[SOLVED] The total cost (in hundreds of dollars)

> 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 Newtonâs law of universal gravitation. G is a constant and F is the gravitational force between two objects havi

> The equation is Newtonâs 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 yâ² 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 yâ² 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.

> 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 yâ² and evaluate yâ² 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 yâ² and evaluate yâ² 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.

> Find ï¦â²(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

> The use of iodine crystals is a popular way of making small quantities of water safe to drink. Crystals placed in a 1-ounce bottle of water will dissolve until the solution is saturated. After saturation, half of the solution is poured into a quart conta

> The number x of bicycle helmets people are willing to buy per week from a retail chain at a price of $p is given by (A) Find dx / dp. (B) Find the demand and the instantaneous rate of change of demand with respect to price when the price is $75. Write

> A single card is drawn from a standard 52-card deck. Calculate the probability of each event. A heart or a number less than 7 (count an ace as 1) is drawn.

> Find each derivative and simplify.

> Give the domain of ï¦, the domain of g, and the domain of m, where m(x) = ï¦ [g(x)].

> In Problems a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A single fair coin is tossed. We are interested in whether the coin falls heads or tails, so an appropriate sample space is S = 5H, T6.

> Give the domain of ï¦, the domain of g, and the domain of m, where m(x) = ï¦ [g(x)].

> A student reasons that the functions ï¦(x) = (x + 1)ln (x + 1) - x and g(x) = (x + 1)1/3 must have the same derivative since she has entered ï¦ (x), g(x), ï¦ â²(x), and gâ&#128

> Find ï¦â²(x) and find the value(s) of x where the tangent line is horizontal.

> Find ï¦â²(x) and find the equation of the line tangent to the graph of ï¦ï at the indicated value of x.

> find the indicated derivative and simplify.

> A single card is drawn from a standard 52-card deck. Calculate the probability of each event. A king or a heart is drawn.

> find the indicated derivative and simplify.

> Find the indicated derivative and simplify.

> Find ï¦â²(x)and the equation of the line tangent to the graph of ï¦ at the indicated value of x. Find the value(s) of x where the tangent line is horizontal.

> Find ï¦â²(x) and simplify.

> An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results. More than 1tail

> Find ï¦â²(x) and simplify.

> Replace ? with an expression that will make the indicated equation valid.

> Find (A) the derivative of T(x) / B(x) without using the quotient rule, and (B) Tâ²(x) / Bâ²(x). Note that the answer to part (B) is different from the answer to part (A).

> Use these frequencies to calculate the approximate empirical probabilities and odds for the events (A) The sum is a prime number or is exactly divisible by 4. (B) The sum is an odd number or exactly divisible by 3

> Exercises write the expression as a quotient of integers, reduced to lowest terms.

> Find (A) the derivative of F(x) S(x) without using the product rule, and (B) Fâ²(x) Sâ²(x). Note that the answer to part (B) is different from the answer to part (A)

> One hour after a dose of x milligrams of a particular drug is administered to a person, the change in body temperature T(x), in degrees Fahrenheit, is given approximately by The rate Tâ²(x) at which T changes with respect to the size of

> According to economic theory, the supply x of a quantity in a free market increases as the price p increases (see the figure). Suppose that the number x of DVD players a retail chain is willing to sell per week at a price of $p is given by (A) Find dx

> A communications company has installed a new cable television system in a city. The total number N (in thousands) of subscribers t months after the installation of the system is given by (A) Find Nâ²(t). (B) Find N(16) and Nâ&#1

> Find each indicated derivative and simplify.

Question: The total cost (in hundreds of dollars)