What is the volume of this composite solid? 5 m 6 m 9 m 12 m
Answers
Thus, the volume of composite solid made up of cone and cylinder is found as: 1099 m³.
Explain about the shape of cone:A form with a convex surface and a round base is called a cone. We can quickly recognise a cone thanks to the following characteristics.
A cone has no edges, one face, and one vertex.The length of a line segment from a cone's apex to any point along the circumference of the cone's base is known as the slant height of the cone.Given data:
height of cylinder H = 12 mradius of base r = 5 mheight of cone h = 6 mVolume of composite solid = volume of cylinder + volume of cone
Volume of composite solid = πr²H + 1/3*πr²h
Put the values
Volume of composite solid = 3.14 * 5² *12 + 1/3*3.14*5²*6
Volume of composite solid = 3.14 * 25 *12 + 2*3.14*25
Volume of composite solid = 942 + 157
Volume of composite solid = 1099 m³
Thus, the volume of composite solid made up of cone and cylinder is found as: 1099 m³.
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complete question:
What is the volume of this composite solid ?
Related Questions
find the reduced radical 36^3/4 • 36^-1/4 (show explanation please)
Answers
Step-by-step explanation:
36^3/4 * 36 ^-1/4 = 36 ^( 3/4 - 1/4 ) = 36 ^1/2 = sqrt (36 ) = 6
Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Y′(−6, −1).
y-axis
x-axis
y = −1
x = 6
Answers
Answer:
To determine the line of reflection if the image of Y, Y′, is at (-6, -1), we need to find the perpendicular bisector of the line segment connecting Y and Y′. This perpendicular bisector will be the line of reflection.
The midpoint of the line segment YY′ is:
[(6 + (-6))/2, (-1 + (-1))/2] = (0, -1)
The slope of the line segment YY′ is:
(-1 - (-1))/(-6 - 6) = 0/(-12) = 0
Since the slope of YY′ is 0, the perpendicular bisector of YY′ is a vertical line passing through its midpoint (0, -1), which is the y-axis. Therefore, the line of reflection is the y-axis.
4. center (3, 6), tangent to the x-axis
Answers
The equation of the circle with center (3,6) and tangent to the x-axis is (x - 3)² + 36 = r²
Describe Tangent?In mathematics, a tangent is a straight line that touches a curve or surface at a single point and is perpendicular to the radius or line that passes through that point. The point of contact between the tangent and the curve or surface is called the point of tangency.
In geometry, the tangent to a circle is a straight line that intersects the circle at exactly one point. This point is called the point of tangency, and the tangent is perpendicular to the radius of the circle at that point.
The tangent is an important concept in calculus, where it is used to define the derivative of a function. The derivative of a function f(x) at a point x=a is defined as the slope of the tangent line to the graph of f(x) at the point (a, f(a)). This slope measures the rate at which the function is changing at that point.
If an equation is tangent to the x-axis, this means that it only intersects the x-axis at one point, which has a y-coordinate of zero. So, we need to write an equation of a circle with center (3,6) that intersects the x-axis at one point with a y-coordinate of zero.
Let the radius of the circle be r. Since the center of the circle is (3,6), the equation of the circle can be written in the form:
(x - 3)² + (y - 6)² = r²
Since the circle is tangent to the x-axis, we know that it intersects the x-axis at (x,0), where x is a point on the x-axis. Substituting y=0, we get:
(x - 3)² + (0 - 6)² = r²
Simplifying this equation, we get:
(x - 3)² + 36 = r²
So, the equation of the circle with center (3,6) and tangent to the x-axis is:
(x - 3)² + 36 = r²
Note that there are many possible values for r that would satisfy this equation, since we haven't specified the size of the circle. We only know that it is tangent to the x-axis and has center (3,6).
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The complete question is :
How do you write an equation with center (3,6), tangent to the x-axis?
12. Higher Order Thinking If a clock face
reads 1:00, how many hours must pass for
the hands to form a straight angle?
own
Answers
Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.
Explain about the hand of clock:To read the time on an analogue clock, look in the direction its hands are pointing. The current hour is indicated by the smallest hand, the current minute by the largest hand, and the current second by the thinnest hand.
