Answers
The solutions for θ between 0 and 2π are:
θ = π/4, 3π/4, 5π/4, 7π/4.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.
Starting with the equation:
√2sinθ + 1 = 0
Subtracting 1 from both sides, we get:
√2sinθ = -1
Squaring both sides, we get:
2sin²θ = 1
Dividing both sides by 2, we get:
sin²θ = 1/2
Taking the square root of both sides, we get:
sinθ = ± √2/2
Using the unit circle, we know that sinθ = √2/2 at π/4 and 3π/4, and sinθ = -√2/2 at 5π/4 and 7π/4.
Therefore, we have:
sinθ = √2/2 at θ = π/4 + 2πn, 3π/4 + 2πn
sinθ = -√2/2 at θ = 5π/4 + 2πn, 7π/4 + 2πn
Thus, the solutions for θ between 0 and 2π are:
θ = π/4, 3π/4, 5π/4, 7π/4.
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Related Questions
A right circular cylinder has a height of 1934 ft and a diameter 125 times its height.
What is the volume of the cylinder?
Enter your answer as a decimal in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Answers
Answer: 545,884,646.36 ft3.
Step-by-step explanation:
The volume of the cylinder is calculated using the formula V=πr2h, where r is the radius of the cylinder and h is the height. The radius of the cylinder can be calculated by dividing the diameter (125 times the height) by 2.
Therefore, the radius = (125 * 1934) / 2 = 118,550 / 2 = 59,275 ft
Plugging in the values of radius and height into the formula, the volume of the cylinder is V = 3.14 * (59,275)2 * 1934 = 545,884,646.36 ft3
Rounding to the nearest hundredth, the volume of the cylinder is 545,884,646.36 ft3.
State whether each investment below realized a profit or loss. Compute the percent of increase or decrease.
Purchase Price: $12.00
Selling Price: $8.25
Answers
The given investment realized a loss of $3.75 with 31.25% decrease.
What is profit?The amount made by selling a product, which should be greater than the product's cost price, is generally referred to as the profit. It is the profit generated by all business activities. In other words, a product is deemed to have made a profit if its selling price (SP) exceeds its cost price (CP). It explains the financial gain realised when the revenue from a company activity outpaces the costs, like as taxes and expenses, involved in maintaining a business activity.
Given : Purchase Price: $12.00
Selling Price: $8.25
Since the purchase price is more than the selling prize, So the investment has been sold at a loss.
The loss on investment = Purchasing price - Selling price
= $ 12 - 8.25
= $3.75.
% of decrease = (loss/ purchasing price) × 100
= 3.75/12 × 100
= 31.25 %
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Which statement is NOT true about the dot plot the right?
Answers
A statement is not true about the dot plot to the right include the following: A. the French Club has a greater mean than the Spanish Club.
What is a dot plot?In Mathematics, a dot plot is a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
How to calculate the mean for a data set?Mathematically, the mean for this set of scores can be calculated by using the following formula:
Mean = [F(x)]/n
Mean of French Club = 1/12(18 + (19 × 4) + (20 × 4) + (21 × 2) + 22)
Mean of French Club = 1/12(238)
Mean of French Club = 119/6 = 19.83.
Mean of Spanish Club = 1/12(18 + (19 × 2) + (20 × 3) + (21 × 3) + (22 × 3))
Mean of Spanish Club = 1/12(246)
Mean of Spanish Club = 123/6 = 20.5.
Therefore, 19.83 is less than 20.5.
Median of French Club = 20
Median of Spanish Club = (20 + 21)/2 = 20.5.
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Tommy goes to the video store and rents 2 video games for $3.99 each. He also rents the latest Sonic The Hedgehog movie for $3.50. He gives the clerk a twenty-dollar bill. How much change should Tommy receive?
Answers
Answer:
8.52
Step-by-step explanation:
add the two 3.99 making 7.98 then add 3.50 making 11.48 then substract that from 20.00 making the final answer 8.52
Plot the following points in the plane: (2, 1), (-1/2, 0), (π, -3). Is there a point in the plane for which you need exactly three numbers to specify its location?
Answers
There is no such point that requires exactly three numbers to specify its location.
