An equation of the line that passes through the points (2, -9) and (-1, 1) is y + 9 = -10/3(x - 2).
What is the point-slope form?In Mathematics, the point-slope form of any straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represent the slope.x and y represent the points.At point (2, -9), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-9) = (1 - (-9))/(-1 - 2)(x - 2)
y + 9 = -10/3(x - 2)
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Find the area of a circle with a circumference of 31. 42 centimeters
From the given data in the question, the circumference of a circle is 31.42 centimeters then the area of the circle is 78.5 cm².
To find the area of a circle with a given circumference, we need to use the formula:
Circumference = 2πr
where π is the mathematical constant pi (approximately 3.14) and r is the radius of the circle. In this case, the circumference is given as 31.42 centimeters. So we can write:
31.42 = 2πr
To solve for r, we can divide both sides by 2π:
r = 31.42 / (2π)
r = 5
So the radius of the circle is 5 centimeters.
Now, to find the area of the circle, we can use the formula:
Area = πr²
Substituting the value of r, we get:
Area = π(5²)
Area = 25π
Area = 78.5 square centimeters
Therefore, the area of the circle with a circumference of 31.42 centimeters is approximately 78.5 square centimeters.
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find the cost in dollars of the operating a 100- w w lamp continuously for 1 week when the power utility rate is 16 cents/kwh c e n t s / k w h . express your answer using two significant figures.
Operating a 100-watt lamp for a week when the power utility rate is 16 cents/k
Wh can be calculated as follows:
Power of the lamp = 100 watts
Time of usage = 1 week = 7 days
Power utility rate = 16 cents/kWh
1 kW = 1000 watts
Power consumed by lamp = 100 watts
Total time of usage in hours = 7 days x 24 hours/day = 168 hours
Energy consumed = Power x Time= 100 watts x 168 hours= 16,800
watt-hours (Wh) = 16.8 kWh
Cost of operating the lamp = Energy consumed x Power utility rate= 16.8 kWh x 16 cents/k
Wh= 2.688 dollars= $2.7 (approx)
Therefore, the cost of operating a 100-watt lamp continuously for 1 week when the power utility rate is 16 cents/kWh is approximately $2.7 using two significant figures.
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A car averages 60 miles per hour on a road trip. Use the graph to represent the relationship between the time and the distance traveled.
please tell me the coordinates for the graphing because you have to graph it.
the picture is the graph I have to use :>
Using the speed formula, the coordinates to plot on the graph are (0, 0), (1, 60), (2, 120), (3, 180), and (4, 240).
What is the speed?
Speed is defined as the distance traveled per unit of time. It is the slope of the distance vs time graph. The formula for speed is:
Speed = Distance / Time
Where:
Speed is the speed of the object, usually expressed in units such as meters per second (m/s)
Distance is the distance traveled by the object, usually expressed in units such as meters
Time is the duration of travel, usually expressed in units such as seconds
To graph the relationship between the time and the distance traveled by the car, we can use the following formula:
Distance Traveled = Rate x Time
In this case, the rate (or speed) of the car is 60 miles per hour, and the distance traveled is a function of time.
So we can write the equation as:
Distance Traveled = 60 x Time
To graph this equation, we can plot a series of points using different values of time. For example:
At 0 hours, the distance traveled is 0 miles. Coordinate: (0, 0)
At 1 hour, the distance traveled is 60 miles. Coordinate: (1, 60)
At 2 hours, the distance traveled is 120 miles. Coordinate: (2, 120)
At 3 hours, the distance traveled is 180 miles. Coordinate: (3, 180)
At 4 hours, the distance traveled is 240 miles. Coordinate: (4, 240)
These points can be plotted on a graph with time on the x-axis and distance traveled on the y-axis. The resulting graph would be a straight line with a slope of 60 (which represents the rate or speed of the car) and passing through the origin (0, 0).
So the coordinates to plot on the graph are:
(0, 0), (1, 60), (2, 120), (3, 180), (4, 240)
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A large game cube with a three inch side length is wrapped with shrink wrap how much shrink wrap will be used to wrap ten game cubes
The quantity of shrink wrap that will be used to wrap ten game cubes is 540 square inches
To calculate the amount of shrink wrap needed to wrap ten game cubes, we need to first find the surface area of one game cube, and then multiply it by 10.
