Зг? Зу? -4 У- У(1) — 0

Q: line with a constant acceleration of -8 ms 2. A De in the direction that the particle is initially…

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Q: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.06 cm…

A: Given information: The diameter of the hemisphere is 52 m that means the radius is 26 m. Formula…

Q: Suppose that a particle moves along a straight line with velocity defined by v(t) =2t2 -t - 3, where…

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Q: 3. A kite holding a fixed altitude of 100 ft is pushed horizontally through the air by wind blowing…

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Q: A jet climbs at a steady rate at an angle of inclination of 0.5° during take-off. What will its…

A: Given that: Angle of inclination, ∅=0.5°Initial ascent = 2.2 km

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 16 cm/min.…

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Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

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Q: A particle has a velocity at time of 4, + 2t meters per minute, where is in minutes. Estimate how…

A: To find the distance traveled using 4 intervals

Q: A stone is thrown downward with an initial velocity of 5m/s from a 20-meter high building. Find the…

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Q: Compute for the interval [2, 3], where y = 6x – 1. Дх Ду 6 Ax What is the slope of the tangent line…

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Q: UST Eco-Tiger vehicle climbed to a hill which is defined by the equation, x² from point A with a…

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Q: A particle moves along the curve y = V1+ x3. As it reaches the point (2, 3), the y-coordinate is…

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Q: # 3 Find the slope of the tangent line to the curve -3x²-3xy + ly = 33 at the point (- 2, 3).…

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Q: 3. What is the equation of the tangent line to the curve x3 + x² = y which is parallel to the line…

A: Given the equation of the curve y=x3+x2 and the tangent line is parallel to 3y+x-5=0

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

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Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: Given : θ = 26.75°

Q: A train, which is 200 m long, approaches a tunnel, which is 120 m long. The train is moving at a…

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Q: 5. Gordon is making a chocolate dome by coating a plastic dome with a layer of chocolate 2 mm thick.…

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Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 14 cm high and…

A: *given:- radius of the cylindrical can, R = 6/2 = 3 cm height of the cylindrical can, h = 14 cm

Q: 4) Find the slope of the tangent line to the curve 4 y = 3(х3 — 2х2 + 3х — 5) at the point (2,) Give…

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Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: A cannonball is fired directly upward from a height of 0 feet, with an initial velocity of 220 feet…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

A: We will solve the following

Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

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Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 30 cm high and…

A: Given a closed cylindrical can has height 30 cm and 6 cm is diameter. the metal in the top  and…

Q: 6. A soccer ball is kicked at an angle of 60 from the ground. If the velocity of the ball is 110…

A: Consider the given angle as 60°

Q: Use Newton's method to approximate the indicated root of x*+x-9 = 0 in the interval [1, 2], correct…

A: According to Newton's method, the root of some equation f(x)=0 can be obtained by: xn+1=f(xn)f ' xn…

Q: A circle has a radius of 5 cm, if the radius is increased by 0.1 mm., what is the estimated increase…

A: Let's find.

Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

A: Given that  Velocity of express train =40km/hr  Breaks apply at 50sec Retardation =0.5m/sec^2 To…

Q: What is the value of the slope of the tangent line to the curve *y+y²=5 passing through the point…

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Q: Use differentials to estimate the amount of paint needed (in m^3) to apply a coat of paint 0.04 cm…

A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

Q: A car travels in a straight line.  It increases its speed from 22 m/s to 28 m/s with a constant…

A: Since distance formula for constant acceleration is  v2=u2+2ax where v is final velocity, u is…

Q: What is the value of the slope of the tangent line to the curve *+4xy+y2=13 passing through the…

A: Note : As per guidelines, I have to answer Only one question, if you want other questions to be…

Q: At noon a car starts from rest at point A and proceeds at constant acceleration along a straight…

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Q: the side of a sqaure is 10 cm. find the approximately, by using differential, the increase in the…

A: Given that side of a square a is 10cm and it is increased by 0.02cm.

Q: Use a linear approximation (or differentials) to estimate the number V100.5

A: To find 100.5Let y=xLet x=100 and ∆x=0.5⇒y=100y=10Differentiate…

Q: The side of an equilateral triangle is increasing at a rate of 3 m/sec, then the rate at which its…

A: Let the side of an equilateral triangle be x cm.∴ Area of equilateral triangle, A = √3/4x2…

Q: Use differentials to estimate the amount of paint needed (in m³) to apply a coat of paint 0.07 cm…

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Q: Compute for the interval [2, 7], where y = 3x - 3. Ay Ax Ду Дх What is the slope of the tangent line…

A: we have y= 3x-3at x=2y=3×2-3 =3at x=7y=3×7-3 =18so,∆y∆x = change in y over the intervalchange in x…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 13 cm/min.…

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Q: 3. A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A: Solved below.

Q: At what exact point on the curve y = 9 + 2ex 5x is the tangent line parallel to the line 5x – y = 4?…

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Q: A baseball diamond is a square with side 90ft. A batter hits the ball and runs toward first base…

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Q: Next, we must find the total distance traveled by the particle in the given time interval. This is…

A: To find the interval for which the velocity is negative and positive.

Q: The equation of the tangent line to the curve x2 + y? = 64, at (5,-13) is. 13 (x – 5) + 13 y = y =…

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Q: Use linear approximation or differentials (but not both) to estimate: V7.98 Is your answer an…

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Q: What is the value of the slope of the tangent line to the x²+4xy + y=13 passing through the point…

A: Topic = Application of Derivative  As per guidelines, At a time only one question can be answered…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 10 cm/min.…

A: Derivative the volume of sphere with respect to t and then put subsequent values.

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: We need to choose correct option.

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.