Answers
The area of sector and perimeter of the sector are 29.04 cm² and 21.12 cm respectively.
The area of the shaded region is 53.81π cm².
The exact area of the shaded region is 3π - 4 - 2√2 cm².
What is the area and perimeter of the sector?To find the area and perimeter of a sector, we use the formulas:
Area of sector = (θ/2) * r²
Perimeter of sector = r + r + θ * r
Using these formulas, we can find the area and perimeter of the sector with r=4cm and θ=4.53 radians:
Area of sector = (4.53/2) * 4²
Area of sector = 29.04 cm²
Perimeter of sector = 4 + 4 + 4.53 * 4
Perimeter of sector = 21.12 cm
To find the area of the shaded region in the sector with r = 12 cm and θ = 1.5 radians, we need to subtract the area of the triangle from the area of the sector.
The angle of the triangle is:
180° - (θ * 180°/π) = 180° - (1.5 * 180°/π)
The angle of the triangle = 68.66°
The radius of the sector is r=12cm, and the central angle is θ=1.5 radians. The area of the sector = (θ/2) * r^2 = (1.5/2) * 12^2 * π
The area of the sector = 81π cm^2
To find the height of the triangle, we can use the sine function:
sin(68.66°) = h / 12
h = 12 * sin(68.66°) = 11.03 cm (rounded to two decimal places)
The base of the triangle is the chord of the sector, which has length:
2 * r * sin(θ/2) = 2 * 12 * sin(1.5/2)
length = 10.28 cm (rounded to two decimal places)
The area of the triangle = (1/2) * base * height = (1/2) * 10.28 * 11.03
The area of the triangle = 56.66 cm²
The area of the shaded region is:
Area of sector - Area of triangle = 81π - 56.66
The area of the shaded region = 53.81π cm²
To find the exact area of the shaded region in the circle with centre O and radius OA=2√2, we first need to find the radius OB. We can use the cosine rule to find the length of OB:
OB^2 = OA^2 + AB^2 - 2 * OA * AB * cos(BOA)
OB^2 = (2√2)^2 + 2^2 - 2 * 2√2 * 2 * cos(135°)
OB^2 = 8 + 4√2
So the radius OB is √(8 + 4√2).
The angle of the sector OAB is:
135° * π/180° = 3π/4 radians
The area of the sector OAB is:
(3π/4) * (2√2)^2 / 2 = 3π cm^2
The area of triangle OAB = (1/2) * OA * OB * sin(OAB) = (1/2) * 2√2 * √(8 + 4√2) * sin(135°)
The area of triangle OAB = (4 + 2√2) cm²
The area of the shaded region = Area of sector OAB - Area of triangle OAB
The area of the shaded region = 3π - (4 + 2√2)
Area of the shaded region = 3π - 4 - 2√2 cm^2
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Related Questions
Five people are to be chosen from a group of 20 to take a trip. In how many ways can this be done if A and B refuse to travel without each other
Answers
Step-by-step explanation:
If A and B refuse to travel without each other, then we can treat them as a single unit. So, we only need to choose 4 people from the remaining 18. The total number of ways to do this is:
${18 \choose 4} = \frac{18!}{4!14!} = 3060$
Therefore, there are 3060 ways to choose 5 people from a group of 20 if A and B refuse to travel without each other.
Obed borrowed $15,640 at 11.5% for 15 years. Use the table below to find his
monthly payment.
Answers
Answer:
Monthly payment is $182.68-----------------------------------
According to given table the amount of monthly payment per $100, when APR is 11.5% and duration of loan 15 years is the intersection of the thrid row and first column. It is 1.168.
Find the amount of monthly payment by dividing the loan amount by 100 and multiplying by the amount mentioned above:
Monthly payment = $15640/100 * 1.168 = $182.68 (rounded to nearest cent)Threfore the montly payment amount is $182.68.
(-7) + (-4) i need to solve this
Answers
A plane a plane took 5 hours to complete a $1,500 Mi trip while flying into the wind coming back it only took 3 hours what is the speed in miles per hour of the plane and the wind
Answers
The speed of the plane in still air is 400 miles per hour and the speed of the wind is 100 miles per hour.
What is speed?
Speed is a measure of how quickly something moves or the distance covered per unit of time.
Let's assume that the speed of the plane in still air is denoted by "p" (in miles per hour) and the speed of the wind is denoted by "w" (in miles per hour).
