Related rates Definition and 361 Threads

Hey guys can anyone please help find the answer for A, I just can't figure out what they want. I mean I was still able to figure out the answer to B, but I just kept getting the answer to A wrong and I only have one try left. Please help...

A cylinder is placed in oven where both the height and base radius expand at 0.1 mm/min. When the height is 250 mm and the radius of the base 30 mm, the volume is expanding at ...mm3 /min. (Answer to nearest whole number) r=30, h=250, dr/dh=0.1, dh/dt=0.1 dV/dt = (pi)r^2(dh/dt) +...

Water is leaking out of a cylindrical tank , with circular base radius 0.8 m at the rate of 0.2 m3/min. The water level is falling at ...? ..m/min. What is the question mark? (Hint: the radius does not change) V=(pi)r^2h, dV/dt = 0.2, r = 0.8 ? Can anyone give me a hand in getting this one...

Related Rates Help please! Homework Statement Two cars start moving from teh same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate is the distance between the cars increasing two hours later?" Homework Equations So far I have the equation...

[SOLVED] Simple Related Rates Homework Statement A baseball diamond is a square 90 ft on a side. A runner travels from home plate to first base at 20 ft/sec. How fast is the runner's distance changing when the runner is half way to first base? Homework Equations a^2+b^2=c^2 The...

Homework Statement You are riding a Ferris wheel 120 feet in diameter. It makes one complete revolution every minute. How fast are you falling when you are halfway to the bottom? Homework Equations None The Attempt at a Solution I really am not sure where to start. I'm actually not even...

Homework Statement "A man pours water into a conical glass (with radius 9cm and height 6cm) at a rate of 8cm^3. At what rate is the height of the water changing per second when the height of the glass is 2/3rd's full of water? NOTE: The answer is supposedly 2/9(pi) cm/sec. I am supposed...

1. Homework Statement A child weighs 34 Kg is seated on a seesaw. While a child who weighs 40 kg is situated on the opposite end of the seesaw. The function B(x)= 34x / 40 gives the distance that the 40 kg child must sit from the center of the seesaw when the 34 kg child sits x meters from the...

Homework Statement A child weighs 34 Kg is seated on a seesaw. While a child who weighs 40 kg is situated on tghe opposite end of the seesaw. The functio B(x)= 34x / 40 gives the distance that the 40 kg child must sit from the center of the seesaw when the 34 kg child sits x meters from the...

A runner sprints around a circular track of radis 100m at a constant speed of 7m/s. The runner's friend is standing at a distance 200m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200m...

Related Rates - Is my set-up correct? A water trough is 10ft long and its ends are isosceles triangles that are 3ft across the top and have height 1ft. If \frac{dV}{dt}=12\frac{\mbox{ft}^{3}}{\mbox{min}}, how fast is the water level rising when the water is 6 inches deep? V=\frac{1}{2}(b_1 +...

[SOLVED] Related Rates - Sort of confused Homework Statement There are two buildings. One 20' high and other 40' high with a 60' distance between them. A person walking between them creates a theta with the buildings (see pic) PICTURE...

A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 14 km and climbs at an angle of 40 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 3 minutes later? The only equation I am using is the...

Homework Statement A boy is standing 50 ft. from the end of a swimming pool when he sees a girl 25 ft. along the end. He can swim 3 ft/s and run 5 ft/s. If he runs x feet, set up an equation for time consumed. Homework Equations There is a visual aid: A rectangle with length...

Homework Statement A man 6 ft tall wlaks at a rate of 5ft/s away from a light that is 15ft above the ground. when he is 10 ft from the base of the light, 1) at what rate is the tip of his shadow moving? 2) at what rate is the length of his shadow changing? The answers are 1) -50/7...

Homework Statement A rocket is 1/2 miles in the air going 40mi/h a bystander is standing 1 mile away from where the rocket took off straight up. What is the rate of change of the angle that the bystander makes with the rocket. Homework Equations The Attempt at a Solution I set...

