Estimate the instantaneous rate of change of h(x)= 5/x−3 at the point x=−3 Your answer should be accurate to at least 3 decimal places.

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Q: A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh…

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

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…

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Q: Find the rate of change of 1/x with respect to x when x=2

A: f(x)=1xrate of change of 1/x with respect to x isdf(x)dxdf(x)dx=-1x2

Q: a tank initialy holds 80 gallon of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

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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 tank with a capacity of 4000 liters holds 2000 liters of brine that contains 50kg of dissolved…

A: The amount of salt at any time t can be denoted by At.  For that first form the differential…

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

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Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 4 inch(es) per…

A: Let r be the radius of the snowball at any time t. The radius r is decreasing at the rate of 4 in/hr…

Q: An executive conference roomof a corporation contains 4500 ft3 of air initially free of carbon…

A: Given :           An executive conference room of a corporation contains 4500 ft3 of air initially…

Q: The tank shown in the figure was filled with 100 liters of substance A in a concentration of 10g /…

A: Given: The tank having 100 liters of substance A in a concentration of 10g / L. Material A is fed…

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A: Solution

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: A tank contains 45 liters of a chemical solution prepared by dissolving 80 g of a soluble substance…

A: We will find out the required value.

Q: A tank contains 2220 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the…

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Q: A wolf puppy fossil was discovered in one of the caves in thawing permafrost in Dawson City, Yukon,…

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Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: For the given statement

Q: Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150 years,…

A: Given: Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150…

Q: What are three methods that can be used to estimate the instantaneous rate of change in g(x) at x =…

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Q: 2. Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150…

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Q: A tank contains 40 L of solution containing 2g of substance per liter. Salt water containing 3g of…

A: Initially there is 40*2 = 80 grams Let Q be the amount of substance in the tank and dQ/dt be the…

Q: The heat index (HI) is an estimate of the temperature felt by the human body based on the actual…

A: Given heat index is HI=-42+2T+10hr-0.22Thr-1.99T2hr2 where, T is the air temperature and hr is the…

Q: 6. How is the instantaneous rate of change found?

A: Answer and explanation is given below..

Q: A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the…

A: If Q(t) is the amount present at time t, then dQ/dt = −rQ, where r > 0 is the decay rate.…

Q: An executive conference room of a corporation contains 4500 ft3 of air initially free of carbon…

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Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Given that rate of decay is proportional tp the current amount x.So,dxdt=kx,    where k is…

Q: A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 2…

A: Given Data: The initial population of bacteria is: P0=260 The population of bacteria after 2 hours…

Q: The rate of proliferation (that is, reproduction) for the cells in a tumor varies depending on the…

A: Here,             We have given  the rate of proliferation for the cells in a tumor varies depending…

Q: Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20%…

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Q: A rectangular sheet of metal has a length of 12 cm decreasing at a rate of 0.2 cm/s, and a width of…

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Q: Find the instantaneous rate of change for the function at the given value. f(x)=x + 2x at x= 0 The…

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Q: One hundred strands of bacteria are placed in a nutrient solution in which a plentiful supply of…

A:

Q: . A tank contains 45 liters of a chemical solution prepared by dissolving 80 g of a soluble…

A:

Q: A tank contains 40 liters of a chemical solution prepared by dissolving 80 g of a soluble substance…

A: Given that, A tank contains 40 liters of a chemical solution prepared by dissolving 80 g of a…

Q: Empirical evidence suggests that the volume V (measured in liters) of a kangaroo's pouch depends on…

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Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: we know that volume of right crcular cylinderV=πr2hdifferentiate…

Q: Numerically estimate the instantaneous rate of change of f(x)=e-x^2

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

A: To find: The time when the concentration of salt becomes 0.15 kglt. Given: The capacity of tank is…

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

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Q: Estimate the instantaneous rate of change of P(x) 5x-3 at the point r = 2 Your answer should be…

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Q: Find the instantaneous rate of change for the function at the given value f(x) =x +2x at x= 0 The…

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Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

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Q: Tank B, a 30-litre tank, initially contains 6 grams of salt in 15 litres of water. At t = 0,…

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Q: What is the result of integrating a population growth rate between two times t= a and t=b, where…

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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 hot object is placed in a room whose temperature is 69°F. After 1 minute the temperature of the…

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Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

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