What is the Euclidean plane?A mathematical notion known as the Euclidean plane symbolizes a two-dimensional environment in which points, lines, and forms may be specified and altered. The Greek mathematician Euclid, who originally described the geometry of the plane in his book Elements, is honoured by the name of the object. The Pythagorean theorem is used to calculate distance in the Euclidean plane, while degrees or radians are used to calculate angles.
The plane doesn't have any points that can be precisely located by three integers. Each point in the Euclidean plane may be found using only two integers, namely its x- and y-coordinates.
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Find the value of the angle θ rounded to 1 DP.
The diagram is not drawn accurately.
Answers
Check the picture below.
[tex]\sin(24^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{17}}\implies 17\sin(24^o )=y \\\\[-0.35em] ~\dotfill\\\\ \sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{y}}\implies \theta =\sin^{-1}\left( \cfrac{4}{y} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{4}{17\sin(24^o )} \right)\implies \theta \approx 35.3^o[/tex]
Make sure your calculator is in Degree mode.
XPO Corporation has a minimum tax credit of $51,000 from 2017. XPO’s 2018 tax liability before any MTC carryover is $30,500. What is XPO’s minimum tax credit carryover to 2019, if any?
Answers
XPO's minimum tax credit carryover to 2019 is $20,500.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.
Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.
To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:
Minimum tax credit carryover = $51,000 - $30,500 = $20,500
Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.
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Before a renovation, a movie theater had 127 seats. After the renovation, the theater has 188 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answers
Answer:
48% hope this helps!
Step-by-step explanation:
188-127= 61 <--(increase)
divide increase by original( 61/127= 0.480)
Multiply by 100 to get percent (0.480x100= 48%)
Calc for business!
Please help!
A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by =-0.088N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?
Answers
(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.
Describe Rate of change?The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.
(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:
N(t) = No e^(-0.088t)
where No is the initial amount of the substance present at t=0.
(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:
N(t) = 400 e^(-0.088t)
To find how much will remain after 3 days, we need to evaluate N(3):
N(3) = 400 e^(-0.088*3) ≈ 323.3 g
Therefore, approximately 323.3 g of the substance will remain after 3 days.
(iii) The rate of change of the amount of the substance after t days is given by:
dN/dt = -0.088N
To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:
dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day
Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.
(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:
N(t) = 200
Substituting No = 400 into the exponential function, we get:
400 e^(-0.088t) = 200
Dividing both sides by 400, we get:
e^(-0.088t) = 0.5
Taking the natural logarithm of both sides, we get:
ln(e^(-0.088t)) = ln(0.5)
Simplifying, we get:
-0.088t = ln(0.5)
Solving for t, we get:
t ≈ 7.88 days
Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.
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At a local bed and breakfast, guests have a choice of 3 themes for their room, 2 sizes of rooms, and 4 breakfast options. How many choices are available to guests when booking their stay?
Answers
Answer:
there are 24 different choices available to guests when booking their stay at the bed and breakfast.
Step-by-step explanation:
To find the total number of choices available to guests at the bed and breakfast, you can use the multiplication principle of counting.
According to the multiplication principle, if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
Using this principle, we can calculate the total number of choices available to guests by multiplying the number of choices for each option:
Choice of 3 themes for their room: 3 options
Choice of 2 sizes of rooms: 2 options
Choice of 4 breakfast options: 4 options
Total number of choices = 3 x 2 x 4 = 24
Therefore, there are 24 different choices available to guests when booking their stay at the bed and breakfast.
There are 100 students in a band. Ninety percent of the students are either 12 or
13 years old. The number of 13-year-olds is 125% of the number of 12-year-olds. The rest of
the students are 14 years old. Write the portion of the band for each age as a fraction and a
percent.
12-year olds: fraction: *blank*, percent: *blank*
13-year olds: fraction: *blank*, percent: *blank*
14-year olds: fraction: *blank*, percent: *blank*
Answers
Answer:
Step-by-step explanation:
Let's first find the number of 12-year-olds and 13-year-olds in the band:
Let x be the number of 12-year-olds.
Then the number of 13-year-olds is 1.25x (125% of x).
The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).
Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.
The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:
The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.
10% of 100 is 10, so there are 10 14-year-olds.