There are 24 hours in a day, and the hour hand completes two full rotations of the clock because the numbers on the dial only go up to 12. once, from noon to midnight, and once, from midnight to noon.
Given data:
Current time on clock = 1:00
Hour hand at 1 .
Minute hand at 12.
Number of hours must pass for the hands to form a straight angle:
When
minute hand is at 12 and hour hand will be at 6.
Number of hours = 6: 00 - 1: 00
Number of hours = 5 hours
Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
Answers
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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What 2 numbers add up to 13 but multiply to -48??
Answers
Answer:
3 and -16
Step-by-step explanation:
To find two numbers that add up to 13 but multiply to -48, we can start by making a list of the factors of -48:
1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48
We can see that the only two numbers in this list whose sum is 13 are 3 and -16. To verify that these numbers multiply to -48, we can simply multiply them together:
3 x (-16) = -48
Therefore, the two numbers that add up to 13 but multiply to -48 are 3 and -16.
Answer: -3, 16
Step-by-step explanation:
-4(2-x) less than or equal to 8
Answers
Answer: less than
Step-by-step explanation:
Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
Answers
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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1. Dorie Sparrow, assistant manager of The Clothes Horse, Inc., must mark all clearance rack dresses back
to their regular selling price. She had marked all of them down 70%. What regular selling price does Dorie
need to sell a dress for that had been marked down to $104.98?
Answers
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
What is selling price?
Selling price refers to the price at which a product or service is sold to customers. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost price, which is the amount that the seller paid to acquire or produce the product or service. The difference between the selling price and the cost price is called the profit margin, and it is the profit that the seller makes on the sale of the product or service.
If a dress had been marked down 70%, this means that it is being sold for only 30% of its original selling price.
Let P be the original selling price of the dress. Then:
0.3P = $104.98
Solving for P, we get:
P = $104.98 / 0.3
P = $349.93
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
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In art class students are mixing blue and red paint to make purple paint. Deondra
mixes 6 cups of blue paint and 7 cups of red paint. Arun mixes 2 cups of blue paint
and 3 cups of red paint. Use Deondra and Arun's percent of red paint to determine
whose purple paint will be redder.
Deondra percent of red paint (to nearest whole number) =
Arun percent of red paint (to nearest whole number) =
O Deondra's purple paint will be redder.
O Arun's purple paint will be redder.
o The two purple paints will be equally red.
Submit Answer
%
%
attempt 1 out of 2
Answers
Arun's purple paint will be redder.
Define percentagePercentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.
Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:
7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.
Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:
3 / (2 + 3) × 100% = 60%.
Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.
Therefore, the answer is Arun's purple paint will be redder.
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How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Answers
Answer:
To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.
First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.
Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.
Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.
However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.
Will mark brainliest if answer is correct
Answers
Answer:
[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]
[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]
[tex]4b - 32 = 12[/tex]
[tex]4b = 44[/tex]
[tex]b = 11[/tex]
For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.
Find the area of the trapezoid. 10 km 8 km 6 km
Answers
the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h
what is trapezoid ?
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid
In the given question,
To find the area of a trapezoid, we use the formula:
A = (1/2) * (b₁ + b₂) * h
where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).
In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.
Using the Pythagorean theorem, we can find the length of the altitude:
a² + (b₁ - b₂)² = (2a)²
Simplifying and solving for a, we get:
a² + (b₁- b₂)² = 4a²
3a² = (b₁ - b₂)²
a = (1/√3) * |b₁ - b₂|
Since we know that the sum of the non-parallel sides is 10 km, we can write:
b₁ + b₂ = 10
Let's assume that b1 is the longer base, so we can write:
b₁ = 8 km
b₂ = 10 - b₁ = 2 km
Substituting these values into the formula for the altitude, we get:
a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km
Now we can use the formula for the area of a trapezoid to find the area:
A = (1/2) * (b1 + b2) * h
A = (1/2) * (8 + 2) * 2√3
A = 10√3 km²
Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).
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Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
Answers
Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)
What is a Graph?A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.
