Example 3: A balloon rising from ground at 140 ft/min is traced by a range finder at point A located 500 ft from the point of lift off. Find the rate at which the angle at A and the distance between A and the balloon are changing when the balloon is 500 ft above the ground.

Q: Find the coordinates of the point P in Figure 19 at which the tangent line passes through (5, 0).…

A: The slope of tangent to any curve is determined by the derivative So, slope of the tangent passing…

Q: A hot air ballon rises vertically upwards from a distance of 170m away. If the angle 0 at which you…

A: To Determine: how fast is the ballon rising when θ=π6 Given: A hot air balloon rises vertically…

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A:

Q: QUESTION 1 The radius of semicircle is increasing at the rate of 0.8 cm/s, calculate the rate of…

A:

Q: A balloon released at point P rises vertically with a constant speed of 6 m/s. Point Q is level with…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Given y be the height of the Ballon ,t be time and theta the angle between the line of sight and the…

Q: Question 17 Let y= Vz+ V8r + I. Using only the definition of rate of change in terms of limit,…

A:

Q: ind the equation of the curve at every point of which the tangent line has a slope of -e-.

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Q: Question 6 Let f(x) = 3x² + x + 5. a) Find the equation of the tangent line at x = 10. b) For what…

A:

Q: A searchlight is trained on the side of a tall building. As the light rotates, the spot it…

A: NOTE: Refresh your page if you can't see any equations. . D=distance between ground level and the…

Q: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

A:

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

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Q: QUESTION 6 A ladder 10 m long leans against a wall in a building. When the lower end of the ladder…

A: A ladder 10m long leans against a wall in a building.when the lower end of the ladder is pulled away…

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: The objective of the problem is to find the speed at which the balloon is rising at the given…

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

A: topic - trigonometric ratios and application of derivatives

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

A: Given that

Q: at FIGURE 10 tomobile past the 232 23. A rocket travels vertically at a speed of 1,200 km/h. The…

A:

Q: A man 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1). (a)…

A: By using similarity rule:

Q: 1. A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the…

A:

Q: A jet airliner is flying at a constant altitude of 12,000 ft above sea level as it approaches a…

A: The diagram of a jet airliner A traveling at a constant height toward a radar station R is shown…

Q: Question 9 If the slope of the tangent line to the graph of y=f(x) at x-a is m(a)=2a+1, and f(1)=5,…

A:

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

A: topic- application of derivatives

Q: radar-tracking dish located 2400 meters from the base of a vehicle’s launching pad is always aimed…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Here we will find how fast is the balloon rising,

Q: QUESTION 5 Figure 1 shows a right triangle with base 6 cm. If x is decreasing at the rate of 2 cm/s,…

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Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

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Q: If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

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Q: Question 12 Find the slope of the tangent line to y = at X = 1 3 - х

A: The given curve is y=23-x, x=1 Differentiate the curve with respect to x      dydx = ddx23-x       =…

Q: A man walks along a straight path at a speed of 4m/s. A searchlight is located on the ground 25m…

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Q: Question 2 2.1 A spotight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the…

A: The problems involves the differentiation to find the respective values. Differentiation is defined…

Q: 11. An airplane is flying parallel to the ground at an altıtude of 2 km and at a speed of 4 km/min.…

A:

Q: Points A and B move along the x-and y-axes, respectively, in such a way that the distance r (meters)…

A: Given:The points A and B move along x and y axes respectively such that the distance r meters along…

Q: 83. Find the coordinates of the point P in Figure 22 at which the tangent line passes through (5,…

A: f(x) =  9 - x2  The tangent lies on point P  if x coordinate is a  then y coordinate = f(a) y…

Q: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the…

A: The given data is: A man 6 feet tall walks at a rate of 7 feet per second away from a light that is…

Q: QUESTION 4 Find the equation of the tangent line to the curve at (1, 4). y = x' + O a. x = 1 O b.y =…

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Q: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

A: A Hot air balloon is rising vertically . Angle between observer's line of sight and ballon is pi/5.…

Q: Find the equation of the tangent to the curve y=√x at the point (1,1) (Figure 4).

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Q: Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is…

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Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A:

Q: 1. Figure 15 shows the velocity of an object over a 3-minute (min) interval. Determine the distance…

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Q: Question 6 2x - 1 What is the slope of the tangent line that touches the graph of In( y) +e='=3y –…

A: Basic derivative problem

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Rate of change

Q: If the minute hand of a clock has length r (in centimeters), find the rate at which it sweeps out…

A:

Q: IN QUESTION 6, WRITE AN EQUATION OF THE TANGENT LINE TO THE CURVE AT THE GIVEN POINT. 6. f(x) = Vx +…

A:

Q: In an airplane control problem, an airplane is flying in still air with an airspeed of 275 mph. the…

A: Let's find.

Q: A man 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1). (a)…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A: From the given information we use trig ratio ,  tan(θ)=oppositeadjacent…

Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: To solve the following problem.

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.