Now we can find the portion of the band for each age group:
12-year olds: fraction = 40/100 = 2/5, percent = 40%
13-year olds: fraction = 50/100 = 1/2, percent = 50%
14-year olds: fraction = 10/100 = 1/10, percent = 10%
Alison saved 15% on the cost of her computer software, which was $355. How much did Alison save?
Answers
Answer:
$53.25
Step-by-step explanation:
$[tex]\frac{355}{100}= 1[/tex]%
$[tex]15\frac{355}{100} = 15[/tex]%[tex]= 53.25[/tex]$
Answer:
53.25
Step-by-step explanation:
Ben drew a rectangle. The length of his rectangle is the width of the rectangle.
1/3
Let & = length.
Let w = width.
W
Complete the table, and graph
Answers
Based on the relationship between the length and width of the rectangle, the length of the rectangle for the various values of the width is given below:
when width, W = 1, Length, l = 1/3when width, W = 3, Length, l = 1when width, W = 7, Length, l = 7/3What is the relationship between the length and the width of the rectangle?The relationship between the length and the width of the rectangle is a linear relationship given by the linear equation below:
l = w/3
where;
l is the length of the rectangle
w is the width of the rectangle
When w = 1
l = 1/3
When w = 3
l = 3/3
l = 1
when w = 7
l = 7/3
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nework activity 8.1 Calculate the perimeter of a wall in a classroom where the length is 10 m and the height of the vall is 3 m. A computer desk has a length of 70 cm and a breadth of 40 cm. Work out the perimeter of the computer desk. The length of a wall in a computer classroom is 15 m. How many computer desks can be placed side-by-side along the wall?
Answers
The perimeter of the wall in a classroom is 26 meters.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Given that, a wall in a classroom measures, the length is 10 m and the height is 3 m.
So, the perimeter of wall is 2(Length+Height)
= 2(10+3)
= 2×13
= 26 meters
A computer desk has a length of 70 cm and a breadth of 40 cm.
Now, the perimeter of a computer desk is 2(Length+Breadth)
= 2(70+40)
= 220 cm
220 cm can be written as 220/100 = 2.2 meters
Number of computers v=can be placed along wall =15/2.2
= 6.8
≈ 7
Therefore, approximately 7 computers desks place along the wall.
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In the given equation, b is a positive constant.
The sum of the solutions of the equation is 5.
What is the value of b?
x²(x+3)(x - b) = 0
Answers
Answer: b = 8
Step-by-step explanation:
From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.
Let's factor the equation and set each factor equal to zero:
x²(x+3)(x - b) = 0
x = 0 or x + 3 = 0 or x - b = 0
Solving for x in each case, we get:
x = 0 or x = -3 or x = b
Since the sum of the solutions is 5, we can write:
0 + (-3) + b = 5
Simplifying, we get:
b - 3 = 5
Adding 3 to both sides, we get:
b = 8
Therefore, the value of b is 8.
b = 8.
Step by step solved:
Since the equation is equal to zero, it can be factored into three parts: x²=0, x+3=0, and x-b=0.
The solutions for x²=0 are x=0 and x=0 (a double root).
The solution for x+3=0 is x=-3.
The solution for x-b=0 is x=b.
Therefore, the sum of the solutions is 0 + 0 + (-3) + b = 5.
Simplifying the equation, we get b = 8.
So the value of b is 8.
A traffic light cycles through red, yellow, and green every 2 minutes. How many seconds does the cycle last? Show your work?
Answers
Answer:
Step-by-step explanation:
number of minuties for whole cycle
green time+yellow time+ orange time
2+2+2=6
min to seconds==> 1min=60 seconds
so 6*60=360 seconds
Enjoy:)
A container holds 2 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
Answers
Answer: 32 Ounces
Step-by-step explanation:
The container holds 32 ounces because if there are 2 pounds of peanuts, and 1 pound = 16 ounces, then you multiply 16 by 2.
16 x 2 = 32
Margo borrows $2000 agreeing to pay it back with 8% annual
Answers
In response to the supplied query, we may state that Margo will thus interest have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The principle balance divided by the interest rate is the most typical approach to compute interest.
Margo will be required to repay the $2000 she borrowed plus an additional 8% of that sum as interest each year if she borrows the money at an 8% annual interest rate.
principle multiplied by the interest rate equals interest.
where "principal" refers to the initial loan amount and "rate" is the interest rate in decimal form. The interest rate in this situation is 8%, or 0.08 in decimal form.
