The velocity of a heavy meteorite enteringEarth’s atmosphere is inversely proportional to √s when it is skm from Earth’s center. Show that the meteorite’s acceleration isinversely proportional to s2.

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Q: Suppose you drive for 60 miles at 60 miles per hour, then for 60 miles at 30miles per hour. In miles…

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Q: The gravitational force, F, between an object and the Earth is inversely proportional to the square…

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Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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Q: find the differential for  y=sqrt(9-(lnx)2)

A: Given: Using:

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Q: Find an equation of the line tangent to the graph of f(x) = at 8,

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Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx +2

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Q: A box weighing 50lbs falls from rest and the air resistance is proportional to his speed V and that…

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Q: 3

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Q: Use differentials to approximate the change in R revenue= 50x-1.5x2 as sales increase from 13 to 15…

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

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Q: A 6-foot-tall woman walks at 7 ft/s toward a street light that is 30 ft above the ground. What is…

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Q: By comparing the surface area of a sphere with its volume and assuming that air resistance is…

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Q: A lamp post 3 m high is 6 m from a wall. A man 2 m tall is walking directly from the post toward the…

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Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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Q: If f(x) = 2x² – 8x + 7, find the equation of the line tangent at æ = 3. Preview TIP

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Q: A man 2m tall is walking at the rate of 2m/s away from a lamp post 7m high. At what rate is the tip…

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Q: Find the equation of the line tangent to f(x) = 4x³ – 5x +4 at (–2, –18). -

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Q: Write the equation of the line tangent to f (x): x2 – 3x + 5 at the x

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Q: After a ball bounces off from the top of a hill, its velocity at t seconds is v(t)=45-30t feet per…

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Q: Find the equation of the line tangent to the curve f(x) = 4x² - 6x +39 at x = 1.

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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.