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 is 400 meters high?
> Use the price–demand 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 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 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 price–demand 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 price–demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.
> use the price–demand 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.
> Find the logarithmic derivative.
>
> Find the logarithmic derivative.
> use the price–demand equation to find E(p), the elasticity of demand.
> use the price–demand equation to find E(p), the elasticity of demand.
> use the price–demand equation to find E(p), the elasticity of demand.
> Find the percentage rate of change of (x) at the indicated value of x. Round to the nearest tenth of a percent.
> Find the percentage rate of change of (x) at the indicated value of x. Round to the nearest tenth of a percent.
> Find the percentage rate of change of (x) at the indicated value of x. Round to the nearest tenth of a percent.
> Find the percentage rate of change of (x) at the indicated value of x. Round to the nearest tenth of a percent.
> Find the relative rate of change of (x) at the indicated value of x. Round to three decimal places.
> Find the relative rate of change of (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 (x) at the indicated value of x. Round to three decimal places.
> Find the relative rate of change of (x) at the indicated value of x. Round to three decimal places.
> Find the relative rate of change of (x) at the indicated value of x. Round to three decimal places.
> Find the relative rate of change of (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
> 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
> Refer to Problem 62. Find dF/dr and discuss the connection between dF/dr and dr/dF. Data from Problem 62: The equation is Newton’s law of universal gravitation. G is a constant and F is the gravitational force between two objects havi
> The equation is Newton’s law of universal gravitation. G is a constant and F is the gravitational force between two objects having masses m1 and m2 that are a distance r from each other. Use implicit differentiation to find dr/dF . Ass
> In Problem 59, find dV/dL by implicit differentiation. Data from problem 59: In biophysics, the equation (L + m) (V + n) = k is called the fundamental equation of muscle contraction, where m, n, and k are constants and V is the velocity of the shorteni
> The number x of compact refrigerators that an appliance chain is willing to sell per week at a price of $p is given by Use implicit differentiation to find dp/dx.
> The number x of fitness watches that people are willing to buy per week from an online retailer at a price of $p is given by x = 5,000 - 0.1p2 Use implicit differentiation to find dp/dx.
> Refer to the equation in Problem 53. Find the equation(s) of the tangent line(s) at the point(s) on the graph where y = -1. Round all approximate values to two decimal places. Equation from Problem 53:
> Find y′ and the slope of the tangent line to the graph of each equation at the indicated point.
> Find y′ and the slope of the tangent line to the graph of each equation at the indicated point.
> In Problems a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A wheel of fortune has seven sectors of equal area colored red, orange, yellow, red, orange, yellow, and red. We are interested in the color
> Find y′ and the slope of the tangent line to the graph of each equation at the indicated point.
> Find y′ and the slope of the tangent line to the graph of each equation at the indicated point.
> Explain the difficulty that arises in solving x3 + y + xey = 1 for y as an explicit function of x. Find the slope of the tangent line to the graph of the equation at the point (0, 1).
> find the equation(s) of the tangent line(s) to the graphs of the indicated equations at the point(s) with the given value of x.
> find the equation(s) of the tangent line(s) to the graphs of the indicated equations at the point(s) with the given value of x.
> Refer to the equation and graph shown in the figure. Find the slopes of the tangent lines at the points on the graph where x = 0.2. Check your answers by visually estimating the slopes on the graph in the figure.
> find x′ for x = x(t) defined implicitly by the given equation. Evaluate x′ at the indicated point. x3 - tx2 - 4 = 0; (-3, -2)
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> What is the probability of getting at least 1 black card in a 7-card hand dealt from a standard 52-card deck?
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point.
> Use implicit differentiation to find y′ and evaluate y′ at the indicated point. 5x3 - y - 1 = 0; (1, 4)
> Find y′ in two ways: (A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly. x + ln y = 1
> Find y′ in two ways: (A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly. 4x2 - ey = 10
> Find y′ in two ways: (A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly. x3 + y3 = 1
> Find y′ in two ways: (A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly. 2x + 9y = 12
> In Problems a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A nickel and dime are tossed. We are interested in the number of heads that appear, so an appropriate sample space is S = 50, 1, 26.
> Replace ? with an expression that will make the indicated equation valid.
> Replace ? with an expression that will make the indicated equation valid.
> Replace ? with an expression that will make the indicated equation valid.
> Find ′(x)
> Find ′(x)
> Find ′(x)
> Find ′(x) (x) = 5 - 6x5
> A yeast culture at room temperature (68°F) is placed in a refrigerator set at a constant temperature of 38°F. After t hours, the temperature T of the culture is given approximately by T = 30e-0.58t + 38 t ≥ 0 What is the rate of change of temperature o
