
So,
4=sqrt((3)^2+(-1)^2-c)
=>16=9+1-c
Therefore, c=-6
Find (g of (26) when f(x) = X-2 and g(x) = 7x + 2.
A) "
B) 54
C) 44
D) 1104
Answers
Answer:
To find g(26) when g(x) = 7x + 2, we simply need to substitute x = 26 into the expression for g(x):
g(26) = 7(26) + 2
g(26) = 184
Now, to find (g of f)(x), we need to substitute f(x) into the expression for g(x):
(g of f)(x) = g(f(x)) = 7(f(x)) + 2
Since f(x) = x - 2, we can substitute x - 2 for f(x) in the expression for g(x):
(g of f)(x) = g(x - 2) = 7(x - 2) + 2
Simplifying this expression, we get:
(g of f)(x) = 7x - 12
Now, to find (g of f)(26), we simply substitute x = 26 into the expression we just found:
(g of f)(26) = 7(26) - 12
(g of f)(26) = 182
Therefore, the answer is A) (not listed).
Find the 36th term.
5, 8, 11, 14, 17, ...
36th term = [?
Answers
Answer:
110
Step-by-step explanation:
nth term = 3n + 2
3 (36) + 2
108 + 2 = 110
Answer:
The 36th term in the sequence is 104.
Here's how to find it:
- Start with the first number in the sequence: 5.
- Add the common difference, which is 3, to get the second number in the sequence: 8.
- Add the common difference to the second number to get the third number: 11.
- Continue adding the common difference to each subsequent number to find the next term in the sequence.
- The 36th term is three less than 37 times the common difference added to the first term.
- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.
- Therefore, the 36th term in the sequence is 104.
A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?
Answers
The volume of this rectangular prism is equal to: B. 8 in³.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;
Dimensions = 16 × (1/2)³ = 2inches.
By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 2 × 2 × 2
Volume of rectangular prism = 8 cubic inches.
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Complete Question:
A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?
A. 2 in³
B. 8 in³
C. 16 in³
D. 32 in³
Select the correct answer.
Credit cards and charge cards differ in two important ways. One is the method of payment. What is the other difference?
A. You can get a credit card from your bank but not a charge card.
в.
You have to pay interest on charge cards but not on credit cards.
C.
You have to pay interest on credit cards but not on charge cards.
Answers
This is the other difference between credit cards and charge cards. With a credit card, you have the option to carry a balance from month to month and accrue interest on the unpaid balance. With a charge card, you must pay the balance in full each month, so interest charges do not apply
18. AB =
A
8
Los
D
B
1
Answers
Answer: the area of the triangle is 150 cm².
Step-by-step explanation:
To solve this problem, we need to use the formula for the area of a triangle:
Area = (1/2) x base x height
From the diagram, we can see that the base of the triangle is 20 cm and the height is 15 cm. Plugging these values into the formula, we get:
Area = (1/2) x 20 cm x 15 cm
Area = 150 cm²
Therefore, the area of the triangle is 150 cm².
A man earns $65000. He pays 18% of that in tax. (a) Calculate how much he has left, after paying the tax. (b) He invests $4500 and earns 6% interest per annum. Calculate the interest after 2 years. (c) He takes out a loan to buy a car. The price of the car is $24750. He pays $25740 altogether. What is the percentage interest?
Answers
a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
We have,
a)
The amount of tax the man pays.
= $65000 x 0.18
= $11700
Therefore, he has left.
= $65000 - $11700
= $53300
(b)
The interest earned after 2 years.
= $4500 x 0.06 x 2
= $540
(c)
The total amount of interest paid on the loan.
= $25740 - $24750
= $990
The percentage interest.
= ($990 / $24750) x 100%
= 4%
Thus,
(a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
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Find the missing point of the following rectangle. (1, 8) (0, 8) (2, 8) (3, 7)
Answers
The missing point of the rectangle is determined as (3, 8).
What is a rectangle?A rectangle is a four-sided flat shape in which the opposite sides are equal in length and parallel to each other, and all four angles are right angle.
The area of a rectangle is equal to the length multiplied by the width, and the perimeter is equal to the sum of the lengths of all four sides.
Since each angle of a rectangle must be 90 degrees, the length of each opposite side must be equal.
the missing side must be parallel to point (0, 8) and perpendicular to point (3, 7).
the side must be (3, 8)
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Write an equation for a parabola with vertex (1,8) and directrix y = 3.
Answers
i Got u Bro!
Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.
Question 3 of 5
What is the median of the data set?
7, 9, 11, 14, 18, 20, 30, 35
Answers
Answer:
16
Step-by-step explanation:
To find the median, we find the middle of the data set.
