The maximum range of a projectile is directly proportional to the square of its velocity. A baseball pitcher throws a ball at 60 mi/h, with a maximum range of 242 ft. What is his maximum range if he throws the ball at 70 mi/h?

Q: It costs a family $324.00 to buy a 10-ft-by-12-ft rug. If the cost is proportional to the area, what…

A:

Q: The distance required to stop a car varies directly as the square of its speed. If it requires 200…

A: The distance is directly proportional to square of the speed. That is, d α s2⇒d=k·s2   →1  where k…

Q: The number of hours it takes Jack to drive from Boston to Bangor is inversely proportional to his…

A: Given- The number of hours is inversely proportional to his average driving speed and he drives at…

Q: Which of the constants in the equation f(x) = a * x ^ 2 + bx + c can be interpreted geometrically?

A: If x=0 then  f(x)=ax2+bx+cf(0)=a(0)2+b(0)+cf(0)=c This means the point is (0,c). This means the…

Q: The stopping distance d of a car after the brakes have been applied varies direclty as the square of…

A: The speed of the car is r1=70 mph. The distance d1=350 and d2=56. We know that the topping distance…

Q: 3. Find the instantaneous velocity of a rocket that hits the ground whose position can be modeled…

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Q: The number of miles a car can be driven is proportional to the number of gallons of gasoline that…

A: The number of miles a car can be driven is proportional to the number of gallons of gasoline…

Q: The weight of a body above sea level varies inversely with the square of the distance from the…

A:

Q: The stopping distance of a car after the brakes have been applied variesdirectly as the square of…

A:

Q: The volume of gas in a gas shock absorber varies inversely with the pressure and directly with the…

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Q: The distance, s, that a body falls from rest varies directly as the square of the time, t, of the…

A: Given: (k is a constant used to remove the proportionality sign) When s=64 feet and t= 2s value of…

Q: The height that a person is above the water is directly proportional to the square of the distance…

A: Given: The height that a person is above the water is directly proportional to the square of the…

Q: The intensity of a light source at a distance is directly proportional to the strength of the source…

A: Given that, the intensity of a light source at a distance is directly proportional to the strength…

Q: In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind…

A: It is known that wind pressure=k(velocity)2.

Q: The distance ss that an object falls varies directly with the square of the time t. If an object…

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Q: A force, f, varies inversely with the square of the distance, d, from an object.

A:

Q: The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve…

A: Given:A force of 200 pound keeps a car of weigth 3200 pound from skidding on curve of radius400ft at…

Q: for a given span, the maximum weight that a wooden beam can support varies directly as the square of…

A: The given question can be solved as shown in step2.

Q: The load L, in pounds, on a certain sail varies directly as the square of the wind speed v, in miles…

A:

Q: The value of a glass varies directly as the square of its radius x cm. glass with radius 5 cm is $…

A: Given':  The value V of glass varies directly as the square ofnits radius " x" c.m  V =k*x^2  If…

Q: The braking distance of a car varies directly as the square of the speed of that car. Assume that a…

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Q: The velocity v of a falling object varies directly with the time t of the fall. If after 3 seconds,…

A:

Q: The load L, in pounds, on a certain sail varies directly as the square of the wind speed v, in miles…

A: If the variable are proportional to each other then they can be equated by using some constants. For…

Q: The maximum safe load for ahorizontal rectangular beam varies jointly with thewidth of the beam and…

A: Let the length, width, thickness and maximum safe load of beam is represented by following…

Q: The cost C of steel tubing varies jointly as its length L, in feet, and diameter D, in inches. If a…

A:

Q: The volume of a box (V) varies directly with its length (). If the box has a volume of 360 cubic…

A: Volume ×length   v×l

Q: The number of hours it takes Jack to drive from Boston to Bangor is inversely proportional to his…

A:

Q: The weight of a can of soup is jointly proportional to its height and to the square of its diameter.…

A: Given according to question

Q: The lift of an airplane wing at takeoff varies jointly as the square of the speed and the area of…

A: Given:- Lift experienced is 1700 lb if plane travels at 50 mi/h with wing area of 500 ft^2.

Q: In the equation x2 + 4x - y + 4 = 0, find the coordinate of the point where the abscissa and the…

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Q: Given that y varies directly as the square root of x and y = 6 when x = 9, find the variation…

A: It is given that y varies directly as the square root of x, thus the equation formed is- y=cx where…

Q: The intensity I of light is inversely proportional to the square of the distance d from the light…

A: topic - ratio and proportion

Q: When  anvil is dropped into a gorge, the speed with which it strikes the ground is  directly…

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Q: The period of a pendulum varies directly as the square root of the length of the pendulum and…

A:

Q: The distance that a freely falling body falls varies directly as the square of the time it falls. If…

A: Let d, in feet, be the distance The distance that a freely falling body falls in time t second Then…

Q: The time it takes to cover the distance between two cities by car varies inversely with the speed of…

A:

Q: The weight of an object above the surface of the Earth varies inversely with the square of the…

A: Let us assume that the weight of the object is w and  the distance of the object from the center of…

Q: The load L, in pounds, on a certain sail varies directly as the square of the wind speed v, in miles…

A:

Q: The distance to stop a vehicle varies directly with the square of its speed.  It takes 200 feet to…

A: First write the equation then put all the values ..and get the final result

Q: Suppose that an object is dropped from a height h. Its velocity v at impact with the ground is given…

A: given: suppose that an object is dropped from a height h. Its velocity v at impact with the ground…

Q: A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per…

A: Let the speed of the boat in still water be x mi/hr. Speed of boat in upstream = x - 3 mi/hr and in…

Q: The relationship between the cost, y, in dollars, ar the pounds of steel bought, x, can be modeled…

A: The relation between cost y in dollars and pounds of steel bought=x

Q: Find the constant of variation and the variation equation. y varies directly as the square root of…

A:

Q: The weight W of an object varies inversely as the square of the distance d from the center of the…

A: If you like the solution then please give it a thumbs up... The Answer is:      Result:   w = 112.69…

Q: The surface area of a balloon varies directly as the square of its radius. The area is 1256 cm when…

A: given that A1=1256 cm square, r1=10 cm,r2=4cm,A2=? according to question surface area Aα…

Q: The velocity of an object at time t seconds is given by v(t) = −t^2 + 3t + 5 meters per second. If…

A: Explanation of the answer is as follows

Q: The distance that a body falls varies directly as the square of the time that it is falling. If…

A: It is given that the distance a body falls varies directly as the square of the time. If distance of…

Q: At a fixed temperature, the volume of a given mass of gas varies inversely as the pressure applied…

A: Given that, At a fixed temperature, the volume (V) of a given mass of gas varies inversely as the…

Q: The intensity of light received at a source varies inversely as the square of the distance from the…

A: Given: The intensity of light received at a source varies inversely as the square of the distance…

Q: The cost of fuel per hour for running a ship is proportional to the cube of the speed and is P1,350…

A: The given problem is solved below in detail.

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.