[SOLVED] use the price–demand equation to determine

> Find the intervals on which ï¦(x) is increasing and the intervals on which ï¦(x) is decreasing. Then sketch the graph. Add horizontal tangent lines.

> Find the intervals on which ï¦(x) is increasing, the intervals on which ï¦(x) is decreasing, and the local extrema.

> Solve the equation P (E) /P (E’) = a/b for P (E). If P (E) = c/d, show that odds in favor of E occurring are c to d – c.

> Find (A) ï¦â²(x), (B) the partition numbers for ï¦â², and (C) the critical numbers of ï¦ .

> Give the local extrema of f and match the graph of ï¦ with one of the sign charts aâh.

> Find the relative rate of change of ï¦(x).

> Use the given equation, which expresses price p as a function of demand x, to find a function ï¦(p) that expresses demand x as a function of price p. Give the domain of ï¦(p).

> An experiment consists of rolling two fair (not weighted) 4-sided dice and adding the dots on the two sides facing up. Each die is numbered 1–4. Compute the probability of obtaining the indicated sums. 7

> Use the given equation, which expresses price p as a function of demand x, to find a function ï¦(p) that expresses demand x as a function of price p. Give the domain of ï¦(p).

> A model for the number of aggravated assaults per 1,000 population in the United States (Table 4) is a(t) = 5.9 - 1.1 ln t where t is years since 1990. Find the relative rate of change for assaults in 2025.

> A model for Mexicoâs population (Table 3) is ï¦(t) = 1.49t + 38.8 where t is years since 1960. Find and graph the percentage rate of change of ï¦(t) for 0 â¤ t â&curr

> Refer to Problem 87. What price will maximize the revenue from selling fries? Data from Problem 87: The price–demand equation for an order of fries at a fast-food restaurant is x + 1,000p = 2,500 Currently, the price of an order of fries is $0.99. If th

> Refer to Problem 87. If the current price of an order of fries is $1.49, will a 10% price decrease cause revenue to increase or decrease? Data from Problem 87: The price–demand equation for an order of fries at a fast-food restaurant is x + 1,000p = 2,5

> Revenue and elasticity. Refer to Problem 85. If the current price of a hamburger is $4.00, will a 10% price increase cause revenue to increase or decrease? Data from Problem 85: The price–demand equation for hamburgers at a fast-food restaurant is x + 4

> The fast-food restaurant in Problem 83 can produce an order of fries for $0.80. If the restaurant’s daily sales are increasing at the rate of 45 orders of fries per day, how fast is its daily cost for fries increasing?

> Find E(p) for x = (p) = Ae-kp, where A and k are positive constants.

> In a group of n people (n ≤ 100), each person is asked to select a number between 1 and 100, write the number on a slip in a hat. What is the probability that at least 2 of the slips in the hat have the same number written on them?

> use the priceâdemand equation to find the values of x for which demand is elastic and for which demand is inelastic.

> If a priceâdemand equation is solved for p, then price is expressed as p = g1x2 and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given by use the priceâdemand equat

> use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph.

> Use the priceâdemand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive.

> An experiment consists of rolling two fair (not weighted) 4-sided dice and adding the dots on the two sides facing up. Each die is numbered 1–4. Compute the probability of obtaining the indicated sums. 5

> Use the priceâdemand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive.

> use the price–demand equation p + 0.004x = 32, 0 ≤ p ≤ 32. If p = $21 and the price is decreased, will revenue increase or decrease?

> use the price–demand equation p + 0.004x = 32, 0 ≤ p ≤ 32. Find all values of p for which demand is inelastic.

> use the price–demand equation p + 0.004x = 32, 0 ≤ p ≤ 32. Find the elasticity of demand when p = $16. If the $16 price is increased by 9%, what is the approximate percentage change in demand?

> use the price–demand equation p + 0.004x = 32, 0 ≤ p ≤ 32. Find the elasticity of demand when p = $28. If the $28 price is decreased by 6%, what is the approximate percentage change in demand?

> use the priceâdemand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.

> Find the logarithmic derivative.

>

> Find the logarithmic derivative.

> use the priceâdemand equation to find E(p), the elasticity of demand.

> Find the percentage rate of change of ï¦(x) at the indicated value of x. Round to the nearest tenth of a percent.

> Find the relative rate of change of ï¦(x) at the indicated value of x. Round to three decimal places.

> An experiment consists of rolling two fair (not weighted) 4-sided dice and adding the dots on the two sides facing up. Each die is numbered 1–4. Compute the probability of obtaining the indicated sums. 3

> Find the relative rate of change of ï¦(x) at the indicated value of x. Round to three decimal places.

> Find the relative rate of change of ï¦(x).

> Assume that x = x(t) and y = y(t). Find the indicated rate, given the other information. y = x3 - 3; dx/dt = -2 when x = 2; find dy/dt

> The height of a right circular cylinder is twice its radius. If the volume is 1,000 cubic meters, find the radius and height to the nearest hundredth of a meter.

> The radius of a spherical balloon is 3 meters. Find its volume to the nearest tenth of a cubic meter.