7, 9, 11, 14, 18, 20, 30, 35
There are 8 values
7, 9, 11, 14, 18, 20, 30, 35
The median is between the 4th and 5th numbers
We need to find the mean of the middle two numbers
(14+18)/2 =32/2= 16
Answer:
16
Step-by-step explanation:
Median means the middle term in a data set.Remember that, you have to arrange the data points from smallest to largest to find the median of a data set.The formula to find the median of a data set is:[tex]\sf (\frac{n+1}{2}\:)^ t^h \:data[/tex]
Here,
n ⇒ number of terms
Let us find it now.
7, 9, 11, 14, 18, 20, 30, 35
[tex]\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data[/tex]
In this case, add 4th and 5th data and divide it by 2.
[tex]\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16[/tex]
complete the following table , what’s C, AC, BC
Answers
Answer:
C = 45
AC = 1
BC = 2
Step-by-step explanation:
C: 180 - (90 + 45) = 45
AC: Because the angles are the same, it is equal to the other leg, 1 cm
BC: a^2 + b^2 = c^2, so 1 + 1 = 2
A first-year teacher wants to retire in 40 years. The teacher plans to invest in an account with a 6.95% annual interest rate compounded continuously. If the teacher wants to retire with at
least $125,000 in the account, how much money must be initially invested? Round your answer to the nearest dollar.
O$10,234
O$10,755
O $7,902
O $7,755
Answers
The money invested by the teacher to have at least 125,000 in her account after 40 years of a 6.95% annual interest rate compounded continuously is 7755. Hence, the right solution to the question is option D
Compound interest is given by
A = P[tex](1+r)^t[/tex]
where A is the amount
P is the principal
r is the rate of interest
t is the time
Given in the question,
A = $125,000
r = 6.95% or 0.0695
t = 40 years
P is to be found
A = P[tex](1+r)^t[/tex]
125000 = P [tex](1 + 0.0695)^{40[/tex]
125000 = P * [tex]1.0695^{40[/tex]
125000 = 16.118P
P = 7755
The teacher should invest $7755 initially.
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what are the answers to these 4? thank you.
Answers
The area of the different types of polygon with given dimensions are,
Area of octagon= 391.07 cm²
Area of pentagon = 232m²
Area of triangle = 21.22in²
Area of hexagon = 11.24square units.
Polygon name = octagon,
Side length = 9cm
Degree of central angle = 360° /8
= 45°
To find Apothem ,
draw right triangle .
base is half of the side length = 4.5
Top angle of the right triangle = (1/2) × 45°
= 22.5°
Using tangent ratio considering top angle as α
tanα = 4.5/ Apothem length
⇒Apothem length = 4.5 / tan22.5°
⇒Apothem length = 4.5 / (√2 - 1 )
⇒Apothem length = 4.5 / 0.414
⇒Apothem length = 10.86cm.
Area of octagon = 2 ( 1 + √2 ) × (side length)²
= 2 × 2.414 × 9²
= 391.07 cm²
Polygon name = Pentagon,
Apothem= 8m
Degree of central angle = 360° /5
= 72°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle = (1/2) × 72°
= 36°
Using tangent ratio considering top angle as α
tanα = half of side length /Apothem length
⇒(1/2) side length = 8 × tan36°
⇒ side length = 16 × (0.7265)
⇒ side length= 11.62m
Area of pentagon
= 5/2 × side length × distance from the center of sides to the center of pentagon
= 5/2 × 11.6 × 8
= 232m²
Polygon name = triangle,
Apothem= 2in
Degree of central angle = 60°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle =60°
Using tangent ratio considering top angle as α
tanα = half of side length / Apothem length
⇒(1/2) side length = 2 × tan60°
⇒ side length = 4 (√3)
⇒ side length= 6.928in
≈ 7 in
Area of triangle = √3/4 × 7²
= 21.22in²
Polygon name = hexagon,
Apothem= 5
Degree of central angle = 60°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle =30°
Using tangent ratio considering top angle as α
sinα = half of side length / Apothem length
⇒(1/2) side length = 5 × sin30°
⇒ side length = 10 (0.5)
⇒ side length= 5
distance from center of sides to the center of hexagon
= √5² - 2.5²
=4.33
Area = (3√3)/2 × distance from center of sides to the center of hexagon
= (3√3)/2 × 4.33
= 11.24square units.
Therefore, the area of the given polygon are octagon = 391.07 cm² , pentagon = 232m² , triangle = 21.22in² , and hexagon = 11.24square units.
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What is the image point of (-7,-8)after the transformation D1/2oT-1,0?
Answers
The image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).
First, we apply the translation T-1,0, which moves every point 1 unit to the right (since the x-coordinate is decreased by 1) and leaves the y-coordinate unchanged. Therefore, the image of (-7,-8) under T-1,0 is (-7-1,-8) = (-8,-8).
Next, we apply the dilation D1/2, which scales every distance from the origin by a factor of 1/2. Therefore, the image of (-8,-8) under D1/2 is (-8/2,-8/2) = (-4,-4).
Thus, the image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).
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