ex - ex 1. Let y = where x and y are in inches. Suppose that y is increasing at a rate of 1/2 in/sec. How fast is x increasing when x = 0?
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Q: Estimate the instantaneous rate of change at the point indicated. f (x) = ex ; x = e
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A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…
Q: 21: Fimd the rate of change of volume at t= 2 Sec if ri= 2t-1 hi=3-t r2= 3++1 hz=2m
A: we are given that r1 = 2t-1 h1= 3t2 -t r2= 3t +1 h2 = 4t3-1 We know that the volume of a cylinder…
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Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…
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Q: and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this mom
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Q: The radius of a spherical balloon is decreasing at a rate of 2 - in/sec. Which of the following is…
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A: Given: r = t + 2 We know that the area of the circle: A = π r2 where r is radius.
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Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0
A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.
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Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is…
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Q: the hypotenuse AB of a right triangle ABC is constantly 5 in long. The side AC is increasing…
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Q: 2. Find the instantaneous rate of change for y= arctan- at x = 3. 2 12 A. 85 2 В. 13 3n D. 4 С. О
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Q: ce of a circle is increasing at a rate of 2 cm/s. rea increasing when r= 6 cm?
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Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…
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Q: The radius of a circular oil slick expands at a rate of 5 m/min. (a) How fast is the area of the oil…
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Q: a. If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…
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Q: A 50 – gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb…
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Q: j. A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a…
A: Given: Height of boat above water level=20 ft……1Length of rope=50 ft……2Rate at which boat is pulled…
Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…
A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…
Q: You are inflating a spherical balloon at the rate of 7 cm³/sec. How fast is it radius increasing…
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Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…
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Q: 6. Air is being pumped into a spherical ball at a rate of 7 cm³/sec. What is the rate of change of…
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Q: Let A be the area of a circle with radius r that is increasing in size with respect to time. If the…
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Q: The volume of a sphere is increasing at a rate of 8 cm3/sec. Find the rate of change of the radius…
A: Given : V= 32π/3 cm3 dV/dt = 8 cm3 /sec
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- Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.A particle moves along the curve below. y = 3+x3 As it reaches the point (1, 2), the y-coordinate is increasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant?
- Consider a rectangular metal box without a top lid which, because of being heated, is increasing in size. At the moment the width is 11 cm, the height is 23 cm and the depth is 14 cm, these measurements are varying at a rate of:2 cm/s, the width6 cm/s, the height2 cm/s, the depth.What is the rate in cm^(2)/s at which the outer surface area of the box is growing?can you expain why the rate of decay is -dy/dt. how come?A particle moves along the curve below. y=(24+(x^3))^(1/2) As it reaches the point (1,5), the y-coordinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?
- A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing when the radius is 8 cm?A hand-tossed pizza crust starts off as a ball of dough with a volume of 400πcm^3. First, the cook stretches the dough to the shape of a cylinder of radius 12 cm. Next the cook tosses the dough. If during tossing, the dough maintains the shape of a cylinder and the radius is increasing at a rate of 15 cm/min, how fast is its thickness changing when the radius is 20 cm?A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level with and 5m from the base of the flagpole. When the flag is 10m high, at what rate is its distance from B changing?
- A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is level with and 5m from the base of the flagpole. When the flag is 10m high, at what rate is its distance from B changing?A)If A is the area of a circle with radius r and the circle expands as time passes, find dA dt in terms of dr dt . b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m2/s) is the area of the spill increasing when the radius is 35 m?a spherical snowball is melting in such a way that its surface area decrease at the rate of 1in^2/min. how fast is the volume shrinking when its radius is 3in?