The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that by 6 (since there are six faces on a cube). In this case, the length of one side is 3 inches, so the surface area of one cube is:
Surface area of one cube = 3 x 3 x 6 = 54 square inches
To wrap ten cubes, we need to multiply the surface area of one cube by 10:
Surface area of ten cubes = 54 x 10 = 540 square inches
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Aisha wants to work out 764+3+2
show two ways she can do this
Answer:
769
764 + 3 + 2 = 769
1. She can do 764 + 3 = 767 767 + 2 = 769
2. OR She can do 2 + 3 = 5 5 + 764 = 769
Which is the better buy? 3-pound bag of rice for $2.25 9-pound bag of rice for $6.66
Answer:
Step-by-step explanation:
To see which bag is the better buy, calculate how much each pound of rice would cost.
To do that divide the price by the amount of costs for each then compare those numbers
$2.25/3 = $0.75 per pound
$6.66/9 = $0.74 per pound
So the 9 pound bag of rice would cost 1 cent less per pound making it the better buy.
which equality represents a proportional relationship
The answer is B hope it helps
Katherine has $8.60 in dimes and quarters. If she has twelve more quarters than dimes, how many dimes does she have? How many quarters does she have?
After addressing the issue at hand, we can state that by function Katherine now has 28 quarters.
what is function?Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.
Let's represent the unknown quantities with variables.
Let d be the number of dimes Katherine possesses.
Let q represent Katherine's number of quarters.
We can deduce from the problem:
Equation 1: Total dimes and quarters value = $8.60 0.10d + 0.25q = 8.60
Number of quarters = Number of dimes + 12 q = d + 12 Equation 2:
Now we can plug equation 2 into equation 1 to eliminate q and find d:
0.10d + 0.25(d + 12) = 8.60
Katherine now has 16 dimes.
We can use equation 2 to calculate the number of quarters:
q = d + 12 = 16 + 12 = 28
Katherine now has 28 quarters.
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HELP SOMEONE PLEASE I'LL GIVE BRAINLIEST AND 5 STARS IF CORRECT
The Uniform Federal Accessibility Standards specify that a wheelchair ramp may not have an incline greater than 4.76°
. You want to build a ramp with a vertical rise of 8 inches. You want to minimize the horizontal distance taken up by the ramp. Label the diagram (in inches) to show the approximate dimensions of your ramp. Round decimal answers to the nearest tenth.
List 3 sides to a right triangle. explain how you can use three pythagorean theorem to know that your three sides will create a right triangle.
The 3 sides to a right triangle are:
Leg 1 (a)Leg 2 (b)Hypotenuse (c)State the pythagorean theorem?The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (called the legs) is equal to the square of the length of the longest side (called the hypotenuse).
So, if we have three sides of a triangle and we want to know if it forms a right triangle, we can use the Pythagorean Theorem in the following three ways:
Check if a² + b² = c², where a and b are the lengths of the two legs and c is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
Check if b² + c² = a², where b and c are the lengths of the two legs and a is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
Check if a² + c² = b², where a and c are the lengths of the two legs and b is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
If none of these equations are true, then the triangle is not a right triangle.
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The demand and supply curves are given by y=10-3x³ and y=4+x²+2x (y represents the price and x quantity). Find the equilibrium price and quantity
If the demand and supply curves are given by y=10-3x³ and y=4+x²+2x, the equilibrium quantity is approximately 1.477 units, and the equilibrium price is approximately $5.44 per unit.
To find the equilibrium price and quantity, we need to find the point where the demand curve intersects the supply curve. At this point, the quantity demanded by consumers is equal to the quantity supplied by producers, which means that the market is in equilibrium.
We can set the two equations equal to each other to find the equilibrium quantity:
10 - 3x³ = 4 + x² + 2x
Simplifying the equation, we get:
3x³ + x² - 2x - 6 = 0
We can solve for x using algebraic methods or by using a graphing calculator. Either method will yield three roots for x, but only one of them will be positive and realistic in the context of the problem.
The positive root for x is approximately 1.477, which means that the equilibrium quantity is approximately 1.477 units.
