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mathematics
calculus

Questions and Answers of Calculus

Each ounce of substance A supplies 5% of the nutrition a patient needs. Substance B supplies 15% of the required nutrition per ounce, and substance C supplies 12% of the required nutrition per ounce.
A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbohydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two
A social agency is charged with providing services to three types of clients: A, B, and C. A total of 500 clients are to be served, with $150,000 available for counseling and $100,000 available for
If funding for counseling is cut to $135,000 and funding for emergency food and shelter is cut to $90,000, only 450 clients can be served. How many of each type can be served in this
Solve the systems of equations by substitution?1.2. 3. 4.
Suppose a calculator manufacturer has the total cost function C(x) = 34x + 6800 and the total revenue function R(x) = 68x. (a) What is the equation of the profit function for the calculator? (b) What
Given C(x) = 21.95x + 1400 and R(x) = 20x, find the profit function. (a) What is the marginal profit, and what does it mean? (b) What should a firm with these cost, revenue, and profit functions do?
A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P, is linear. If 200 units sold results in $3100 profit and 250 units sold results in
Suppose that the total cost function for an MP3 player is linear, that the marginal cost is $54, and that the total cost for 50 players is $8700. Write the equation of this cost function and then
Extreme Protection, Inc. manufactures helmets for skiing and snow boarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of this model are $35, and
A manufacturer of DVD players has monthly fixed costs of $9800 and variable costs of $65 per unit for one particular model. The company sells this model to dealers for $100 each. (a) For this model
The figure shows graphs of the total cost function and the total revenue function for a commodity.(a) Label each function correctly. (b) Determine the fixed costs. (c) Locate the break-even point and
1. A jewelry maker incurs costs for a necklace according to C(x) = 35x + 1650 If the revenue function for the necklaces is R(x) = 85x how many necklaces must be sold to break even? 2. A manufacturer
1. A small business recaps and sells tires. If a set of four tires has the revenue function R(x) = 89x and the cost function C(x) = 1400 + 75x find the number of sets of recaps that must be sold to
Suppose a stereo receiver manufacturer has the total cost function C(x) = 210x + 3300 and the total revenue function R(x) = 430x. (a) What is the equation of the profit function for this
A manufacturer sells watches for $50 per unit. The fixed cost related to this product are $10,000 per month, and the variable cost per unit is $30. (a) Write the equations of the revenue and cost
(a) Write the profit function for Problem 19. In problem 19, A manufacturer sells belts for $12 per unit. The fixed costs are $1600 per month, and the variable cost per unit is $8. (b) Set profit
(a) Write the profit function for Problem 20. In problem 20, A manufacturer sells watches for $50 per unit. The fixed cost related to this product are $10,000 per month, and the variable cost per
Electronic equipment manufacturer Dynamo Electric, Inc. makes several types of surge protectors. Their base model surge protector has monthly fixed costs of $1045. This particular model wholesales
Financial Paper, Inc. is a printer of checks and forms for financial institutions. For individual accounts, boxes of 200 checks cost $0.80 per box to print and package and sell for $4.95 each.