Related Rates! help please! A and B are walking on straight paths that meet at right angles. A approaches at 2m/sec; B moves away from the intersection at 1m/sec. At what rate is the angle \vartheta changing when A is 10m from the intersection and B is 20m from the intersection. Ans in degrees...

Question A street light is mounted at the top of a 15 foot tall pole. A man 6 ft tall walks away from the pole with a speed of 6 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole? Attempt Well actually, I've drawn it out and stuff, but I was...

Homework Statement A flagpole 40 ft high stands on level ground. A flag is attached to a 120 ft rope passing through a pulley at the top of the flagpole. The other end of the rope is tied to a car at ground level. If the car is driving directly away from the flagpole at 3ft/sec, how fast is...

Homework Statement The length of the hypotenuse of a right triangle is 10 cm. One of the acute angles is decreasing at a rate of 5 degrees/s. how fast is the area decreasing when this angle is 30 degrees?Homework Equations The Attempt at a Solution I got the a and b using the cos and sin of...

Need help guys, not understanding this at all. Can anyone help me out? Two sides of a triangle and their included angle are changing with respect to time. The angle increases at the rate of 1 radian/sec, one side increases at the rate of 3ft/sec, and the other side decreases at the rate of...

Homework Statement A rectangle is expanding so that its length is always twice its width. The perimeter of the rectangle is increasing at a rate of 6cm/min. Find the rate of increase of the area of the renctangle when the perimeter is 40 cm. Homework Equations The Attempt at a Solution p = 6x...

Here is the solution to one of my problems: When inserting dV/dt to differentiate the equation as a function of time, why doesn't the book use the power rule on r^2 and multiply the entire equation by 2? I thought when dr/dt was put into the equation you had to differentiate?

I was pondering a question today. If you have a cube with a sphere inside of it, and the sphere is growing at 2 m/s. The cube itself is expanding at 1 m/s. If the cube is 5 x 5 x 5, and the sphere has a radius of 2. Is it possible to calculate when the sphere and the cube will be expanding...

Homework Statement "On a certain clock the minute had is 4in long, and the hour hand is 3in long. How fast is the distance between the tips of the hands changing at 9 o'clock?" Homework Equations - a^{2} + b^{2} = c^{2} - Law of Cosines? The Attempt at a Solution Ok i drew a clock...

Let x & y be differentiable functions of t and let s = sqrt(x^2+y^2) be the distance between the points (x,0) and (0,y) in the xy-plane. How is ds/dt related to dx/dt if y is constant? So I attempted to implicitly take the derivatives of the changing rates. ds/dt= 1/(2sqrt(x^2+y^2)) times 2x...

Related rates, roflcopter! Homework Statement A helicopter takes off from a landing pad at 10:48am and travels eastward at a speed of 120km/h. A second helicopter traveling south at 150km/h is planning to land at 10:59am, How fast is the distance between them chaging at 10:50am and is...

Homework Statement A light shines from the top of a pole 50 ft high. A ball is dropped from the same height at a point 30 ft away. (see thumbnail). How fast is the shadow of the ball moving along the ground .5 seconds later assuming ball falls a distance of s=16t^2 Homework...

Homework Statement #19 Homework Equations Implicit Differentiation The Attempt at a Solution I have a diagram and I am using the info given to establish some relationships. I guess my main concern is whether I have established a correct relationship between r and y as to eliminate one of...

The volume of a cap, of depth h cm, cut from a sphere of radius a cm (a>h) is given by V = {\textstyle{1 \over 3}}\pi h^2 (3a - h) . A bowl is in the shape of a cap of depth a/2 cm cut from a spherical shell of radius a cm. Water is being poured into the bowl at a constant rate of \frac{{\pi...

Consider the graph of y=x2. A point is moving along the x-axis in such a way, that its speed is proportional to its distance from the origin. At the same time, a point is moving along the curve of the graph, which always has the same x-value as the point moving along the x-axis. At what rate is...

1) (Related Rates) One end of a rope 20 meters long is attached to a box resting on the floor. The other end is passed over a pulley directly above the box, 5 meters above the floor, and attached to the back of a truck at a point 1 meters above the ground. The truck then drives in a straight...