To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply equation. Let's use the demand equation:
y = 10 - 3(1.477)³
Solving for y, we get:
y ≈ 5.44
Therefore, the equilibrium price is approximately $5.44 per unit.
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A bottle filling machine fills 25 bottles per minute. A second machine fills 15 bottles per minute. The second machine starts filling bottles 20 minutes after the first machine starts. Both machines stop filling bottles after 300 minutes after the first machine started. Which equation represents the situation of how many bottles will be filled?
A) 300(25)+290(15)
B) 300(25)+280(25)
C) 300(25)+300(25)
D) 300(25)+280(15)
25 bottles every minute are filled using a filling and capping machine in [tex]11700[/tex]
What use does a machine serve?Even though both pressures and movements are involved in a machine's functioning, one of its principal functions can either be force amplification or motion modification. A lever essentially adds force, but a gearbox often acts as a speed reducer.
What in mathematics is a machine diagram?A machine diagram represents a function operation on a variable x to create a variable output y diagrammatically. If x falls inside the scope of the f(x, the machine will accept x as an input and output y in accordance with the function's rules.
[tex]25 bottles/minute * 20 minutes = 500 bottles.[/tex]
During the remaining [tex]280[/tex] minutes, both machines are running and together they fill
[tex]25 bottles/minute + 15 bottles/minute = 40 bottles/minute[/tex]
So, the total number of bottles filled during this period is
[tex]40 bottles/minute * 280 minutes = 11,200 bottles.[/tex]
[tex]500+ 11,200= 11,700[/tex]
None of the given options represents this equation.
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Please refer to the photo
Which expression is equivalent to….
Maria is a baker. Her cost to make a cake is $4.00. She sells her cakes to local grocery stores at a price which includes a 20% markup for profit. The grocery stores then sell the cakes at a price which includes an additional 25% for their profit. What is the price of one of Maria's cakes at a grocery store?
Answer : 6 Dollars
Explanation : 4.00 × 20/100 = 0.8 + 4 = 4.8 * 25/100 = 6
Answer : 6 doolarz ThanK me
Write and simplify polynomial expressions that represents the perimeter and area of the cornfield (7y) (6x)
The expressions that represent the perimeter and area of the cornfield are: Perimeter = 14y + 12x,Area = 42xy
What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth of a rectangle.
The given expression represents the dimensions of a rectangular cornfield, where one side measures 7y units and the other side measures 6x units.
The perimeter of a rectangle is the sum of the lengths of all its sides. Therefore, the perimeter of this cornfield is:
P = 2(7y) + 2(6x) = 14y + 12x
To find the area of a rectangle, we multiply its length by its width. Therefore, the area of this cornfield is:
A = (7y) (6x) = 42xy
Therefore, the expressions that represent the perimeter and area of the cornfield are: Perimeter = 14y + 12x,Area = 42xy
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What is the area of a sector with a central angle of 30° and a radius of 12.5 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the sector is equal to 40.89 cm².
How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.Substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θπr²/360
Area of sector = 30(3.14/360) × (12.5)²
Area of sector = 0.2617 × 156.25
Area of sector = 40.89 cm²
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Two 10 by 10 grids are shown. The first grid has 4 columns and 6 squares shaded green. On the same grid, 6 squares and 4 columns are shaded red. On the same grid, 8 squares are shaded blue. On the second 10 by 10 grid, 3 columns and 8 squares are shaded blue. Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B Explain the expression written in Part A. Include the final product and how it is shown with the model. 1000
a) Tοtal squares shaded is 4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)
b) The expressiοn gives the tοtal number οf squares.
Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn. dοing same fοr all cοlοrs and adding them, we will get the Tοtal squares shaded
c) On simplifying the expressiοn, we get 138 squares
What is an expressiοn?Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a cοmplete sentence. Any οne οf the fοllοwing mathematical οperatiοns can be used. A sentence has the fοllοwing structure: Number/variable, Math Operatοr, Number/Variable is an expressiοn.
In each cοlumn, there are 10 squares
The first grid has 4 cοlumns and 6 squares shaded green
=> 4*10+(1*6) = 46 green squares
On the same grid, 6 squares and 4 cοlumns are shaded red.
=> 4*10+(1*6) = 46 red squares
On the same grid, 8 squares are shaded blue. => (1*8) blue squares
On the secοnd 10 by 10 grid, 3 cοlumns and 8 squares are shaded blue.