A company manufactures and sells bookcases. The selling price is $54.90 per bookcase. The total cost function is linear, and costs amount to $50,000 for 2000 bookcases and $32,120 for 800
A company distributes college logo sweatshirts and sells them for $50 each. The total cost function is linear, and the total cost for 100 sweatshirts is $4360, whereas the total cost for 250
In Problems 1 and 2 some of the graphs of total revenue (R), total cost (C), variable cost (VC), fixed cost (FC), and profit (P) are shown as functions of the number of units, x.(a) Correctly label
1. As the price of a commodity increases, what happens to demand?2. As the price of a commodity increases, what happens to supply?3. (a) How many units q are demanded when the price p is $100?(b) How
Suppose a ceiling fan manufacturer has the total cost function C(x) = 43x + 1850 and the total revenue function R(x) = 80x.(a) What is the equation of the profit function for this commodity?(b) What
1. (a) How many units q are demanded when the price p is $200?(b) How many units q are supplied when the price p is $200?(c) Will there be a market surplus or shortage when the price p is $200?The
If the demand function and supply function for Z-brand phones are p + 2q = 100 and 35p + 20q = 350, respectively, compare the quantity demanded and the quantity supplied when p = 14. Are there
Suppose a certain outlet chain selling appliances has found that for one brand of stereo system, the monthly demand is 240 when the price is $900. However, when the price is $850, the monthly demand
Suppose a certain home improvements outlet knows that the monthly demand for framing studs is 2500 when the price is $4.00 each but that the demand is 3500 when the price is $3.60 each. Assuming that
Suppose the manufacturer of a custom board game will supply 10,000 games if the wholesale price is $15 each but will supply only 5000 if the price is $10 each. Assuming that the supply function is
Suppose a mining company will supply 100,000 tons of ore per month if the price is $30 per ton but will supply only 80,000 tons per month if the price is $25 per ton. Assuming that the supply
1. (a) Label each function as "demand" or "supply."(b) Label the equilibrium point and determine the price and quantity at which market equilibrium occurs.2.(a) If the price is $30, what quantity is
Suppose a computer manufacturer has the total cost function C(x) = 85x + 3300 and the total revenue function R(x) = 385x.(a) What is the equation of the profit function for this commodity?(b) What is
1. (a) If the price is $20, what quantity is supplied?(b) If the price is $20, what quantity is demanded?(c) Is there a surplus or a shortage when the price is $20? How many units is this surplus or
1. Will a price below the equilibrium price result in a market surplus or shortage?2. Find the market equilibrium point for the following demand and supply functions?Demand: p = - 2q + 320Supply: p =
Find the market equilibrium point for the following demand and supply functions. Demand: 2p = - q + 56 Supply: 3p - q = 34
Find the equilibrium point for the following supply and demand functions. Demand: p = 480 - 3q Supply: p = 17q + 80
Find the equilibrium point for the following supply and demand functions. Demand: p = -4q + 220 Supply: p =15q + 30
Retailers will buy 45 cordless phones from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 35 phones at $30 each and 70 at $50 each. Assuming the
A group of retailers will buy 80 televisions from a wholesaler if the price is $350 and 120 if the price is $300. The wholesaler is willing to supply 60 if the price is $280 and 140 if the price is
A linear cost function is C(x) = 5x + 250.(a) What are the slope and the C-intercept?(b) What is the marginal cost, and what does it mean?(c) How are your answers to parts (a) and (b) related?(d)
A shoe store owner will buy 10 pairs of a certain shoe if the price is $75 per pair and 30 pairs if the price is $25. The supplier of the shoes is willing to provide 35 pairs if the price is $80 per
(a) What is the amount of the tax?(b) What are the original equilibrium price and quantity?(c) What are the new equilibrium price and quantity?(d) Does the supplier suffer from the tax even though it
1. (a) If the tax is doubled, how many units will be sold?(b) Can a government lose money by increasing taxes?2. If a $38 tax is placed on each unit of the product of Problem 47, what are the new
If a $56 tax is placed on each unit of the product of Problem 46, what is the new equilibrium point?In problem 46,Find the equilibrium point for the following supply and demand functions.Demand: p =
Suppose that a certain product has the following demand and supply functions.Demand: p = -0.05q + 65Supply: p = 0.05q + 10If a $5 tax per item is levied on the supplier and this tax is passed on to
Suppose that a certain product has the following demand and supply functions.Demand: p = - 8q + 2800Supply: p = 3q + 35If a $15 tax per item is levied on the supplier, who passes it on to the
Suppose that in a certain market the demand function for a product is given by 60p + q = 2100 and the supply function is given by 120p - q = 540. Then a tax of $0.50 per item is levied on the
Suppose that in a certain market the demand function for a product is given by 10p + q = 2300 and the supply function is given by 45p - q = 360. If the government levies a tax of $2 per item on the
A linear cost function is C(x) = 27.55x + 5180. (a) What are the slope and the C-intercept? (b) What is the marginal cost, and what does it mean? (c) How are your answers to parts (a) and (b)
A linear revenue function is R = 27x. (a) What is the slope? (b) What is the marginal revenue, and what does it mean? (c) What is the revenue received from selling one more item if 50 are currently
A linear revenue function is R = 38.95x. (a) What is the slope? (b) What is the marginal revenue, and what does it mean? (c) What is the revenue received from selling one more item if 50 are
Let C(x) = 5x + 250 and R(x) = 27x. (a) Write the profit function P(x). (b) What is the slope of the profit function? (c) What is the marginal profit? (d) Interpret the marginal profit?