In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.
For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.
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A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answers
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
Answers
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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I BEG U FOR HELP WILL GIVE BRAINLIEST PLLSSSS
Answers
Answer:
3,4,5 is the answer
Step-by-step explanation:
for the explanation using pythagoras theoem
[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]
may you give me branliest as you promised
Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used. 2 one half 4 one fourth
Answers
Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)
Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).
The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,
A' = 2A
A'(8, -12) = 2×A(4, -6)
These facts are all you need to know to choose the correct answer (shown above).
Answer: 1/2
Step-by-step explanation:
I took the quiz!
Can someone please help me with this problem? I'm really struggling and the assignment is already late :(
Answers
The simplified exponential expression is given as follows:
[tex]21^6[/tex]
How to simplify the exponential expression?The exponential expression in the context of this problem is defined as follows:
[tex]\frac{21^3 \times 21^5}{21^2}[/tex]
First we look at the numerator, when we have two terms with the same base and different exponents multiplying, we keep the base and add the exponents, hence:
21^3 x 21^5 = 21^8
Now we have the following division operation:
21^8/21^2.
When we have two terms with the same base and different exponents dividing themselves, we keep the base and subtract the exponents, hence:
21^(8 - 2) = 21^6.
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Which statement explains the type of function that is represented by the equation y = x^2 + 9?
Answers
The function is nonlinear because the variable x is raised to the second power. So, the correct option is D) .
Describe Linear Function?A linear function is a mathematical equation that can be represented by a straight line. It is a function in which the independent variable, say "x," is raised only to the first power, and the dependent variable, say "y," is not multiplied or divided by any variable. Linear functions have a constant rate of change, which means that the slope of the line is the same at all points.
The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line crosses the y-axis. The slope m represents the rate of change of y with respect to x, and can be calculated as the change in y divided by the change in x between any two points on the line.
A linear function is a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a constant amount. A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
In the given equation y = x² + 9, the variable x is raised to the second power, which means that the rate of change of y with respect to x is not constant. This is the characteristic of a nonlinear function. Moreover, the graph of the function is a parabola, which is also a characteristic of a nonlinear function.
Therefore, the correct answer is D) The function is nonlinear because the variable x is raised to the second power.
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The complete question is :
Which statement explains the type of function that is represented by the equation y=x² +9?
A The function is linear because it contains more than one term.
B) The function is linear because the variable x is raised to the second power.
C) The function is nonlinear because it contains more than one term.
D) The function is nonlinear because the variable x is raised to the second power.
Need help with is question
Answers
Answer:
27.78%
Step-by-step explanation:
To calculate the percentage of the total spending that is on rent, we need to divide the amount spent on rent by the total amount spent, and then multiply by 100 to get the percentage.
Total spending = food + rent + other + fun
Total spending = $400 + $500 + $600 + $300
Total spending = $1800
So, the percentage of the total spending that is on rent is:
($500 / $1800) x 100% = 27.78%
Therefore, approximately 27.78% of the total spending is on rent.
5. What is the perimeter of polygon XYDB?
Answers
option D 20 is correct answer .the perimeter of polygon XYDB is 20.
what is polygon ?
A polygon is a closed geometric shape made up of straight line segments connected end-to-end. It is a two-dimensional figure that has three or more sides and angles. Polygons can be classified according to the number of sides
In the given question,
To find the perimeter of polygon XYDB, we need to add up the lengths of all its sides. Since all side lengths are given as 5, we can simply multiply 5 by the number of sides to get the perimeter.
Polygon XYDB has four sides, so the perimeter is:
Perimeter = 4 × 5 = 20
Therefore, the perimeter of polygon XYDB is 20.
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Answer:
D. 20 cm
Step-by-step explanation:
A car, van, truck and bike are all travelling in the same direction on the road. Each travels at a constant speed, but the speeds of the 4 vehicles may be different. At 10 am the car overtakes the van. At noon it overtakes the truck. At 2 pm it overtakes the bike. At 4 pm the truck overtakes the bike. At 6 pm the van overtakes the truck. When does the van overtake the bike?