=> 3*10+(1*8) blue squares
a)Tοtal squares shaded
= shades οn first grid + shades οn secοnd grid
= ( green squares + red squares + blue squares ) + ( blue squares )
= 4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)
b) The expressiοn gives the tοtal number οf squares.
Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn. dοing same fοr all cοlοrs and adding them, we will get the Tοtal squares shaded
c) On simplifying the expressiοn, we get
= 46+46+8+38
= 138 squares
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Lucia fue a comprar el regalo de cumpleaños de la abuela. Le compró un vestido que tiene un precio de $750 pesos, pero la tienda cuenta con el 20% de descuento en todas las prendas. ¿Qué cantidad terminó pagando Lucia por el vestido?
Answer:
[tex]\boxed{ \$600}[/tex]
Step-by-[tex]\boxed{/$600}[/tex]step explanation:
El enunciado nos dice que toda la tienda cuenta con 20% de descuento, así que por cada artículo paga el 80% de su valor (100%-20%).
Una forma rápida de resolver el ejercicio es con regla de 3.
[tex]\$750 \Rightarrow 100 \% \newline x \Rightarrow 80\%[/tex]
para encontrar [tex]x[/tex]:
[tex]x=\frac{80*750}{100} \\x=\$600[/tex]
Por lo que la cantidad que termina pagando por el vestido es de $600.00
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
What is this written as an algebraic expression? the sum of number and 9.
Answer:
The sum of a number and 9 can be written as:
x + 9
where "x" represents the number being referred to.
Alternatively, if we want to use a different variable, we can write it as:
n + 9
where "n" represents the number being referred to.
Hope this helped, if not I'm sorry! If you need more help, feel free to ask! :]
A shop sells bottles of orange juice for £1.60, but will take 20% off the total cost when you buy more than 20 bottles. How much does it cost, in pounds (£), to buy 40 bottles of orange juice?
Answer: 51.2 pounds
Step-by-step explanation: The problem states that 20% of the total cost is taken when you purchase more than 20 bottles.
We start by finding the total cost without the 20% off
Multiply the unit price by the number of bottles
[tex]1.60*40 = 64 pound[/tex]
Next use the discount, since we are getting 20% off we only have to pay 80% of it and 80/100 simplifies to 4/5 so we can just multiply 64 by that.
[tex]64*4/5 = 51.2[/tex]
The cost of buying 40 bottles of orange juice, with a 20% discount, is £51.20.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The cost of one bottle of orange juice is £1.60.
To find the cost of 40 bottles of orange juice
40 bottles x 1.60 per bottle = £64
The total cost without the discount would be £64.
To calculate the discount, we can multiply the total cost by 20% or 0.20:
Discount = 20% x £64 = £12.80
The discount on 40 bottles of orange juice is £12.80.
To find the final cost, we need to subtract the discount from the total cost:
Final cost = Total cost - Discount
= £64 - £12.80
= £51.20
Therefore, the cost of buying 40 bottles of orange juice, with a 20% discount, is £51.20.
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xplain how you would calculate the area of a cross section of the dam without using calculus. use your explanation to calculate the area of the cross section. is the area you found exact? why or why not?
Cross-sectional area of the dam can be calculated without using calculus as explained below:
Step 1: Draw the cross-section of the dam on a graph paper and divide it into simple shapes like triangles, rectangles, and circles.
Step 2: Calculate the area of each shape separately using the appropriate formulae. For example, the area of a rectangle is length times width, area of a triangle is 1/2 times base times height and the area of a circle is pi times radius squared.
Step 3: Add the areas of all the shapes to find the total cross-sectional area of the dam. This gives an approximate value of the area since the actual shape of the cross-section is not perfectly regular.If we take a concrete example of a dam with a cross-section of a trapezoid,
we can calculate the cross-sectional area using the above steps:
Step 1: Draw the cross-section of the dam on a graph paper as shown below. The cross-section of the dam can be divided into a rectangle and a triangle.