> The legs of a right triangle have lengths 54 feet and 69 feet. Find the length of the hypotenuse to the nearest foot.

> A central pivot irrigation system covers a circle of radius 400 meters. Find the area of the circle to the nearest square meter.

> A person who is new on an assembly line performs an operation in T minutes after x performances of the operation, as given by operations per hours, where t is time in hours, find dT/dt after 36 performances of the operation

> Explain how the three events A, B, and C from a sample space S are related to each other in order for the following equation to hold true:

> A circular spinner is divided into 15 sectors of equal area: 6 red sectors, 5 blue, 3 yellow, and 1 green. , consider the experiment of spinning the spinner once. Find the probability that the spinner lands on: Yellow.

> Price–demand. Repeat Problem 45 for x2 + 2xp + 25p2 = 74,500 Data from Problem 45: The price p (in dollars) and demand x for a product are related by 2x2 + 5xp + 50p2 = 80,000 (A) If the price is increasing at a rate of $2 per month when the price is

> Political campaign. Refer to Problem 43. If $20 million has been spent on television advertising and the rate of spending is $6 million per week, at what rate (in percentage points per week) will the polling percentage increase? Data from Problem 43: A

> The price p (in dollars) and demand x (in bushels) for peaches are related by x = 3p2 - 2p + 500 If the current price of $38 per bushel is decreasing at a rate of $1.50 per week, find the rate of change (in bushels per week) of the supply.

> Refer to Problem 38. Find the associated revenue function R(p) and the rate of change (in dollars per week) of the revenue. Data from Problem 38: The price p (in dollars) and demand x for microwave ovens are related by

> The price p (in dollars) and demand x for microwave ovens are related by If the current price of $124 is increasing at a rate of $3 per week, find the rate of change (in ovens per week) of the demand.

> Repeat Problem 35 for s = 50,000 - 20,000e-0.0004x Data from Problem 35: A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by s = 60,000 - 40,000e-0.0005x The current weekly advertising costs are

> Cost, revenue, and profit rates. Repeat Problem 33 for C = 72,000 + 60x R = 200x - x2 30 P = R - C where production is increasing at a rate of 500 calculators per week at a production level of 1,500 calculators. Data from Problem 33: Suppose that for a

> A point is moving on the graph of x3 + y2 = 1 in such a way that its y coordinate is always increasing at a rate of 2 units per second. At which point(s) is the x coordinate increasing at a rate of 1 unit per second?

> A point is moving along the x axis at a constant rate of 5 units per second. At which point is its distance from (0, 1) increasing at a rate of 2 units per second? At 4 units per second? At 5 units per second? At 10 units per second? Explain.

> Refer to Problem 27. At what rate is the person’s shadow growing when he is 20 feet from the pole? Data from Problem 27: A streetlight is on top of a 20-foot pole. A person who is 5 feet tall walks away from the pole at the rate of 5 feet per second. At

> (A) Is it possible to get 7 double 6’s in 10 rolls of a pair of fair dice? Explain. (B) If you rolled a pair of dice 36 times and got 11 double 6’s, would you suspect that the dice were unfair? Why or why not? If you suspect loaded dice, what empirical

> A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing on the ground 300 meters from where the balloon was released. At what rate is the distance between the observer and the balloon changing when the balloon i

> Boyle’s law for enclosed gases states that if the temperature is kept constant, the pressure P and volume V of a gas are related by the equation VP = k where k is a constant. If the volume is decreasing by 5 cubic inches per second, what is the rate of

> Refer to Problem 21. How fast is the surface area of the sphere increasing when the radius is 10 centimeters? Data from Problem 21: The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How fast is the volume changing

> Refer to Problem 19. How fast is the circumference of a circular ripple changing when the radius is 10 feet? Data from Problem 19: A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increasing by 2 feet per second,

> Refer to Problem 17. Suppose that the distance between the boat and the dock is decreasing by 3.05 feet per second. How fast is the rope being pulled in when the boat is 10 feet from the dock? Data from Problem 17: A boat is being pulled toward a dock a

> A point is moving on the graph of 4x2 + 9y2 = 36. When the point is at (3, 0), its y coordinate is decreasing by 2 units per second. How fast is its x coordinate changing at that moment?

> Assume that x = x(t) and y = y(t). Find the indicated rate, given the other information. x2 - 2xy - y2 = 7; dy/dt = -1 when x = 2 and y = -1; find dx/dt

> Assume that x = x(t) and y = y(t). Find the indicated rate, given the other information. x2 + y2 = 4; dy/dt = 5 when x = 1.2 and y = -1.6; find dx/dt

> if it is possible to solve for y in terms of x, do so. If not, write “Impossible.” y2 + ex y + x3 = 0

> if it is possible to solve for y in terms of x, do so. If not, write “Impossible.” 2 ln y + y ln x = 3x

> What is the probability that a number selected at random from the first 60 positive integers is (exactly) divisible by 6 or 9?

> if it is possible to solve for y in terms of x, do so. If not, write “Impossible.” 4y2 - x2 = 36

> if it is possible to solve for y in terms of x, do so. If not, write “Impossible.” -4x2 + 3y + 12 = 0

Question: use the price–demand equation to determine