When the plane flew into the wind, it was flying against the wind resistance which reduced its ground speed. Let's assume that the wind was blowing with a speed of "w" (in miles per hour) during the flight. Then the speed of the plane relative to the ground (i.e. ground speed) would be:
p - w
Similarly, when the plane was flying with the wind on its way back, the ground speed would be:
p + w
Now, we can use the given information to set up two equations:
Distance = Speed x Time
For the first part of the trip (against the wind), the equation becomes:
1500 = (p - w) x 5
Simplifying this equation, we get:
p - w = 300 (Equation 1)
For the second part of the trip (with the wind), the equation becomes:
1500 = (p + w) x 3
Simplifying this equation, we get:
p + w = 500 (Equation 2)
Now we have two equations with two variables. We can solve for "p" and "w" by adding Equations 1 and 2:
2p = 800
p = 400
Substituting this value of "p" into Equation 2, we get:
400 + w = 500
w = 100
Therefore, the speed of the plane in still air is 400 miles per hour and the speed of the wind is 100 miles per hour.
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Use the table and the following information. A survey of students' favorite sports was taken from a random sample of students at Ousley Jr. High. The results are shown in the table.
There are 550 students in the school. Predict how many students at the school prefer Track & Field based on the facts from the table.
Answers
110 students at the school prefer Track & Field based on the facts from the table.
How to predict how many students at the school prefer Track and Field?
To predict how many students at the school prefer Track and Field, we can use this information and assume that the same proportion of students who prefer Track and Field in the sample will also prefer it in the larger population.
Based on the table, we know that out of a total of 20 students surveyed, 4 prefer Track and Field.
We can set up a proportion:
[tex] \frac{4}{20} = \frac{ x}{550}[/tex]
where x is the number of students at the school who prefer Track and Field.
Solving for x, we get:
[tex]x = \frac{4}{20} \times 550 = 110[/tex]
Therefore, we can predict that about 110 students at the school prefer Track and Field based on the given information.
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(ANSWER ASAP!! :) GIVING BRAINLIEST WHEN I CAN)
There are 3 teaspoons in each tablespoon. Which equation best represents y, the total number of teaspoons in x tablespoons?
A: x = 3 + y
B: y = 3x
C: y = 3 + x
D: x= 3y
Answers
The equation that best represents y, the total number of teaspoons in x tablespoons is B: y = 3x.
What is an equation?An equation is a mathematical statement showing the equality or equivalence of two or more mathematical expressions.
While mathematical expressions combine variables, numbers, constants, and values with algebraic operands, equations are two or more expressions combined with the equation symbol (=).
The number of teaspoons in each tablespoon = 3
Let the number of teaspoons = y
Let the number of tablespoons = x
Equation:y = 3x.
Thus, the correct equation is Option B.
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12 X 1 and 1 and 6/10
Answers
The value of the expression is 12.6.
Given is an expression, (12 × 1) + (1 × 6/10), we need to simplify it,
(12 × 1) + (1 × 6/10)
= 12 + 6/10
= 126 / 10
= 12.6
Hence, the value of the expression is 12.6.
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x + 63 = 200=what bro can you solve it
Answers
Answer:X= 137
Step-by-step explanation: 137 + 63 = 200
Answer:137
Step-by-step explanation: 200 - 63 = 137 = X
Plot and label 2 on the number line. Use the relationship between 1 and 10/4 to help you
Answers
To plot 2 on the number line, we first need to locate the point for 1 and 10/4, and then we can find the midpoint between them.
We know that 1 is located to the left of 10/4, because 10/4 is equal to 2.5, which is greater than 2. So we can plot 1 to the left of the midpoint of the segment between 2 and 3.
To find the midpoint of the segment between 2 and 3, we can use the relationship between 1 and 10/4. We know that 10/4 is equal to 2.5, which is halfway between 2 and 3. So if we take the average of 1 and 2.5, we get:
(1 + 2.5) / 2 = 1.75
So 1.75 is the midpoint of the segment between 2 and 3. We can plot this point on the number line and label it as 10/4.
Finally, we can find the point halfway between 1.75 and 2, which is:
(1.75 + 2) / 2 = 1.875
Thus, 1.875 is the point halfway between 1 and 2. We can plot this point on the number line and label it as 2.
