A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15 ft/sec. At what rate is the player's distance from third base decreasing when she is half way from first to second base?

Q: Coffee is draining out of a conical filter at a rate of 2.25 in3>min. If the cone is 5 in tall…

A: Given: The change in volume for the filter is -2.25 in3/min The change in volume for the coffee pot…

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A: 6)

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: Assuming your car can slow at a constant rate of 15 ft/sec2, how much distance will your car cover…

A:

Q: A helicopter takes o from a point 80 m away from an observerlocated on the ground, and rises…

A: Thus when the helicopter is 60 m above the ground the elevation angle of theobserver’s line of sight…

Q: The side of a cube is increasing at a rate of 5cm/sec, find the related change in surface area wher…

A:

Q: A rectangular trough is 10ft. long and 3ft. wide. Find how fast the surface rises, if water flows in…

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

Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: Find the rate at which the water level is rising when the water level is 2 cm.

A:

Q: A baseball diamond is a square with side 90 feet. A batter at home base hits the ball and runs…

A:

Q: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at…

A:

Q: A rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. If water flows in at rate 2…

A:

Q: A light is at the top of a 16 ft pole. A man 6 ft tall walks away from the pole at a rate of 5ftsec…

A:

Q: A trough is 10 ft long and its ends have the shape of isoscelestriangles that are 3 ft across at the…

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: Question 4

A: Let a be the acceleration, v be the velocity, s be the position and t be the time of braking.

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

Q: A rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. If water lows in at rate 2…

A: It is given that rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. Suppose that x…

Q: the tires of a bicycle have a radius of 14inches and are turning at the rate of 230 revolutions per…

A: Given that the tires of a bicycle have a radius of 14inches and are turning at the rate of 230…

Q: A light is hung 15ft above a straight horizontal path. If a man 2 ft tall is walking away from the…

A:

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what…

A: Let x  be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: A baseball diamond has the shape of a square with sides 90 ft long, as shown. A player is running…

A: A baseball diamond has the shape of a square with sides 90 feet long. A player running from second…

Q: A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope…

A: To find: The speed of the boat approaching the dock when the total length of rope out is 50 feet.…

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm4/min, find the rate at…

A: Note that snowball has a shape of sphere.

Q: A car braked with a constant deceleration of 40 ft/s2, producing skid marks measuring 80 ft before…

A: Deceleration = dv/dt And v = dx/dt where v is the velocity and x is the displacement Hence,…

Q: A street light is at the top of a 29 ft pole. A 4 ft tall girl walks along a straight path away from…

A: Draw a diagram that illustrates the given information Let x be the distance to the girl from the…

Q: A baseball diamond is a square with with side 90 feet (between the bases). A batter hits the ball…

A: Roughly draw the situation first Where x= Distance covered by batter at time t D= Distance of the…

Q: A car braked with a constant deceleration of 18 ft/s2, producing skid marks measuring 100 ft before…

A:

Q: a 5-ft tall person walks away from a 20-ft tall streetlamp at a constant rate of 3 ft/s . at which…

A: Let us denote: x= distance of the person from the post y=length of the shadow Given that, dx/dt=3 ,…

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: A car braked with a constant deceleration of 8 ft/s2, producing skid marks measuring 100 ft before…

A: constant deceleration of 8 ft/s2  skid marks measuring 100 ft

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: . A vertical cylinder is leaking water at a rate of 1 ft /sec. If the cylinder has a height of 10 ft…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: Given information:

Q: If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at…

A:

Q: A street light is at the top of a 26 ft pole. A 5 ft tall girl walks along a straight path away from…

A: Given:

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Let the volume of the water in the trough at time be V. The rate of change of V is,

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

Q: A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 50 ft before…

A:

Q: The base x of the right triangle in the figure increases at a rate of 6 cm/s, while the height remai

A: In this question we will use basic of calculus i.e application of differentiation. We will first…

Q: The legs of an isosceles right triangle increase in length at a rate of 4 m/s. a. At what rate is…

A:

Q: An arrow is shot vertically up word from a platform 20 feet high at a rate of 179 ft./s, when will…

A: We will use the quadratic equation approach to solve the problem given: Height , h = 2ft speed = 179…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.