Q#3. The radius and height of a right circular cone are measured with errors of at most 1% and 4%, respectively. Use differentials to approximate the maximum percentage error in the calculated volume.

Q: Q3/ The dimensions of a rectangular solid at a given instant (t.) are: L(t.)= 13 cm. W(t)-9 cm.…

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Q: The position of a particle at time t is s(t) = t³ + 5t. Compute the average velocity over the time…

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Q: (1) Where on the line r = ay does the function f(x, y) = (r - a)? + (y - 2)² attain its smallest…

A: We need to calculate minimum of f(x,y)=(x-a)2+(y-2)2.........(1) on the line x=ay...............(2)…

Q: Find the approximate increase by the use of differentials, in the volume of the sphere if the radius…

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Q: A ball having mass m falls from a tower with heigh h from the ground. The velocity of the ball…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

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Q: A mining expert estimates that the production growth rate of copper overtime, or ,is given by dt' dy…

A: By using integration.

Q: he position of a moving particle is given by s(t) = 3t2 – 18t on 3 <t< 6 here 's' is in meters and…

A: Instantaneous velocity = ds/dt

Q: which then evaporates at a rate proportional to the area of the surface of the water. Show that the…

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Q: Q3) the radius of the base and high of right circular cone at given instant (t ) are r 20cm and…

A: Volume of a cone = 13πr2hVolume r→radius and h→ height∴V = 13πr2h   dvdt =13πddtr2h   dvdt =…

Q: The temperature T= T(x,y) in °C at point (x,y) satisfies Ty(1,3) = 5 and Ty(1,3) = - 7. If x = e…

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Q: 1 6) The volume V of a right circular cone of radius r and height h is V =-ar²h. Suppose the radius…

A: We have to find the change in the volume of cone using total differential.

Q: Detemire follaw ing Hhe R3 50 12 25 32 9750 19250 26548= Linear valle ? Exponential R value ? Power…

A: R      3       5       7      12      25      32       65      100       E     50     200…

Q: A mining expert estimates that the production growth rate of copper overtime, or "/dt, is given by…

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Q: Write the differential formula that estimates the given change in volume or surface. Then, use the…

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Q: 5. Calculate the average rate of change for the function ft) = 2x'+5 over the interva -1 < x < 2.

A: We have to find average rate of change

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: A detailed solution is given below.

Q: Given a cube with sides x inches, let x(t) = t + 2. What is the instantaneous rate of %3D change of…

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Q: (c) Suppose instead that we have a rectangular tank containing the same volume of water (pictured…

A: c Volume of cube =8m×1.5m×3m=36m3 volume of water =12×3×3×8=36m3 Volume of water is equal to volume…

Q: Water is being drained from a spout in the bottom of a cylindrical tank. According to the…

A: Given  , Rate if drain: dV/dt = - 1.8L/min By integrating the equation we get the volume.

Q: Write a differential formula that estimates the given change in volume or surface area. Then use the…

A: S=4πr2 Differentiating with respect to r, we get ⇒dSdr=4π2r⇒dS=8πr dr Now when radius changes from…

Q: A population of E. coli bacteria will grow at a rate given byw′(t) = (3t + 2)1/3,where w is the…

A: Given: w't=3t+21/3

Q: (а) The flow (in cm³/s ) of blood from an artery into a small capillary can be modeled by CTx…

A: Given - The flow of blood from an artery into a small capillary can be modeled by Fx, y, z = cπx24y…

Q: The volume V of a nght circular cylinder of radius r and height h is V= 7rh. (a) How is related to…

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Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

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Q: Consider a pool shaped like the bottom half of a sphere, being filled at a rate of 25ft^3/min.the…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find da/dt in…

A: Given that  Area of the circle =A  Radius of the circle =r  To find the rate of change of area

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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Q: A circle has a radius of 9 cm. If the radius is increased by 0.2 mm, using differentials, what is…

A: We have to find the increase in area

Q: 2. A ball 6 inches in diameter is to be covered by a rubber material which is in-thick. Using…

A: Given, A ball 6 inches in diameter is to be covered by a rubber material which is 3/16 in thick.…

Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

A: Given that, A tank initially holds 10 gal of fresh water. At t=0, a brine solution containing 1/2 lb…

Q: Q.2. The side of a cube is measured with a possible percentage error of ±2%. Use differentials to…

A: Using differential

Q: he velocity v(t) in the table above is decreasing, 2 raveled, find O An upper estimate = units

A: Here we have,

Q: dx 11. The percent error in the measurement of the side x of a cube is 0.01, or 1%. Use…

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Q: The position of a particle at time t is s(t) = t³ + 4t. Compute the average velocity over the time…

A: We need to find velocity.

Q: Q4// The following PDE describes a specific fluid-flow problem in a porous medium. After examining…

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Q: A reservoir discharging water through sluices at a depth h feet below the water surface, has a…

A: Consider the provided question,

Q: A volunteer rescue truck goes downhill to relocate families situated at the lowlands of Taal…

A: Path of truck is inclined downwards 35 degrees with the horizontal. We must visualize it and try to…

Q: n a culture of yeast the rate of growth dy/dt is proportional to its population present at any time…

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Q: Given z = x?(1 + y)³, the value of (x,y) changes from (2,9) to (2.03,8.9). Use the total…

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Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

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Q: The table below gives the result of an observation, is the observed temperature in degrees…

A: We have to solve the given problem by Newton's forward differential equation.

Q: 33. The atmospheric pressure at altitude h (kilometers) for 11 <h< 25 is approximately P(h) =…

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Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

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Q: r. Using differentials, approximate the percent error in computing the length of the hypotenuse.

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Q: The velocity v of a falling parachutist is given by v- gm/c (1 - o^-(c/m)t) where g- 9.8 m/s^2. For…

A: “Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: The edge of a cube is measured at 3 cm, with a possible measurment error of 0.2 cm. Use…

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Q: f the measurement of the side of a cube is increased from 5 cm to 5.2 cm, the approximate increase…

A: Side of cube is increased from 5 to 5.2