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Mathematics test score
550 to 599
Check
600 to 649
650 to 699
700 to 749
750 to 799
Frequency
6
10
15
12
8
ILL He test scores from a study which looked at 51 students who completed preparation
Students on a particular nationwide math test. Included in the ar
Based on the frequency distribution, using the midpoint of each data class, estimate the mean mathematics test score for the students in
intermediate computations, use four or more decimal places, and round your answer to one decimal place.
Answers
Answer: The estimated mean mathematics test score for the students is 685.7.
Step-by-step explanation: To estimate the mean mathematics test score, we can use the midpoint of each data class and the formula for calculating the weighted mean:
Midpoint of 550-599 class = (550 + 599) / 2 = 574.5
Midpoint of 600-649 class = (600 + 649) / 2 = 624.5
Midpoint of 650-699 class = (650 + 699) / 2 = 674.5
Midpoint of 700-749 class = (700 + 749) / 2 = 724.5
Midpoint of 750-799 class = (750 + 799) / 2 = 774.5
Weighted mean = (frequency of 550-599 class * midpoint of 550-599 class + frequency of 600-649 class * midpoint of 600-649 class + frequency of 650-699 class * midpoint of 650-699 class + frequency of 700-749 class * midpoint of 700-749 class + frequency of 750-799 class * midpoint of 750-799 class) / (total frequency)
Weighted mean = (6 * 574.5 + 10 * 624.5 + 15 * 674.5 + 12 * 724.5 + 8 * 774.5) / (6 + 10 + 15 + 12 + 8)
Weighted mean = 685.7 (rounded to one decimal place)
Therefore, the estimated mean mathematics test score for the students is 685.7
A Kenkey seller operates in two markets. In market 1, research indicates that the price elasticity of demand is (-) 0.25 while that for market 2 is (-) 2.5. The seller has decided to reduce the price of Kenkey by 10% this month in both markets.
i. Calculate the percentage change in quantity demand for Kenkey in both markets. Explain the result of the Kenkey seller’s action on the total revenue for both markets.
ii. Compute the marginal revenue for both markets if the price charged in market 1 and 2 are GH¢ 2 and GH¢ 1.50 respectively.
iii. As the firm’s adviser, suggest an alternative pricing strategy to the Kenkey seller.
Answers
In market 1, the quantity demanded will increase by 2.5% while in market 2, the quantity demanded will increase by 25%.
How to calculate the value% Change in Quantity Demanded (Market 1) = (-) 0.25 * (-10%) = 2.5%
% Change in Quantity Demanded (Market 2) = (-) 2.5 * (-10%) = 25%
The negative sign for price elasticity of demand means that demand is inversely related to price.
For market 1:
Price = GH¢ 2
Quantity demanded = Q1
Change in price = -10% x GH¢ 2 = -GH¢ 0.20
Change in quantity demanded = 2.5% x Q1
Change in revenue = GH¢ 2.00 x 2.5% x Q1 = GH¢ 0.05 Q1
Marginal revenue = Change in revenue / Change in quantity demanded
Marginal revenue = (GH¢ 0.05 Q1) / (2.5% x Q1)
Marginal revenue = GH¢ 2.00
For market 2:
Price = GH¢ 1.50
Quantity demanded = Q2
Change in price = -10% x GH¢ 1.50 = -GH¢ 0.15
Change in quantity demanded = 25% x Q2
Change in revenue = GH¢ 1.50 x 25% x Q2 = GH¢ 0.375 Q2
Marginal revenue = Change in revenue / Change in quantity demanded
Marginal revenue = (GH¢ 0.375 Q2) / (25% x Q2)
Marginal revenue = GH¢ 1.50
iii. An alternative pricing strategy for the Kenkey seller could be to implement a tiered pricing system based on the price elasticity of demand in each market.
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1. Assuming a project produces export goods and uses imported and non traded inputs, the OER is 17.5birr/dollar the SER is 21 birr/dollar. Assume further all output is exported at annual value of 3500 dollar. The cost of investment has foreign components of 1200 dollar and non traded component of 7500 birr. There are traded inputs of 900 dollar and non traded inputs of 12,000birr annually. The project life is 3 years. Calculate the net benefit of the project using the two approaches (UNIDO & Littele-Mirrles).
Answers
The total revenue over the project life of 3 years is $10,500, the total costs over the project life of 3 years is 111,750 birr and Net benefit of the project is $4,107
The annual value of exports is $3,500.
Therefore, the total revenue over the project life of 3 years is 3 × $3,500 = $10,500.