Margo will so be required to pay the following interest each year:
interest: $160 x ($2,000 x 0.08)
Margo will thus have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.
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Write 2 multiplication or division expressions that equal -360
Answers
This expression divides 360 by -1 to get -360.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.
Here are two possible multiplication/division expressions that equal -360:
18 x (-20) = -360
This expression multiplies 18 by -20 to get -360.
360 ÷ (-1) = -360
Therefore, This expression divides 360 by -1 to get -360.
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- Find the truth set of 4x +2 = 3(2x)
Answers
Answer:
y = −x2 + 2x −5
Step-by-step explanation:
To find the truth set of the equation 4x + 2 = 3(2x), we need to solve for x and then determine the values of x that make the equation true.
Starting with the equation:
4x + 2 = 3(2x)
Distribute the 3 on the right-hand side:
4x + 2 = 6x
Subtract 4x from both sides:
2 = 2x
Divide both sides by 2:
1 = x
Therefore, the truth set of the equation 4x + 2 = 3(2x) is {1}. In other words, the equation is only true when x is equal to 1.
14 1/2 x 6 1/2 x 6 1/2
Answers
14[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex]
= 14[tex]\frac{1}{2}[/tex] x 36[tex]\frac{1}{4}[/tex]
= 504[tex]\frac{1}{8}[/tex]
Answer:
273/2
Step-by-step explanation:
Pilots can make quick calculations by solving one-step equations. For instance: the distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. If an aircraft is 10,000 feet above the ground, write and solve an equation to find the distance the pilot should begin descending.
Answers
Let d be the distance in miles from the airport that a plane should begin descending. According to the problem statement, we can write the equation:
d/3 = 10
To solve for d, we can isolate it by multiplying both sides of the equation by 3:
d = 3 * 10
Therefore, the pilot should begin descending when the plane is 30 miles from the airport.
A new employee at a woodworking repair shop is asked to remove some minor stains from a wooden patio table. He decides to use grade 1 steel wool thinking that a higher grade of steel wool will be most effective in quickly removing the stains.
What faulty inference did the employee use to make this decision?
There is little difference between grade levels of steel wool.
The coarser the steel wool grade, the less steel wool needed.
The higher the steel wool grade, the less muscle power required.
The coarser the steel wool, the better for all woodworking repair jobs
Answers
The higher the steel wool grade, the less muscle power required.
What faulty inference did the employee use to make this decision?The faulty inference the employee used to make this decision is that a higher grade of steel wool will be more effective in quickly removing stains. In reality, higher grade steel wool is more abrasive and can actually damage the wood surface, leaving behind scratches and making the problem worse.
Grade 1 steel wool is the finest grade and is typically used for finishing and polishing wood. It is not suitable for removing stains, as it is not abrasive enough to remove the outer layer of the wood where the stain is located. To remove stains from wood, it is recommended to use a lower grade of steel wool or a non-abrasive cleaning solution specifically designed for wood.
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The length of a gulf park is 2.5km long is represented on a map by a line 250mm long.What is the scale of the map.
Answers
The scale of the map is 1/10,000.
The formula used to find the formula to find the scale is
scale = length on the map / actual length
Given,
Actual length of the golf park = 2.5 km
length on map = 250 mm
Here, we need to convert both lengths into the same units
2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm
we know that,
scale = length on the map / actual length
= 250 mm / 2,500,000 mm
= 1/10,000.
Therefore, the scale of the map is 1/10,000.
i.e, one unit on the map is equal to 10,000 units of length in reality.
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A political scientist takes a simple random sample of n = 140 registered voters in Maricopa County, AZ to determine the proportion of registered voters who consider themselves Democrats. Assume the (unknown) true proportion of registered voters who are Democrats is 46%.
Answers
Using percentage, the true proportion of registered voters who are Democrats is = 64.
What do you mean by percentage?
A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.
It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.
In the question,
Sample size, n = 140.
Now 46% of the registered voters are Democrats.
Now the no. of registered voters =
46% of 140
= 46/100 × 140
= 6440/100
= 64.4
≈ 64
Therefore, 64 is the true proportion of registered voters who are Democrats.
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Find the H.C.F by division method a) 30,45,60
Answers
The H.C.F. of 30, 45, and 60 using the division method is 30.