Step 2: Calculate the area of the rectangle and the triangle separately using the formulae for the area of the rectangle and the triangle respectively.Area of the rectangle = base times height = 10 m times[tex]4 m = 40 m²[/tex]Area of the triangle = 1/2 times base times height = 6 m times 4 m = 12 m²
Step 3: Add the areas of the rectangle and the triangle to get the total cross-sectional area of the dam.Area of the cross-section = area of rectangle + area of triangle= [tex]40 m² + 12 m²= 52 m²[/tex]The area found using the above method is not exact since it is an approximation of the actual area of the cross-section of the dam. It can be more accurate by dividing the cross-section into smaller and simpler shapes and calculating their areas individually.
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Write the following ratio in its simplest form: 64:18
Answer:
32:9
Step-by-step explanation:
64 :18
32: 9
So 32: 9 is its simplest form.
Answer:
32:9
Step-by-step explanation:
64 : 18
Divide both sides by a common number 2
32 : 9
This cannot be further divided
NEED HELP ASAP (100 points)
Answer:
Ill help you figure out how to graph.
Step-by-step explanation:
The value in front of x (like 2x or 7x) is the slope (rise over run) rise is how much the line goes up, and run is how much it goes to the side. the second number (in the bottom left graph, it is -5) is the y intercept. it is where the line crosses the y axis. (in this case on -5) Here is an example. (of the problem y=x-5)
I will give Brainliest! =D
Determine the rest of the side lengths, and describe your strategies!
Considering the figure, the missing lengths are
the topmost is 15the other length is 4What is similar triangles?In geometry, the phrase "similar triangles" refers to triangles whose respective sides are proportionate and whose corresponding angles are congruent.
Hence, if the triangle's corresponding angles are congruent, the side should be in proportion.
The proportions are as follows
say the side on top of 10 (in horizontal line) is y
y / (10 + 15 + 12.5) = 10 / (10 + 15)
y / 37.5 = 10 / 25
cross multiplying
25y = 37.5 * 10
25y = 375
y = 15
say the side below side 10 (in horizontal line) is x
x / 10 = 10 / (10 + 15)
x / 10 = 10 / 25
cross multiplying
25x = 100
x = 4
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The height of a student is measured as 1.6m to the nearest tenth of a meter. Find to one significant figure, the greatest possible percentage error
Answer: 7.4
Step-by-step explanation:
A school sports team contains 68 students. 33 do field events, 40 do track events, 23 do swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events, how many students do a) swimming knly b)track events only c) all three events?
Answer:
9, 20 and 4
Step-by-step explanation:
Swimming only 9
Track only 20
All 3 events
14 did track and field
10 did track and swimming
Those who sis all 14- 10 = 4
The answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4
What is a Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Given that, a school sports team contains 68 students. 33 do field events, 40 do track events, 23 go swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events,
Please refer to picture attached
Therefore,
15+a+c+d = 33.......1
b+c+d+e = 40.........2
a+b+d+f = 23..........3
c+d = 14...............4
a+d = 8.............5
b+d = 10.............6
Now, solving for variables,
From 1 and 4,
a = 4
Therefore, from 5,
d = 4
From 6,
b = 6
Put these in eq 3,
f = 9
c = 10
e = 20
Therefore,
Swimming only = 9
Track events = 20
All three = 4
Hence, the answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4
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an angle measures 2.8 radians and the initial ray of the angle points in the 3-o'clock direction. a circle with a radius 2.6 cm long is centered at the angle's vertex. the terminal point is how many radii to the right of the circle's center? radii the terminal point is how many cm to the right of the circle's center? cm
Therefore, the terminal point is 0.26 radii to the right of the circle's center and 0.67 cm to the right of the circle's center.
The angle in question has an initial ray pointing in the 3-o'clock direction and measures 2.8 radians. It is centered at the vertex of a circle with a radius of 2.6 cm. To calculate the number of radii and the number of cm the terminal point is to the right of the circle's center, we need to use the formula for arc length. Arc length is equal to the circumference of the circle multiplied by the central angle's measurement, divided by 2π.
So, the arc length of this angle is equal to 2.6 cm times 2.8 radians divided by 2π, or[tex]2.6 x 2.8 / 6.28 = 0.67 cm.[/tex] The terminal point is 0.67 cm to the right of the circle's center, which is equal to [tex]0.67/2.6 = 0.26 radii.[/tex]
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Consider the following linear programming problem:Maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3)
The maximum value of the objective function is 33, which occurs at the corner point (3, 3)
According to the question we have to maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3).Linear programming is a mathematical method that aims to maximize or minimize an objective function subject to a set of linear constraints. In this problem, we are asked to maximize the objective function 6x + 5y subject to the constraints given by the inequalities 1, 2, and 3.
