Solve the following time rates problems: A softball diamond has the shape of a square wide sides 60 ft long. If a player is running from second base to third at a speed of 24 ft/sec, at what rate is his distance from home plate changing when she is 20 ft from the third?

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: From the Pythagorean theorem, BC2+AB2=AC2

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

A:

Q: Problem 11. A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of…

A: Given: A 13 foot ladder is leaning agaist a wall. If the top slips down the wall at a rate of2 ft/s.…

Q: Solve the following situational problems involving circular functions. 1.The radius of the wheel of…

A: Solve the following situational problems involving circular functions. 1.The radius of the wheel of…

Q: 1. A ladder 10 meters long leans against a wall. If the bottom of the ladder is being pulled away…

A: Given: A ladder 10 meters long leans against a wall. If the bottom of the ladder is being pulled…

Q: Problem #2 One airplane is approaching an airport from the north at 199 km/hr. A second airplane…

A: We have to find the rate at which distance between the planes is changing.   According to our…

Q: . Determine how long will it take for the thermometer to reach 15°F in Problem 1?

A:

Q: This question is designed to be answered with a calculator. When the volume of a sphere is 200 cubic…

A: To find at what rate the volume of the sphere is Changing we use the formula for finding the volume…

Q: 2. The highest point of the underground tank from Problem 1, is at depth 6 feet from the surface of…

A: Work done =force* displacement Here force is the weight of the body due to gravitation.

Q: One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knats.…

A: Let the time at 2:00 Pm be t  The two ships will form a right angled triangle, with horizontal side…

Q: Problem 3. Two boats are racing with constant speed toward a finish marker, boat A sailing from the…

A: Given : Boat A is sailing from south at 13 mph and boat B is approaching from the east.

Q: Two airplanes are flying in the air at the same height: airplane A is flying east at 290 mi h and…

A: Given that:                      Speed of plain A, vA=290 mi/hSpeed of plain B, vB=290 mi/hDistance…

Q: A 4.5 ft tall man is walking away from a 25 ft tall lamp post.  If he is walking at a rate of 2…

A:

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Simple rate of decay of radium problem....

Q: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: Please see the explanation below

Q: Solve the following rate of change problems (SOLVE a and b) a) A man starts walking north at 4 ft /…

A: Note: According to Bartleby guidelines; for more than one question asked, only the first one is to…

Q: if water rises 1/2 inch in 3/7 of a week in a water reservoir, at what rate is the water rising per…

A:

Q: Consider an object in a surrounding with constant temperature of 25°C. If the temperature of the…

A:

Q: A car traveling at the rate of 20m/s is approaching an intersection. When the car is 100 meters from…

A: Given: dadt=20 m/s and   dbdt=100m/s at   t=2 sec first we convert m into ft so, 20m/s×3.281=65.62…

Q: Problem 4. A 10ft ladder is leaning against a wall. If the top of the ladder slides down the wall at…

A: Given- 10 ft  ladder is leaning against a wall and the top of the ladder slides down the wall at a…

Q: A boat is being pulled with a rope towards a dock that is 10 ft above the water, as shown in the…

A: Let the distance of the boat= x ft y=length of the rope.  So,  given that dy/dt= 1.5 ft/min We have…

Q: Solve the following problems. 1. A ladder 7.5 meters long is leaning against the wall of a house.…

A: In the question we have to find the rate at which ladder is sliding down.

Q: A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the…

A:

Q: An airplane flying on a straight flight path will be exactly above a radar tracking station, which…

A: Given: Perpendicular distance between station and plane is 5,000 km To find rate of distance of…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: Question 6 of 10, Step 1 of 1 Correct Incorrect The selling price for a classic speedboat is…

A:

Q: Problem 7. The base of a 50-foot ladder is being pulled away from a wall at a rate of 10 feet per…

A: Given: Length of ladder = 50 foot Rate at which it is pulled, VC = 10 feet/sec

Q: One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knots.…

A: Given that at time 2 p.m the second ship is at the place occupied by the first ship one hour before.…

Q: Question 9 A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of…

A:

Q: A runner starts at the beginning of a runners' path and runs at a constant rate of 5 mi/hr. Fifteen…

A: First, we need to calculate the relative speed which is, the difference between the speed of the…

Q: Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the…

A: topic - application of derivatives

Q: Suppose car A is heading south at 85 km/h and car B is heading east at 90 km/h. Both are headed for…

A: Consider

Q: At what fraction of the speed of light does Alice have to travel relative to Bob so that Alice does…

A: Given Alice does everything three times as slowly as Bob Find The fraction of speed

Q: A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start…

A: How far did the adults go? How long did that take?

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

Q: When Apollo 15 astronaut David Scott dropped a hammer and a feather on the moon to demonstrate that…

A: An astronaut dropped a hammer and feather on the moon.These are dropped from about 4 ft above the…

Q: Consider an aquarium with a 75 gallon tank.  If the aquarium has a water pump that pumps water at a…

A:

Q: Two cars start moving from the same point. One travelssouth at 60 mih and the other travels west at…

A:

Q: A man 6 feet tall walks at a rate of 3 feet per second away from a light that is 15 feet above the…

A:

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is…

A: Given :Radius of thr ripple increasing by 2 feet per secondCircumference = 2πr

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: Let OA= height of light      CD= height of man      BC= length of shadow…

Q: The rate of fingernail growth depends on many factors, but in adults, nails grow at an average rate…

A:

Q: chapter 3.7 problem 40 person is standning at end of a pier 12 ft above the water and is pulling in…

A: Let us assume the distance of boat from pier is x and the  rope length when boat is x =16 ft from…

Q: If you leave a 100-W light bulb on for a week, how many joules of energy will be consumed?

A:

Q: A certain population of rabbits grows proportionally to its size. If initially there are 1000…

A:

Q: The requirement for computer server capacity at a particular company is expected to increase at a…

A:

Q: Solve the following time rates problems. A girl starts at a point A and runs east at the rate of 10…

A: Given that, A girl starts at a point A and runs east at the rate of 10 ft/sec. One minute later,…

Q: A certain illness is spreading at a rate of 10% per hour. How long will it take to spread to 1200…

A: Assuming exponential growth    31.1t=1200

Q: In this calculus question, there is a shadow length question that deals with a 6 foot man walking at…

A: Follow the procedure given below.

Q: Ship A is 15 miles east of P and moving west at 20 mi/hr; ship B is 60 miles south of P and moving…

A: Given data: The speed of  A is dxdt=-20 mph. The speed of  B is dydt=15 mph. Position of A is xA=15…

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.