What is the HCF of the numbers?To find the H.C.F. (Highest Common Factor) of the given numbers using division method, we can follow these steps:
Step 1: Divide the larger number by the smaller number and find the remainder.Step 2: Now, divide the smaller number obtained in the previous step by the remainder.Step 3: Continue this process of dividing the previous divisor by the remainder until the remainder becomes zero.Step 4: The last divisor obtained in the above process is the H.C.F. of the given numbers.Let's apply this method to find the H.C.F. of 30, 45, and 60.
Step 1: We start by dividing the larger number, 60, by the smaller number, 30.
60 ÷ 30 = 2 with a remainder of 0
Step 2: Now, we divide the smaller number, 30, by the remainder, which is 0.
30 ÷ 0 = undefined
Since the remainder is zero, we stop the process here. The last divisor we obtained is 30. Therefore, the H.C.F. of 30, 45, and 60 is 30.
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Hello, I need help with this problem. Thanks
Answers
Graph the following functions and determine where F(x) = G(x). State the x values only. Select all that apply.
f(x)= -x^2+8x-13 and g(x)= x+3
a. 4
b. no solution
c. all real numbers
d. -13
Answers
For the specified functions, there is no answer. By graphing the functions, the answer has been discovered.
What does graphing a function mean?The method of graphing a function begins with creating the graph of a pertinent function. The function equation will be satisfied at a point on a curve if it reflects the function at that location.
According to the given information:We are given two functions as f(x) = -x² + 8x - 13 and g(x) = x + 3
The graph of the given functions has been plotted and attached below.
In the graph, the red function represents the f(x) function and the blue line represents the g(x) function.
From the graph, we can see that the two does not meet.
Hence, there is no solution for the given functions.
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Suppose a university raises its tuition from $3,000 to $3500. As a result, student enrollment falls from 5,000
to 4,500. Calculate the price elasticity of demand using the mid-point formula. (Round to three decimal places). Is the demand elastic, unitary elastic or inelastic?
For full credit please tell me the following:
1. What is the numerator
2. What is the denominator?
3. What is the numerator divided by the denominator?
4. Is the demand is elastic, unit elastic or inelastic.
Hint: When calculating the midpoint formula start by determining the starting quantity Q1 and the starting
price P1. Next, determine the ending quantity Q2 and the ending price P2.
Answers
Answer: The numerator is the percentage change in quantity demanded, which is (Q2 - Q1)/[(Q2 + Q1)/2] = (4500 - 5000)/[(4500 + 5000)/2] = -0.1818
The denominator is the percentage change in price, which is (P2 - P1)/[(P2 + P1)/2] = (3500 - 3000)/[(3500 + 3000)/2] = 0.1429
The numerator divided by the denominator is -0.1818/0.1429 = -1.2727
The price elasticity of demand is greater than 1 in absolute value, which means the demand is elastic.
Using the midpoint formula, we can calculate the price elasticity of demand as:
[(Q2 - Q1)/((Q1 + Q2)/2)] / [(P2 - P1)/((P1 + P2)/2)]
Substituting the given values, we get:
[(-500)/((5000 + 4500)/2)] / [(3500 - 3000)/((3500 + 3000)/2)]
Simplifying, we get:
-0.1818 / 0.1429 = -1.2727
Since the price elasticity of demand is greater than 1 in absolute value, the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price, and the university can expect a relatively large decrease in enrollment due to the tuition increase.
Step-by-step explanation:
In figure AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively. If ∠POQ = 140°, then (∠APQ + ∠CQP) is equal to
(i)120 (ii)130 (iii) 140 (iv)150
Answers
The answer is (iv) 150. This result can be obtained by applying the alternate segment theorem.
What is circle?A circle is a shape with all points at an equal distance from the center. It has no sides or angles and is the only two-dimensional shape with this property. It is also the most basic of all shapes, and is found in nature in many forms, such as raindrops, the sun, and even the human pupil. Circles are often used in art, design, and architecture, and are sometimes even used to represent infinity.
This theorem states that if two chords of a circle intersect at right angles, then the angles in the alternate segments of the circle are equal. In this case, the alternate segments are APQ and CQP. Hence, ∠APQ + ∠CQP = 150°.
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