True or False If the average rate of change of a linear func- 2 then if y 3' tion is increases by 3, x will increase by 2.

Q: Find the average rate of change of the function on the interval specified. h(x) = 3 − 6x2  on  [−2,…

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Q: A solid steel shaft at room temperature of 27°C is needed to be contracted so that it can be shrunk…

A: Given that, dθdt=-5.33×10-6(θ+33)-3.69×10-6θ4+2.33×10-5θ3+1.35×10-3θ2+5.42×10-2θ+5.588 θ=27°C when…

Q: The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled…

A: Given: Nx=0.03x2+0.315x+34.23x is no of years after 2000

Q: true or false? the second derivative of a quadratic function is twice the leading coefficient.

A: Given: Quadratic equation is given:

Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: The length of a rectangle is increasing at the rate of 4 cm/sec, while the width is increasing at…

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Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. The most…

A: Given that the brightness of the Delta Cephei at time t( in days) has been modelled by the function…

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per hour…

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Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per minute…

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Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at a…

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Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given: Rate of increase in length of a rectangle, dldt=5 cm/s Rate of decrease in width of a…

Q: When treating cancer, it is an advantage to know the rate of growth of the cancer tumor. A…

A: Since the tumor is spherical, its volume is given by, V=43πR3 Substitute diameter D=2R in the above…

Q: Determine the average rate of changes in the value of y in moving from x=-1 and x=2 f (x) = 5x3

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Given: The rate at which the radius is decreasing is, drdt=-0.4 cm/min. To determine the rate at…

Q: A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x − x2 ), where x and f(x) are…

A: The given function is f(x)=0.048x-x2

Q: Suppose that the online retailer Amazon needs to use larger and larger cardboard boxes over time.…

A: It is given that, the volume increases by 80 cubic inches each year and  height increases by 0.5…

Q: A point is moving along the circle x2 + (y − 2)2 = 26 in such a way that its x-coordinate is…

A: Given:

Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

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Q: How to find the rate of change of y=x^2-3 over the interval (-2,0)

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Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given a rectangle whose length is increasing at rate of 5cm per second and width is decreasing at…

Q: 7. How does the average rate of change for a square root function behave, for intervals of fixed…

A: Average rate of change can be found by calculating the change in y values of two points divided by…

Q: w many times between two points do we have an Instantaneous Rate Of change equalling Average ro

A: To determine the number of times the instantaneous rate of change equals to the average rate of…

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at…

A: Given :- The length of a rectangle is increasing at a rate of 5 cm per second and its width is…

Q: A circle is inside a square. The radius of the circle is increasing at a rate of 3 meters per minute…

A: Let radius of circle be r, side of square be a, the required area be A.

Q: can be sold at a price of $p. for  x = cube root of 9,000 - p^4 (close cube root), find the rate of…

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Q: Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume…

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Q: Find the rate of change of the arts of a rectangle at the moment when it’s sides are 40 meters and…

A: We have to find the rate if change if rectangle area.

Q: A particle is moving along the curve y=4sqrt(2x+3). As the particle passes through the point (3,12),…

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Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at a…

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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Q: It is known that a bacterial culture increases at a rate that is proportional to its current amount.…

A: Given- Number of bacterial fibers after 1 hour=1000 Number of bacterial fibers after 4 hour=3000

Q: Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on  [−2,…

A: To Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on…

Q: The price P of gasoline increases to a maximum and then stays at a fixed price. What is the rate of…

A: Given: The price P of gasoline increases to a maximum and then stays at a fixed price. What is the…

Q: 5. A heap of garbage in the shape of a cube is being compacted. Given that the volume decreases at a…

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Q: 5. Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other…

A: Given that the lengths of the rectangle are begin increased at the rate of 20 mm /sec. The other two…

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 5 meters per minute…

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Q: A circle is inside a square.The radius of the circle is increasing at a rate of 3 meters per minute…

A: First, find the area outside the circle but inside the squareLet ‘s’ be the side of the square and…

Q: ladder 5 meters long is leaning against a vertical wall. Due to the smooth floor, the foot of the…

A: Given query is to find the rate of change of y with respect to x.

Q: 44. The dimensions of a rectangular plate are changing so that the plate maintain its rectangular…

A: Let the length of Rectangle =x Let the width of Rectangle =y since,  Area = (length)×(width)…

Q: A circle is inside a square. The radius of the circle is increasing at a rate of 1 meter per hour…

A: Given circle is inside a square. Radius of circle is increasing at a rate of 1 mph. Side of square…

Q: A tank initially contains 200 liters of brine with 20 kg of salt solution. Brine containing 0.25 kg…

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Q: Suppose total cost in dollars from the production of x printers is given byC(x) = 0.0001x3 + 0.005x2…

A: average rate of change of cost between point [a,b] is given by

Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,          The total cost in dollars from the production of x printers is given by…

Q: An emply container is filled with liquid. The height of the liquid in the container is x cm and its…

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Q: A Cepheid variable star is a star whose brightness alternately increases and decreases.The most…

A: The rate of change of a function f(t) is the first derivative of f(t) with respect to t.

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 2 meters per hour…

A: We need to find rate of change of area.

Q: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

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