Answers
Answer:
at 6 pm
Step-by-step explanation:
I'm 99.9% sure that it's correct, please tell me if I'm wrong
Evaluate the expression for the given value.
–a – 7 for a = –4
A11
B–11
C3
D–3
Answers
Solve the equations using suntraction. Show all your work.
X-6y=11 and 2x-5y=1
Answers
To use this method, we need to choose one variable to eliminate. In this case, we can eliminate the variable "x" by multiplying the first equation by 2 and the second equation by -1, and then adding the two resulting equations. This will give us an equation in terms of "y" that we can solve, and then use the solution to find the value of "x".
Here are the steps:
Multiplying the first equation by 2, we get:
2x - 12y = 22
Multiplying the second equation by -1, we get:
-2x + 5y = -1
Adding the two resulting equations, we get:
-7y = 21
Dividing both sides by -7, we get:
y = -3
Now that we have solved for "y", we can substitute this value back into either of the original equations to find the value of "x". Let's use the first equation:
x - 6y = 11
x - 6(-3) = 11
x + 18 = 11
Subtracting 18 from both sides, we get:
x = -7
Therefore, the solution to the system of equations using the method of subtraction is:
x = -7 and y = -3.
A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?
A$24
B$13
C$15
D$16
Answers
Answer:
24
Step-by-step explanation:
Answer:
A. $24
Step-by-step explanation:
Given:
total of $288number of values is 12 tablesSolve for average tip:
Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24Answer:
Thus, the waiter's average tip per table is $24.
The answer is A.
Need help Asap please
Answers
Answer:
Summer for 9th Graders: 0.14
Fall for 10th Graders: 0.15
Spring overall total: 0.36
Summer overall total: 0.22
Fall overall total: 0.33
Winter overall total: 0.09
Step-by-step explanation:
Relative frequencies are related to percentages so you can find the answer through that given the total from each grade.
However, adding or subtracting makes the process easier (in my opinion) to find the relative frequency
2. A non-Jewish woman meets with a Jewish counselor to seek guidance on dealing with he
future Jewish in-laws. The Jewish counselor has strong personal beliefs against interfaith
marriages. At the end of the third session, the counselor recommends that the client
reconsider marrying her fiancé.
Harmful use of bias?
Unharmful use of bias?
Answers
As the counselor recommends that the client reconsider marrying her fiancé based on his belief discretion, this is an example of harmful use of bias.
Why is the Scenario an example of harmful Bias?The counselor's personal beliefs against interfaith marriages are influencing their professional advice, which can be harmful to the client's well-being and may even violate ethical guidelines for mental health professionals.
The counselor should provide unbiased and objective guidance to the client based on their specific needs and circumstances, rather than imposing their own beliefs or values onto the client's decision-making process.
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rewrite the equation in Ax +By = C. y -5 = 2(x - 1)
Answers
-2X + y = 3
y-5=2(x-1)
y=2x-2+5
-2x+y=3
A local department store can sell 100 gaming systems at a price of $180 each. Research
shows that for each $18 price increase, the store will sell 4 fewer systems, and vice versa.
a. Find a linear price equation for the gaming system. That is, express the price, p, as a
function of the quantity, q. (2 points)
b. Use your answer from (a) to find the revenue equation.
c. Use your knowledge of quadratic functions to find the price and quantity sold that will maximize revenue.
Answers
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
What is the unit price?
In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.
According to given information
a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:
y - 0 = (-2/9)x
y = (-2/9)x
Substituting x = 18n, where n is the number of $18 price increases, we have:
y = (-2/9)(18n) = -4n
Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:
p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),
where q0 is the quantity of gaming systems sold at the original price of $180.
b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:
R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q
c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:
R'(q) = 9q - 9q0/2 = 0
q = q0/2
Substituting q = q0/2 into the revenue equation, we have:
R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)
R(q0/2) = (9/8)*q0^2 + (45/2)*q0
To find the corresponding price, we can use the expression for p(q) found in part (a):
p(q0/2) = 180 + (9/2)(q0/2 - q0)
p(q0/2) = 135
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
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