The cost of investment has foreign components of $1,200, which is equivalent to 21,000 birr (1,200 × 17.5).
The non traded component of the cost of investment is 7,500 birr.
The total cost of investment is therefore 21,000 + 7,500 = 28,500 birr.
The annual cost of traded inputs is $900, which is equivalent to 15,750 birr (900 × 17.5).
The total cost of traded inputs over the project life of 3 years is 3 × 15,750 = 47,250 birr.
The annual cost of non traded inputs is 12,000 birr.
The total cost of non traded inputs over the project life of 3 years is 3 × 12,000 = 36,000 birr.
Therefore, the total costs over the project life of 3 years is 28,500 + 47,250 + 36,000 = 111,750 birr.
Net benefit = Total revenue - Total costs
= $10,500 - (111,750 ÷ 17.5)
= $10,500 - 6,393
= $4,107
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Find the rate of change on the interval [0, 3] for the function below
A. 7/3
B.3/7
C.2
D.7
Answers
The average rate of change of the function on the interval [0,3] is given as follows:
A. 7/3.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
The numeric values for the function are given as follows:
When x = 0, y = 1.When x = 3, y = 8.Hence the average rate of change is given as follows:
r = (8 - 1)/(3 - 0)
r = 7/3.
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Write an explicit formula for an, the nth term of the sequence 30, 35, 40
Answers
Answer:
The sequence is increasing by 5 at each step. So, we can write:
a1 = 30
a2 = 30 + 5 = 35
a3 = 30 + 25 = 40
a4 = 30 + 35 = 45
a5 = 30 + 4*5 = 50
We notice that the nth term is given by:
an = 30 + (n-1)5
So, the explicit formula for the nth term is:
an = 25n + 5
6b. What does point (10,30) mean in this situation?
This has multiple answers. You must pick all the correct choices for it to be marked
correct
r
C
The point (10,30) is a solution to the equation 27x+15y=645
The point (10,30) is not a solution to the equation 27x+15y=645
The point (10,30) means 10 adult tickets and 30 children tickets that cost $545 total
The point (10,30) means 4 adult tickets and 30 children tickets that do not cost
$645
Answers
The correct answers are:
The point (10,30) is a solution to the equation 27x+15y=645
The point (10,30) means 10 adult tickets and 30 children tickets that cost $545 total.
For the data shown, answer the questions. Round to 4 decimal places where possible. Find the mean: Find the median: Find the standard deviation: 25.8 6.4 21.4 24 3.2 18.3 20.3 23.1
Answers
The mean is equal to 17.8125.
The median is equal to 20.85.
The standard deviation is equal to 61.6386.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
25.8, 6.4, 21.4, 24, 3.2, 18.3, 20.3, 23.1
For the total number of data, we have;
Total, F(x) = 25.8 + 6.4 + 21.4 + 24 + 3.2 + 18.3 + 20.3 + 23.1
Total, F(x) = 142.5
Mean = 142.5/8
Mean = 17.8125.
For the median, we have;
By sorting from least to greatest 3.2,6.4,18.3,20.3,21.4,23.1,24,25.8
Median = (20.3 + 21.4)/2
Median = 20.85
For the standard deviation, we have;
Standard deviation, S = √(1/n × ∑(xi - u₁)²)
Standard deviation, S = √(1/8 × (25.8 - 17.8125)² ..... + (23.1 - 17.8125)²)
Standard deviation, S = 493.10875/8
Standard deviation, S = 61.6386
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Janine is planning on creating a water-based centerpiece for each of the 30 tables at her wedding reception. She has already purchased a cylindrical vase for each table. The radius of the vases is 6 cm and the height is 28 cm. She intends to fill them halfway with water and then add a variety of colored marbles until the waterline is approximately three-quarters of the way up the cylinder. She can buy bags of 100 marbles in 2 different sizes, with radii of 9 mm or 12 mm. A bag of 9 mm marbles costs $3 and a bag of 12 mm marbles costs $4.
Answers
using 12 mm marbles would be more cost-effective, with a total cost of $360 compared to $810 for 9 mm marbles.
How to solve?
To calculate the number of marbles needed per vase, we first need to calculate the volume of each vase. The volume of a cylinder can be calculated using the formula V = πr²2h, where r is the radius and h is the height.