Solve the equations in Problems.1. 3x - 8 = 232. 2x - 8 = 3x + 53.4.
1. If p = 3q3, is p a function of q? 2. If y2 = 9x, is y a function of x? 3. If R = 3(x + 4, is R a function of x? 4. What are the domain and range of the function y = (9 - x?
If f(x) = x2 + 4x + 5, find the following.(a) f(-3)(b) f(4)(c)
If g(x) = x2 + 1/ x, find the following.(a) g(-1)(b)(c) g(0.1)?
If f(x) = 9x - x2, findAnd simplify?
Determine whether each graph represents y as a function of x?1.2.3. For the function f graphed in Exercise 18, what is f(2)?4. For the function f graphed in Exercise 18, for what values of x does
If f (x) = 3x + 5 and g(x) = x2, find (a) (f + g)(x) (b) (f / g)(x) (c) f(g(x)) (d) (f ◦ f)(x)
In following question find the intercepts and graph.1. 5x + 2y = 102. 6x + 5y = 93. x = - 2
Find the slope of the line that passes through each pair of points? 1. (2, -1) and (-1, -4) 2. (-3.8, -7.16) and (-3.8, 1.16)
Find the slope and y-intercept of each line. 1. 2x + 5y = 10 2. x = - ¾ y + 3/2
Write the equation of each line described. 1. Slope 4 and y-intercept 2 2. Slope -1/2 and y-intercept 3 3. Through (-2, 1) with slope 2/5 4. Through (-2, 7) and (6, -4)
In Problems graph each equation with a graphing calculator and the standard viewing window.1. x2 + y - 2x - 3 = 02.
In Problems use a graphing calculator and(a) Graph each equation in the viewing window given.(b) Graph each equation in the standard viewing window.(c) Explain how the two views differ and why.1. y =
1. What is the domain ofCheck with a graphing utility?2. Use a graphing utility and the x-intercept method to approximate the solution of 7x - 2 = 0?
Solve each system of equations?1.2.3.4.
By using Social Security Administration data for selected years from 1950 and projected to 2050, the additional years of life expectancy at age 65 can be described by y = 0.077x + 13.8 where x equals
In a certain course, grades are based on three tests worth 100 points each, three quizzes worth 50 points each, and a final exam worth 200 points. A student has test grades of 91, 82, and 88, and
The owner of a small construction business needs a new truck. He can buy a diesel truck for $58,000 and it will cost him $0.76 per mile to operate. He can buy a gas engine truck for $53,200, and it
1. The Multiple Risk Factor Intervention Trial (MRFIT) used data from 356,222 men aged 35 to 57 to investigate the relationship between serum cholesterol and coronary heart disease (CHD) risk. The
For many species of fish, the weight W is a function of the length L that can be expressed by W = W(L) = kL3 ........... k = constant Suppose that for a particular species k = 0.03 and that for this
The distance d (in miles) to a thunderstorm is given by d = t / 4.8 where t is the number of seconds that elapse between seeing the lightning and hearing the thunder. (a) Graph this function for 0 (
Body-heat loss due to convection depends on a number of factors. If Hc is body-heat loss due to convection, Ac is the exposed surface area of the body, Ts - Ta is skin temperature minus air
A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P, is linear.(a) If 200 units sold results in $3100 profit and 250 units sold results
The average annual cost per consumer for health care can be modeled by A = 427x + 4541 where x is the number of years from 2000 and projected to 2018.(a) Is A a linear function of x?(b) Find the
Temperature Write the equation of the linear relationship between temperature in Celsius (C) and Fahrenheit (F) if water freezes at 0 C and 32 F and boils at 100oC and 212oF?
