(t) s(t) xt)

Q: Suppose the cost function of a product is given as C=3q -0.0014³. If the cost is increasing at a…

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Q: he marginal cost (rate of change of cost) in euros per unit of production for artilugios in a ertain…

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Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

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Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: A spherical balloon is deflating and its radius r is decreasing at the rate of 5 mm per minute.…

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Q: A point on the graph of y = is moving along the curve in such a way that its x-coordinate is…

A: Given graph- y=1x Rate of increase of x-coordinate,dxdt= 6 units per second y-coordinate = 5 Then,…

Q: What is the rate of change for h(x) = 8x - 9 on the interval [1, 4]?

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Q: 4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle,…

A: We need to find rate of change.

Q: 4.) The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x? + 10x + 5000.…

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Q: The length { of a rectangle is decreasing at a rate of 8 cm/ sec while the width w is increasing at…

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Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

Q: 2. What is the average rate of change between x = 2 and x = 3 for the function g(x) = 5(x – 2) - 3 ?

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Q: In a first order chemical reaction with no backorder reaction the concentration of the reactant is…

A: We solve for C(t)

Q: 8. Given that y=/2x +7 and y is increasing at a rate of 5 units s. Find the rate of change in X,…

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Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

Q: Water is flowing into a cylindrical tank at the rate of 2 m^3/min. If the radius of the tank is 0.5…

A: Water is flowing into a cylindrical tank at the rate of 2 m3/min.If the radius of the tank is 0.5 m,…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

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Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

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Q: What is the concentration of glucose in the bloodstream after 10 min if r =5 g per min, k = 5, and…

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Q: 1. a) A car is driving toward an intersection from the east at 40 mi/h, and a second car is driving…

A: Here the two cars are approaching each other at right angles with different speeds. Therefore the…

Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 4…

A: The exponential growth formula is given by: P(t)=P0 ekt...(1) where P0 is initial population, k is a…

Q: What will be the rate of change of the surface of the sphere when the radius of the sphere is 5.00…

A: Given; Radius= 5cm And time rate of change in Radius is= π/2.

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: (4) The temperature at a point (x, y) is given by T(x, y) = xy + x². (a) (2, –1)? What is the rate…

A: (1) The rate of change in temperature can be determined by finding the gradient,…

Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: Solve parts a,b, and c.

A: Here we need to apply some basic concepts of derivatives to find the answers

Q: At time t = 0, Car A passes through an intersection and goes east at a speed of 40 feet per second.…

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Q: 4. Mauritius island is 2 km due south of its closest point along a straight coastline. Gibril is…

A: Given data:-

Q: 16. Find the average rate of change for y = x² –9x+20 from x=5 to x=7. А. 3 В. -3 С. 1/3 D. -1/3 E.…

A: Given function

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: The line with the rule y = 3x + 4 intersects the curve with equation ¦(x) = x2 at the points (-1, 1)…

A: Given:- The line with the rule y = 3x + 4 intersects the curve with equation f(x) = x2 at the points…

Q: Solve the following problems completely. A solid cylindrical cord of elastic material has length 32…

A: Given query is to find rate of change of radius.

Q: approaching

A: Please refer to the image below

Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

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Q: When air expands adiabatically (without gaining or losingheat), its pressure and volume are related…

A: Given that When air expands adiabatically (without gaining or losing heat), its pressure and volume…

Q: 9. Suppose an object is moving along a path described by; f(t) = t - 6t, where f (t) is measured in…

A: The objects velocity at t is equal to 4 will be the objects instantaneous rate of change at that…

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

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Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

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Q: How would I solve for the left endpoint and the right endpoint? Find the average rate of change of…

A: Given :f(t) = 4t2 − 3,      [3, 3.1] formula for average rate of change :

Q: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

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Q: 2. For a certain rectangle the length of one side is always three times the length of the other…

A: Let length of the rectangle be "x"       breadth of the rectangle be "y"     let "x" be the longer…

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

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Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: z = x2 + y2, where x and y are increasing at the constant rates of 2 units per second and 3 units…

A: