18' Shadow A

Q: A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at…

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Q: The base x of the right triangle in Figure increases at a rate of 5 emfs, while the height remains…

A: Write the tangent ratio for angle .

Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

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Q: What is the instantaneous rate of change of the graph of y = = cos x when x= 2n?

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Q: What is the equation of the line tangent to the curve e'+cos(x) = 1 at the point .0?

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Q: Find an equation of the tangent line to the graph of y = ln(x2) at the point (5, ln(25)).

A: Given:

Q: A hot-air balloon is 140 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Given the height in which the hot air balloon placed above the ground is 140 ft. Velocity of the…

Q: A 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

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Q: A ladder of length 3 meters is placed on a wall, with the distance from the wall x and the height of…

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Q: The slope of the tangent line to the curve at (x,y) point is defined by (1+ k) ete .If the curve…

A: The slope of the tangent line to the curve at (x,y) is dy/dx=(1+k)e2x+e^2x.

Q: A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2 feet per…

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Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form a…

Q: An inverted conical water tank with a height of 12ft and a radius of 6ft ft is drained through a…

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Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

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Q: A town library estimates that, when the population is x thousand persons, approximately y thousand…

A: A town library estimates that, when the population is x thousand persons, approximately y thousand…

Q: 9. A man 5 n tall is walking toward a building at the rate of 3 A/sec. If there is a light on the…

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Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

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Q: A man of 2 mts tall is approaching a lamp post at the rate of 0.5m/sec.if the lamp post is situated…

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Q: A man of height 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

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Q: The cone is 12 cm tall and has a radius of 4 cm. If the ice cream fills the cone evenly at a rate of…

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Q: 17. A man of height 1.8 m walks away from a 5-m lamppost at a speed of 1.2 m/s (Figure 9). Find the…

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Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: (플아 What is the equation of the line tangent to the curve e + cos(x) = 1 at the point ,0?

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Q: 4. Find the equation of the tangent line to the curve y = 4+ e2 sin at the point (0, 5).

A: First find the slope at given point with the help of derivative than write the equation of tangent…

Q: A point is moving along the graph of the equation y = −8x2.  At what rate is y changing when x = 3…

A: Given that dx/dt= 5 units/sec And x= 3 We have to find dy/dt

Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume the…

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Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

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Q: Point B moves from point A to point C at 2 cm/ sec in the accom- panying diagram. At what rate is 0…

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Q: A ladder 14 ft long rests against a vertical wall. Let 0 be the angle between the top of the ladder…

A: Given:

Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the…

A: Let the point of contact is (h,ln(h)) We find the slope of the tangent using dy/dx

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

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Q: 3. For the function g(x) = x' - 2x -1, at what tangent point is the instantaneous rate of change…

A: Instantaneous rate of change of f(x) at x=a is given by f'(a), where f'(x) is the first order…

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

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Q: At time t = 0, Car A passes through an intersection and goes east at a speed of 40 feet per second.…

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Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: Given Data: The height of the man is: h=1.9 m The height of the lamppost is: H=5 m The increasing…

Q: 4. A street light is at the top of a 16 ft pole. A 6 ft tall woman walks along a straight path away…

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Q: Find the equation of the line tangent to the graph of y = arcsin (tanh(x)) at r = = 0.

A: we have to follow next step

Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: At what point on the curve y = sinh x does the tangent line have a slope of 1?

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 − x2 −…

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Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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Q: A hot air balloon is 120 ft. above the ground when a motorcycle (travleing in a straight line on a…

A: Given that, A hot air balloon is 120 ft. above the ground when a motorcycle (traveling in a straight…

Q: A balloon is 20m horizontally away from an observer. At an constant, the balloon rises vertically at…

A: Let the distance between ballons and observer is y and vertically distance from the ground is x m…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

Q: A 15-foot ladder is leaning against a vertical wall when Josiah begins pulling the foot of the…

A: This question is based on application of Derivative and Pythagoras theorem.

Q: Find an equation of the tangent line to the graph of y = ln(x2) at the point (3, ln(9)). y=_____

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Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: Let the particle is at the point (x,y) at any time t in first quadrant where y=x2  Its x-coordinate…