The amount y of photosynthesis that takes place in a certain plant depends on the intensity x of the light present, according toy = 120x2 - 20x3 .... for x ( 0(a) Graph this function with a graphing
The speed at which water travels in a pipe can be measured by directing the flow through an elbow and measuring the height to which it spurts out the top. If the elbow height is 10 cm, the equation
A retired couple have $150,000 to invest and want to earn $15,000 per year in interest. The safer investment yields 9.5%, but they can supplement their earnings by investing some of their money at
A botanist has a 20% solution and a 70% solution of an insecticide. How much of each must be used to make 4.0 liters of a 35% solution?
A certain product has supply and demand functions p = 4q + 5 and p = -2q + 81, respectively.(a) If the price is $53, how many units are supplied and how many are demanded?(b) Does this give a
Market analysis of the equations p + 6q = 420 and p = 6q + 60, one is the supply function for a product and one is the demand function for that product. (a) Graph these equations on the same set of
The total cost and total revenue for a certain product are given byC(x) = 38.80x + 4500R(x) = 61.30x(a) Find the marginal cost.(b) Find the marginal revenue.(c) Find the marginal profit.(d) Find the
A certain commodity has the following costs for a period. Fixed cost: ................. $1500 Variable cost per unit: ....... $22 The commodity is sold for $52 per unit. (a) What is the total cost
The supply function and the demand function for a product are linear and are determined by the tables that follow.(a) Write an equation for the supply function and one for the demand function.(b)
Suppose that for a certain product the supply and demand functions prior to any taxation are Supply: p = q/10 + 8 Demand: 10p + q = 15 If a tax of $2 per item is levied on the supplier and is passed
Solve the inequality and graph the solution.1. 3x - 9 ( 4(3 - x)2. 2x/5 ( x + 43. 5x + 1 ( 2/3 (x - 6)
Write the equations in general form.1. 2x2 + 3 = x2 - 2x + 42. x2 - 2x + 5 = 2 - 2x23. (y + 1)(y + 2) = 44. (z - 1)(z - 3) = 1
Solve each equation by using the quadratic formula. Give real answers (a) exactly and (b) rounded to two decimal places?1. x2 - 4x = 42. x2 + 7 = 6x3. 2w2 + w + 1 = 04. z2 + 2z + 4 = 0
Find the exact real solutions to each equation, if they exist. 1. y2 = 7 2. z2 = 12 3. 5x2 = 80 4. 3x2 = 75
Use any method to find the exact real solutions, if they exist?1. x2 + 5x = 21 + x2. x2 + 17x = 8x - 143.4. x2 + 17x = 8x - 14
Solve each equation by using a graphing utility?1. 21x + 70 = 7x22. 3x2 + 6 =11x3. 300 - 2x - 0.01x2 = 04. - 9.6 + 2x - 0.1x2 = 0
Multiply both sides of the equation by the LCD and solve the resulting quadratic equation?1.2.3.4.
In following question solve using quadratic methods?1. (x + 8)2 + 3(x + 8) + 2 = 02. (s - 2)2 - 5(s - 2) - 24 = 0
If the profit from the sale of x units of a product is P = 90x - 200 - x2, what level(s) of production will yield a profit of $1200?
If the profit from the sale of x units of a product is P = 16x - 0.1x2 - 100, what level(s) of production will yield a profit of $180?
Suppose the profit from the sale of x units of a product is P = 6400x - 18x2 - 400.(a) What level(s) of production will yield a profit of $61,800?(b) Can a profit of more than $61,800 be made?
Suppose the profit from the sale of x units of a product is P = 50x - 300 - 0.01x2.(a) What level(s) of production will yield a profit of $250?(b) Can a profit of more than $250 be made?

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