The inequalities 1, 2, and 3 define a feasible region in the xy-plane, which is a region that satisfies all the constraints. The feasible region can be found by graphing the three inequalities and shading in the region that satisfies all of them.
In this case, the feasible region is a triangle with vertices (0, 0), (3, 3), and (4, 1), as shown below:
The objective function 6x + 5y is evaluated at each corner point as follows:
At (0, 0), 6(0) + 5(0) = 0, At (3, 3), 6(3) + 5(3) = 33, At (4, 1), 6(4) + 5(1) = 29. Thus, the optimal solution is x = 3 and y = 3, and the maximum value of the objective function is 33.
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Consider 3 individuals in a small town: Alice, Bianca, and Claire. There is an NGO who can provide an art museum for their town with the help of local contributions. The higher the contributions, the larger the art collection of the museum. Their respective direct marginal benefits from N works of art are: MBA=7-N, MBB=7-½N, MBC=23-½N2, and their respective marginal costs are: MCA=2, MCB=3, MBC=5.
a. Find each person’s optimal number of art works.
b. Who will contribute and how many works of art will be provided?
Altruism: now consider the case where each individual cares about the benefit from the museum to the other two. For example any additional utility to Alice or Bianca is also a utility gain for Claire.
c. Find each person’s optimal number of art works.
d. Who will contribute and how many works of art will be provided?
Now consider the case where each individual cares only about their direct marginal benefit from the public good plus an additional warm-glow marginal benefit from giving as follows: WMBA=6-NA, WMBB=6-NB, and WMBC=24-NC, where NA, NB, and NC respectively represent Alice, Bianca, and Claire’s individual contributions. For example, Alice’s total marginal benefit is TMBA=MBA+WMBA=7-N+6-NA.
e. Who will contribute and how many works of art will be provided?
The Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.
a. In order to find each person's optimal number of art works, one must solve for the point at which the marginal benefit and the marginal cost intersect. For Alice, that point is when N = 7 and MBA = MCA, resulting in an optimal number of works of art of 7. For Bianca, the intersection point is when N = 14 and MBB = MCB, resulting in an optimal number of works of art of 14. For Claire, the intersection point is when N = 8.3 and MBC = MCC, resulting in an optimal number of works of art of 8.3.
b. Without considering altruism, Alice will contribute 7 works of art, Bianca will contribute 14 works of art, and Claire will contribute 8.3 works of art.
c. With altruism, the optimal number of art works for each individual can be calculated in the same way as without altruism, but with the warm-glow benefit added to their respective total marginal benefits. For Alice, that point is when N = 7.3 and TMBA = MCA, resulting in an optimal number of works of art of 7.3. For Bianca, the intersection point is when N = 14.6 and TMBB = MCB, resulting in an optimal number of works of art of 14.6. For Claire, the intersection point is when N = 8.7 and TMBC = MCC, resulting in an optimal number of works of art of 8.7.
d. With altruism, Alice will contribute 7.3 works of art, Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.
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Elizabeth is mountain climbing with Frank and has just climbed a 16-meter vertical rock face. Frank is standing 30 meters away from the bottom of the cliff, looking up at Elizabeth. How far away are Elizabeth and Frank?
Pythagorean theorem: word problems ⬆️
Please respond.
Answer:
34m
Step-by-step explanation:
To find:-
Distance between Frank and Elizabeth.Answer:-
We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .
We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;
[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]
Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .
So on substituting the respective values, we have;
[tex]\rm\implies h^2 = (16m)^2+(30m)^2 \\[/tex]
[tex]\rm\implies h^2 = 256m^2 + 900m^2 \\[/tex]
[tex]\rm\implies h^2 = 1156m^2\\[/tex]
[tex]\rm\implies h =\sqrt{1156 \ m^2} \\[/tex]
[tex]\rm\implies \red{h = 34 m} \\[/tex]
Hence the distance between Elizabeth and Frank is 34m .