Part A. The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? Part B. The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm?

Q: The edges of a cube increase at a rate of 2 cm/sec. How fast is the volume changing when the length…

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Q: The edges of a cube increase at a rate of 2 cm/s. How fast is the volume changing when the length of…

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Q: The radius of a circular oil slick expands at a rate of 8 m/min. (a) How fast is the area of the…

A: drdt=8 m/min

Q: Wheat is poured through a chute at the rate of 6 ft³/min and falls in a conical pile whose bottom…

A:

Q: A square changes its area at a rate of 300 units^2/s. If a circle is always inscribed in this…

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Q: The length of a rectangle is increasing at a rate of 7cm/s and its width is increasing at a rate of…

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Q: The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: We have to find the rate of change of surface area.

Q: A stalk of corn grows from a height of 1 foot to a height of 7 feet in 2 months. What is its average…

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Q: hypothetical

A: We will find the rate of change of sides of the cube.

Q: 3. Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Area of the square is increasing at a rate of  48cm2/sec.

Q: 3 Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A: Given the data:

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

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Q: Homework: 1. When a circular plate of metal is heated in an oven its radius increases at a rate of…

A: Given that The rate of increase of radius is 0.01 cm/min Radius is 50 cm To find The rate in the…

Q: TRUE or FALSE: If a skater is skating directly away from a 6 meter tall lamp at 7 meters per second,…

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Q: The edges of a cube increase at a rate of 2 cm/sec. How fast is the volume changing when the length…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

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Q: The length of a rectangle is increasing at a rate of 9cm/s and its width is increasing at a rate of…

A: To Determine: How fast is the area of the rectangle increasing? Given: we have the length of a…

Q: Solve the following related rates problems: A stone dropped into a still pond sends out a circular…

A: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

Q: 1. Sand being dumped from a funnel forms a conical pile whose height is always one￾third the…

A:

Q: 3 p Show that the area of an equilateral triangle with sides p cm is A = 4 If the side is changing…

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Q: Wheat is poured through a chute at the rate of 14 ft³/min and falls in a conical pile whose bottom…

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Q: How well does the average rate of change describe how the mold changes for these 6 days?

A: Formula used : Average rate of change of f (x) in between a and b is  f(b) - f(a) / b-a

Q: 21. The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Given:- The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the…

Q: Wheat is poured through a chute at the rate of 22 ft³/min and falls in a conical pile whose bottom…

A: Given: dv/dt=22 ft3/min altitude(h)=2r

Q: Wheat is poured through a chute at the rate of 14 ft3/min and falls in a conical pile whose bottom…

A: Explained below

Q: A rumor is spreading through town at a rate of ť + 10t new people/day. Approximately how many people…

A: Given rate t2+10t new people/day

Q: shrinking

A:

Q: All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the surface…

A:

Q: A square changes its area at a rate of 300 units^2/s. If a circle is always inscribed in this…

A: Suppose S be the area of the square and r be the radius of the circle.   Draw the figure of the…

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is…

A:

Q: Bacteria in a certain culture increase at the rate proportional to the number umber? bacteria…

A: The rate of increase dNdt in number of bacteria is proportional to the number of bacteria present N…

Q: A box is partially filled with sand. The length of the box is 12 mm. The width of the box is 18 mm.…

A:

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: In this we are going to use formula for area of triangle and then differentiation of that. So I'm…

Q: 6. The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when…

A:

Q: Crude oil is leaking from a tank at the rate of 10% of the tank volume every 3 hrs. If the tanker…

A: Given:capacity of tank=600,000 gallonsrate of oil leaking every 3 hrs=10% of tank volume

Q: 5) A thin sheet of ice on a lake is in the shape of a circle. If the ice is melting such that the…

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Q: Sand is being dropped at the rate of 5 63/min onto a conical pile. If the height of the pile is…

A:

Q: Wheat is poured through a chute at the rate of 14 ft/min and falls in a conical pile whose bottom…

A: Wheat is poured through a chute at the rate of 14 ft3 /minute. Wheat is falling into a conical pile…

Q: Wheat is poured through a chute at the rate of 10 ft/min and falls in a conical pile whose bottom…

A: Given  Rate of change in volume= 10ft3/min. '  Radius of cone = r  Height of cone = h  And h= 2r  We…

Q: The radius of a sphere, initially zero, increases at rate 6 ft per seconds. Find how fast the volume…

A: By using differentation and integration and rate of change

Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A:

Q: 1. A 10 ft ladder is leaning a gainst a wall. If the top of the ladder slides down the wall at a…

A: Note: We are entitled to solve only one question at a time. Given: A 10 ft ladder is leaning against…

Q: 1.The sides of an equilateral triangle are increasing at the rate of 3 cm/min. a) the rate of change…

A: dadt=3 cmmin. (a) Perimeter of triangle = a+a+a      P=3a   dPdt=  3dadt=3×3 =9 cmmin.

Q: The area of a square is increasing at the constant rate of 16 sq. ft./min. When the perimeter of the…

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Q: The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of…

A:

Q: The base of a 45-foot ladder is being pulled away from a wall at a rate of 6 feet per second. How…

A: Use Pythagoras theorem

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

A:

Q: 2. A circle's radius, r, is increasing at a rate of 5 inches per second, as shown below. How quickly…

A: Given : Circle's radius is r. Radius is increasing at a rate of 5 in/sec