Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is approximated by the equation below. p(x) = 29.92e-0.2x   (x  0) If the barometric pressure as measured by a hot-air balloonist is 20.5 in. of mercury, what is the balloonist's altitude? (Round your answer to two decimal places.)

Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

A: Let us consider  We plug x=2 in it

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A: Given that the building is 74 feet away from the point where the angle is measured.  Let x=75. The…

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A: Topic- application of derivatives

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A: We have to solve this question:

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Q: A 2. A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration ? Is this…

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Q: A 10-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: Solve for x accurate to three decimal places.

A: The equation: 9-2ex=7

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Q: (1) The rate of healing for a skin wound in cm² per day is given approximately by A'(t) = -0.9e-01t.…

A: dAdt = -0.9e-0.1t Now, integrate this equation A =∫-0.9e-0.1tdt So, A = -0.9e-0.1t-0.1 + C   but, we…

Q: After sitting on a shelf for a while, a can of soda at a room temperatu placed inside a refrigerator…

A: Given, Ta= 39°F To= 68°F T= 61°F t= 15 min

Q: A population of bacteria is growing according to the equation P(t) = 450e"2t. Estimate when the…

A:

Q: A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A: Recall: Pythagoras Theorem:        Pythagoras theroem states that In a right angled triangle , the…

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A: The ladder makes a right triangle with the wall.  So using Pythagorean theorem:

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A: D=ct2 Now if the time increases from 3 seconds to 12 seconds, then it is increased by a factor of 4…

Q: 3. The height, in metres, of an object thrown from a rooftop is given by the equation h(t) = -x? +…

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Q: A round underwater transmission cable consists of a core of copper wires surrounded by nonconducting…

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Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

A: The nearest number to 35.4 whose square root can be taken is 36, so let us consider that x=36 And…

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Q: A pot of boiling soup with an internal temperature of  105∘F was taken off the stove to cool in a…

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Q: If a rock is thrown upward on the planet Mars with a velocity  of 10 mys, its height (in meters)…

A: Given: The equation of height of the rock is thrown upward on the planet Mars with a velocity 10…

Q: The number of hits on a certain website (in thousands) is approximated by f(x) = 70 e 0.1769x where…

A: The number of hits on a certain website is f(x)=70 e0.1769 x, where x=0 corresponds to 2000.

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A: (a) Given that, the velocity of the tip of the bore is V=kh0.5. Let h be the initial height and V be…

Q: Find the root of an equation f(x) = x^3 - x - 1 = 0 until estimated error Ea falls below the level…

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Q: 1 S(1) = fi-

A: The given function is ft=t2-1t2. The f'(t) means derivative of f(t) with respect to t.

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A: given: newton's law of heating tells us that the difference between the temperature of the oven and…

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A: Given: A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12 feet…

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: Given expression is D=3000.98t where D is the temperature difference between the oven and the potato…

Q: we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: GivenInitiall potato temp = 75° oven temp = 375°difference = 375-75difference =300°D = 300 x 0.98tD…

Q: The pH of a solution is given by the formula pH = −0.4343 In a, where a is the activity of hydrogen…

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Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

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Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A:

Q: Under certain conditions, tsunami waves encountering land will develop into bores. A bore is a surge…

A:

Q: I asked this question last night, and received a response, but was told the answer you gave me was…

A:

Q: Solve for x accurate to three decimal places −4 + 3e−2x = 6

A: Given, the equation is -4 + 3e-2x = 6. We have to calculate the value of x.

Q: The half-life of a radioactive substance is 37 hours. If f ( t ) = a e ^ k t gives the amount of…

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Q: A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following…

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Q: The value of a machine, V, at the end of t years is given by V = C(1 – r)', where Cis the original…

A: The value of the machine is:-

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A: Given data- AC= 10 foot. AB=X=6 ft. dxdt=0.7ft/sec. We have to find dydt.

Q: With snow on the ground and falling at a constant rate, a snowplow began plowing down a long…

A: Answer is mentioned below

Q: One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate…

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Q: The area of a circle increases at a rate of 6 cm2/s. a. How fast is the radius changing when the…

A: Given that the area of a circle increases at a rate of 6 cm2/s .

Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C…

A: The given problemis from Newton's law of cooling.Form a differential equation of the given situation…

Q: 15. A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.