V = π(6 cm)²2(28 cm) / 2 = 3,758.76 cm²3
Since Janine intends to fill each vase halfway, the volume of water needed per vase would be:
V_water = 3,758.76 cm²3 / 2 = 1,879.38 cm²3
To calculate the volume of marbles needed per vase, we can subtract the volume of water from the total volume of the vase:
V_marbles = 3,758.76 cm²3 - 1,879.38 cm²3 = 1,879.38 cm²3
We can now calculate the number of marbles needed per vase based on the size of the marbles:
For 9 mm marbles:
The radius is 0.9 cm (9 mm / 10)
The volume of one marble can be calculated using the formula V = (4/3)πr²3
V_marble = (4/3)π(0.9 cm)²3 ≈ 2.138 cm²3
Number of marbles needed = V_marbles / V_marble = 879.38 cm^3 / 2.138 cm²3 ≈ 826 marbles
Total cost = 30 tables × $3/bag × 9 bags = $810
For 12 mm marbles:
The radius is 1.2 cm (12 mm / 10)
The volume of one marble can be calculated using the formula V = (4/3)πr²3
V_marble = (4/3)π(1.2 cm)²3 ≈ 7.238 cm²3
Number of marbles needed = V_marbles / V_marble = 1,879.38 cm²3 / 7.238 cm²3 ≈ 260 marbles
Total cost = 30 tables × $4/bag × 3 bags = $360
Therefore, using 12 mm marbles would be more cost-effective, with a total cost of $360 compared to $810 for 9 mm marbles.
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Jimoth has 5 apples. Brian has 3 more apples than Jimoth. Jamal has 2 apples less than brian. If jamal has X apples, what is X?
Answers
Answer: X = 6
Step-by-step explanation:
Answer: x = 6 beaues 3 + 5= 8 and 8-2 = 6 ezzz
Step-by-step explanation:
Miranda is describing the bowling season: "I did okay. They ranked the bowlers on my team according to average scores and I was somewhere in the middle. Not as well as some of the other players, but not as bad as some. When I looked at the sores of all my games, I noticed that they were close to each other, so at least I was consistent."
Which statement best describes Miranda's performance?
Answers
My scores were near the median for my team and my MAD was low.
PLEASE HELPPPP LOOK AT THE PICTURE BELOW
Answers
Answer:
a) 29.0%
b) 25.2%
Step-by-step explanation:
denote T: total number of MM; G: green MM; R: red MM
a)
(G)/(T) * (G-1)/(T-1)
(32)/(27+32) * (32-1)/(27+32-1)
=(32/59) *(31/58)
=0.289888953
b)
(R)/(T) * (G)/(T-1)
(27)/(27+32) * (32)/(27+32-1)
=(27/59) * (32/58)
=0.252483927
To test the hypothesis that 55% of those families who plan to purchase a vacation residence in Florida want a condominium, the null hypothesis is π = 0.55 and the alternate is π ≠ .55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. To perform the hypothesis testing, we need to satisfy two things. The first thing is to have a binomial distribution in the question, which is the number of families who planned to buy condominiums in the sample. What is the other requirement we need to meet?
Answers
The answer of the given question based on hypothesis is ,(a) the number of family is the sample size of 400 satisfies this requirement. (b) that the sample size should be sufficiently large.
What is Hypothesis?In mathematics, a hypothesis is statement or proposition that is assumed to be true for sake of argument or investigation, but has not been proven or demonstrated to be true. It is an educated guess or prediction that is based on previous observations or knowledge, and is used to guide further investigation or experimentation.
The other requirement that we need to meet to perform the hypothesis testing is that the sample size should be sufficiently large. A general rule of thumb is that the sample size should be at least 10 times larger than the number of successes and 10 times larger than the number of failures.
In this case, since we have 228 successes (families who want a condominium) and 172 failures (families who do not want a condominium), the sample size of 400 satisfies this requirement.
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Convert the sum to a percent, 2.3% + 3/4 + .01
Answers
Converting the sum to a percentage, we find that the sum of 2.3%, 3/4 and 0.01 equals 78.3%.
How to convert sum to a percentage?The first step is to add the numbers:
2.3% + 3/4 + 0.01 = 0.023 + 0.75 + 0.01 = 0.783After the sum, we can convert this decimal to a percentage by multiplying by 100:
0.783 × 100 = 78.3%Therefore, to convert a sum of different units to a percentage, we need to first convert all the values to a common unit, then add them together, and finally multiply the sum by 100 to express it as a percentage. In this particular case, we converted the fraction 3/4 to a decimal, added all three values together, and then multiplied the result by 100 to obtain the answer of 78.3%.
