7. A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12 feet above ground. At what rate is the length of his shadow changing when he is 20 feet away from the base of the light? At what rate is the tip of his shadow moving?

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: A light is hung 6 meters above a straight horizontal path.  If a man 2 meters tall is walking toward…

A:

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: 2) Water is pouring into an inverted cone at the rate of 8 cubic me- ters per minute. If the height…

A: Given that Height of cone h=12 m radius of its base r=6 m rate of pouring water into cone dVdt=8 m3

Q: The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square…

A:

Q: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

Q: 22) A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is %…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

A:

Q: A woman 1.5 m tall walks directly away from a street light which is 6 m above the ground at a rate…

A:

Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

A:

Q: . A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking…

A: We make diagram of the situation .

Q: The sides of a square increase in length at a rate of 5 m/sec. a. At what rate is the area of the…

A: We apply chain rule of differentiation. Area of the square is: A= s2.  Where s is the side of a…

Q: a) Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right…

A: Given that  The water is flowing into a leaky cistern at the rate of 31.4 cu ft./min ⇒dVdt=31.4…

Q: 4. A spotlight is on the ground 20 feet away from a wall and a 6-ft tall person is walking towards…

A: Spot light and the wall is at the distance 20 ft.  Person height is 6 ft. He is walking towards the…

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…

A:

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…

A:

Q: 2. a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down the…

A: Given:-  a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down…

Q: If I am blowing up a balloon at a rate of 3 cubic feet per minute, what is the rate of change of the…

A: Since, it is given that a person is blowing up a balloon at a rate of 3 cubic feet per minute, then…

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

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

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

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: Area of square = a2 Where a is length of side of square.

Q: 1. One leg of a right triangle decreases at 1 in./min. and the other leg increases at 2 in./min. At…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at10…

A: From the given data , Man walks across a bridge in one second AC=5 feet and boat passes in one…

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Consider the provided information, Let x and y be the traveled by the cars after time t. We can…

Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

A:

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

A:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: 5. A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second…

A:

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: 4. A car travelling north at 60 mph and a truck travelling east at 45 mph leave an intersection at…

A: Let the distance travelled by car travelling at 45 mph from intersection be x at any point of time.…

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…

A:

Q: 1. Suppose the length of the diagonal of a square is increasing at the rate of 2 inches per second.…

A:

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 2 m3/hour. If the base radius of…

A: Given that

Q: The volume of a cube is increasing at the rate of 1200 cm3/min at the instant its edges are 20 cm…

A: Let the length of the sides of the cube = xAnd the volume of the cube = V = x^3

Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

A:

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: a kite 100 ft ft above the ground moves horizontally at a speed of14ft/s. at what rate is the…

A: If you like the solution then please give it a thumbs up..... The Answer is:     Result = - 0.035…

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

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

A: Given: -

Q: 2. A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A:

Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.