82 Answered Questions for the topic Related Rates

#### Related rates are confusing. Can someone please explain how to do this problem. should I be using the formula for a right triangle?

The hypotenuse of a right triangle is a fixed length but the lengths of the other 2 sides x and y vary with time. How fast is y changing when dx/dt=4 and x=20 if the length of the hypotenuse is...
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01/02/22

#### Related Rates: Ladder Problem

A ladder 3 meters long leans against the wall of a building. The top slides down at a rate of 0.25 m/sec. How fast is the angle between the ladder and the ground decreasing when the angle is 30°?

Related Rates Calculus

12/15/21

#### A small stone is dropped into a still pool, creating a circular ripple that moves outward from the point of impact at a constant rate

How is the area enclosed by the ripple changing after 2 s if the circumference of the ripple is changing at a rate of 2π m/s at this instant?

#### Related Rates question

road perpendicular to a highway leads to a farmhouse located 5 mile away. An automobile traveling on the highway passes through this intersection at a speed of 50mph.How fast is the distance...
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#### Related Rates problem

The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius. The volume of the rind is growing at the...
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#### [Related Rates] A ladder 20 feet long leans up against a house. The bottom of the ladder starts to slip away from the house at 0.17 feet per second.

A ladder 20 feet long leans up against a house. The bottom of the ladder starts to slip away from the house at 0.17 feet per second. How fast is the tip of the ladder along the side of the house...
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#### [Related Rates] Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute.

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is...
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#### Related Rates: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 square centimeters/minute.

The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 square centimeters/minute. At what rate is the base of the...
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Related Rates Calculus

10/19/21

#### If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 11 cm

#### A spherical balloon is being inflated at a rate of 8pi cm^3/s At what rate is the surface area of the balloon increasing at the instant that the radius of the balloon is 1cm?

A spherical balloon is being inflated at a rate of 8pi cm^3/s At what rate is the surface area of the balloon increasing at the instant that the radius of the balloon is 1cm?

05/06/21

#### Water is draining from an inverted conical tank that has a height of 12 metres and diameter of 8 metres.

a) As the water is draining out, the depth of the water, h, in the conical tank is decreasing at a rate of(h – 12) m/minute. At what rate is the volume of the water in the conical tank changing...
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03/01/21

#### How do you solve this pesky related rates problem? (Daily Supply)

Hi. I am stuck trying to solve this problem:In a certain market, x thousand crates of apples are supplied daily. Each crate costs p dollars, and the supply equation ispx - 20p - 3x + 105 = 0.If the...
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Related Rates Calculus

02/09/21

#### Kanto market is supplied n thousands of crates of dalandan daily when it is sold at p pesos per crate and the supply equation is...

pn - 3p - 100n - 100 = 0If the daily supply is decreasing by 250 crates per day, at what rate is the price changing when the daily supply is 5000 crates?

Related Rates Calculus

02/06/21

#### [CALCULUS RELATED RATES] A supplier produces n thousand boxes of orange daily when it is sold at p dollars per box. Suppose the relationship between n and p is (continuation in description)

A supplier produces n thousand boxes of orange daily when it is sold at p dollars per box. Suppose the relationship between n and p is; pn-3p-100n-100=0If the daily supply is decreasing by 250...
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02/05/21

#### Calculus problem for my youngest son!

A store is given n thousands of crates of lemons daily when it is sold at c pesos per crate and the supply equation iscn - 3c - 100n - 100 = 0If the day by day supply is diminishing by 250 crates...
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Related Rates Calculus

07/30/20

#### the volume of spherical tumor is observed to be decreasing at a rate of 2 cubic centimeters per month when the radius is 5 centimeters. at what rate is the radius of the tumor decreasing?

the volume of a sphere is this formula(V=4/3pir^3)

#### Related rates problem, Find the velocity of the top of the ladder

A 20 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time 𝑡=0 and slides away from the wall at a rate of 1ft/sec. Find the velocity of the top of the ladder at...
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02/13/20

#### calculus word problem - related rates

two people leave the same point at the same time. one walks due east at a rate of 3 miles per hour. the other one walks due north at 2 miles per hour. find the rate at which the distance between...
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01/30/20

#### Related Rates with shadows

On a morning of a day when the sun will pass directly overhead, the shadow of a 72-ft building on level ground is 30 ft long, as shown in the figure. At the moment in question, the angle theta...
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Related Rates Calculus

12/08/19

#### A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.

At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?
At what rate is the tip of the shadow moving away from the person when the person is 25 ft...
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12/04/19

#### Optimization and Related Rates problem

This question uses the inverse-square law, which states that the light intensity experienced at a distance x from a light source is proportional to the luminosity of the source times x^(-2).It is...
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12/04/19

#### Optimization and Related Rates problem

This question uses the inverse-square law, which states that the light intensity experienced at a distance x from a light source is proportional to the luminosity of the source times x^(-2).It is...
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Related Rates Calculus

11/12/19

#### How to find rate of change of an area between a circle and square

a circle is inside a square. At a particular time, the radius of the circle is decreasing at a rate of 3 m/min and the sides of the square are decreasing at a rate of 2 m/min. when the radius is 3...
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