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What is the purpose of headings in a table?
A. To help users understand the categories of information found in
each column and row
B. To identify the specific source of the information or data found in
the columns
C. To provide detailed and colorful information that is easy to
understand
OD. To briefly describe what information is included in the table as a
whole
SUBMIT
Answers
The purpose of headings in a table is option A. To help users understand the categories of information found in each column and row
Headings in a table.A table is a method of classifying a given set of information into appropriate number of columns with respect to their individual class called headings.
Headings are used in the categorization of a set of information into a presentable form of columns called a table. It thus helps to identify a the source of an information as presented in the table.
Therefore, the purpose of headings in a table is that given in option A. That is; To help users understand the categories of information found in each column and row.
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Select the postulate of equality or inequality that is illustrated. If 5 = x + 2, then x + 2 = 5, Thank you
Answers
1. A hummingbird's nest is 5.7 meters high in a tree and a flower is on the ground 12.3 meters away from the
base of the tree. How far will the hummingbird need to fly to get from its nest to the flower?
Answers
If you put all the sunflowers together end to end, what would be the total length of all the sunflowers?
inches
Answers
Using multiplication, the total length of all the sunflowers in the garden is 1,260 inches.
What is multiplication?Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.
Multiplication operation involves the multiplicand, the multiplier, and the product.
The total number of sunflowers in the garden = 210
The length of each sunflower = 6 inches
The total length of all the sunflowers = 1,260 inches (210 x 6)
Thus, based on multiplication operation, the total length of the sunflowers in the garden can be stated to be 1,260 inches.
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Question Completion:Assume that each sunflower measures 6 inches in length and there are 210 sunflowers in the garden.
A person must pay
5 to play a certain game at the casino. Each player has a probability of 0.13 of winning
15. Each player has a probability of 0.87 of losing the game and winning nothing.
What is the Expected Value for the player? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.
Expected Value = $
If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind?
behind
ahead
Answers
The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $[tex]2.40[/tex] for each game played.
What is the probability of losing by the amount paid?To calculate the Expected Value for the player, we can multiply the probability of winning by the amount won, and subtract the probability of losing by the amount paid.
Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Paid)
Given the following information:
Probability of winning [tex]= 0.13[/tex]
Amount won = $15
Probability of losing [tex]= 0.87[/tex]
Amount paid = $5
Plugging these values into the formula:
Expected Value [tex]= (0.13 \times $15) - (0.87 times $5)[/tex]
Expected Value [tex]= $1.95 - $4.35[/tex]
Expected Value = [tex]-$2.40[/tex]
If a person plays this game a very large number of times over the years, we expect them to come out financially behind, as the Expected Value is negative. This indicates that, on average, the player will lose money over time by playing this game repeatedly.
Therefore, The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $2.40 for each game played.
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Graph the circle whose equation is x^2 + y^2 =16
a. What is the center of this circle? Plot and label it on the graph.
b. What is the radius of this circle?
Answers
The center of this circle is (0, 0) and the radius is 4 units
What is the center of this circle?The equation x^2 + y^2 = 16 represents a circle centered at the origin (0, 0), since the x-coordinate and y-coordinate terms are squared and added together.
The center of the circle is therefore (0, 0), which we can plot on the graph
What is the radius of this circle?The radius of the circle is the square root of the constant term on the right-hand side of the equation,
Which in this case is 16.
So the radius is 4.
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d. tan 0 = 0.7536
Hypotenuse = 29 miles
Opposite side?
Answers
In this case, we know that the hypotenuse is 29 miles and the value of sin(theta) is given as 0.7536. Therefore, opposite side = 29 * 0.7536 = 21.8344 miles (rounded to four decimal places).
Therefore, the opposite side is approximately 21.8344 miles.
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Answers
22 inches is the measure of the unknown side ZW
Properties of a parallelogramGiven a parallelogram WXYZ, since the opposite sides of a parallelogram is equal, hence WX = YZ
Given the following
WX = 8x + 2
YZ = 5x + 11
Substitute
8x + 2 = 5x + 11
8x - 5x = 11 - 2
3x = 9
x = 3
Determine the measure of ZW
ZW = XY = 6x + 4
ZW = 6(3) + 4
ZW = 18 + 4
ZW = 22
Hence the measure of the side ZW is 22 inches
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