I have this problem, and I have attepmted a classical approach without much success. A man 5 ft tall runs at a rate of 8ft/sec towards a source of light that arises vertically at a point A. The height of the light source H, is given by the formula h(t)=t^3 +1, in feet, where time t is...

Homework Statement The first problem is a related rates question: A swimming pool if 5m wide and 25m long, 1m deep at the shallow end and 4.5 deep at the deepest point. A cross section is shown in the figure below. The pool is being filled at a rate 0.5m^3/hr. Use calculus techniques to...

Homework Statement The side of a cube increases at 1 cm / s. How fast is the diagonal of the cube changing when the side is 1 cm? Homework Equations Involves: a^2+b^2=c^2 Implicit Differentiation Derivation The Attempt at a Solution I'm attempting to find the diagonal of the cube...

Homework Statement Water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area 400 \pi square feet. The depth, h, in feet, of the water in the conical tank is changing at the rate of (h-12) feet per minute. A) Write an...

Homework Statement This last related rates HW problem is givin me trouble for some odd reason. A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 11 km and climbs at an angle of 25 degrees. At what rate, in km/min is the distance from the plane...

Homework Statement 2. Coffee is draining from a conical filter into a cylindrical coffee pot at the rate of 10 in3/min. a) How fast is the level in the pot rising? ____________ b) How fast is the level in the cone falling when the level in the cone is 5 in.? _________ Homework...

Homework Statement A particle is moving along the curve y=\sqrt{x}. As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant? Homework Equations The Attempt at a Solution I...

the altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm^2. do i use the pythagorin theorem for this

2 cars start moving from the same point. one travels south at 60 mi/h and the other travelks west at 25 mi/h. at what rate is the distance between the cars increasing 2 hourse later. What do i do. I need help some serious help with this one.

Homework Statement A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. How rapidly is the area enclosed by the ripple increasing at the end of 10 s?Homework Equations How do I even set up implicit differentiation? The Attempt at a...

If two resistors with resistances and are connected in parallel, as in the figure, then the total resistance R measured in ohms , is given by 1/R=1/R1+1/R2. If and are increasing at rates of .6 and .7 respectively, how fast is R changing when R1=80 and R2=100? so i take the derivative of...

A man starts walking north at 6 ft/s from a point P. Five minutes later, a woman starts walking south at 2 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 30 min after the woman starts walking? so i was ableto set up a right triangle using the x-y plane (y...

The volume V of a cone (V = 1/3*pi*r^2*h) is increasing at the rate of 28pi cubic units per second. At the instant when the radius r of the cone is 3 units, its volume is 12pi cubic units and the radius is increasing at 1/2 unit per second. At the instant when the radius of the cone is 3 units...

1. A rectangle has a constant area of 200 square meters and its length L is increasing at the rate of 4 meters per second. Find the width W at the instant the width is decreasing at the rate of 0.5 meters per second. 2. Know: dL/dt= 4 m/s, dW/dt=.5 m/s Want: W 3. LW=A. Then DL/dt...

Homework Statement A trough has an isosceles trapezoidal cross section as shown in the diagram. Water is draining from the trough at 0.2m^3/s At what rate is the surface rea of the water decreasing? Dimensions are: base width=0.4m, top width= 0.8m...

please help me with this assignment question. Q: gasoline is pumped from the tank of a tanker truck at a rate of 20L/s. if the tank is a cylinder 2.5 m in diameter and 15 m long, at what rate is the level of gasoline falling when the gasoline in the tank is 0.5m deep? express in exact answer...

What are some OTHER applications of algebra's related rates problems, beyond the typical examples given as textbook exercises? The textbooks usually emphasize rate-time-distance in which an agent moves at different rates between two situations; or two agents move each at a different rate than...

A water tank is in the shape of an inverted cone with depth 10 meters and top radius 8 meters. Water is flowing into the tank at 0.1 cubic meters/min but leaking out at a rate of 0.001h2 cubic meters/min, where h is the depth of the water in the tank in meters. Can the tank ever overflow...