ne length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing at a

Q: The length of a rectangle is increasing at a rate of 5 m/s. The width is increasing at a rate of 2…

A:

Q: A dirty lake was contaminated by a toxic substance. The lake has a volume of 1.2M liters of water…

A: Here first we form the differential equation for the amount of toxic substance at time t as follows…

Q: A box is partially filled with sand. The length of the box is 8 mm. The width of the box is 17 mm.…

A: Given: Length of box=8 mm Width of box=17 mm Volume of sand is decreasing at rate of 562 mm3/min.…

Q: 5) Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If…

A: Note: Rate of change of volume of conical pile is equal to rate of change of sand pouring from the…

Q: oil

A: We will find how much oil is left in the rank after 3 hours.

Q: The city of Anville is currently home to 17000 people, and the population has been growing at a…

A: Formula: A=P1+r100n where A= Population after n years P= Initial population r= Growth rate n= Time…

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: To find the distance.

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: We need to find rate of change of the base.

Q: A bacteria culture is known to grow at a rate proportional to the amount present. After two hours,…

A: Let dx/dt = the rate of growth of the bacteria  Let t = time (in hours) after start of culture  Let…

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: given: dA = 5 cm2/min dh = 1 cm/min A = 86 cm2 h = 11 cm   Equation for area of a triangle: A = .5 b…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

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Q: Suppose a forest starts with a deer population of 50 deer the population is increasing at a rate of…

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Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: Given- The altitude of  a triangle is increasing at a rate of 1 cm/min. and the area of the triangle…

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A:

Q: A rectangle initially has dimensions 4 cm by 7 cm. All sides begin increasing in length at a rate of…

A:

Q: Zakiya, a biologist is observing the growth pattern of a virus. she starts with 149 of the viruses…

A: Given : Initial Population  , P = 149 Growth Rate , r = 0.13 per hour

Q: a population of bacteria originates with 2500 bacteria. After a harmful substance is introduced into…

A: Initial population of bacteria= 2500 The rate of decline of the bacteria population= 10% Also,…

Q: a population of 30 bunnies is increasing at a rate of 40% per year. How many bunnies will be there…

A: In the given question we have to find the population of bunnies after 5 years.

Q: A population of cattle is increasing at a rate of 800 + 80 t per year, where t is measured in years.…

A: Growth of population is given by the eq. 800+80t. We have to determine the population increase in…

Q: 5. At 1:00 PM a ship traveling at 9 miles per hour sets sail N60°E. An hour later, a second ship…

A:

Q: A bacteria culture starts with 300 bacteria and grows at a rate proportional to its size. After 5…

A: " Since you have posted a question with multiple subpart, we will solve first three subpart for you.…

Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

A: First we formulate an area function in terms of  the base ( b) and altitude (h). Differentiate the…

Q: 21. The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Given:- The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the…

Q: A rectangle initially has dimensions 4 cm by 8 cm. All sides begin increasing in length at a rate of…

A: Given dimensions of rectangle  is 4 cm by 8cm. And sides of rectangle increasing in length at rate…

Q: 20. The population of a small town is 1600 and is increasing at a rate of 3% per year. What will the…

A:

Q: shrinking

A:

Q: 5. A ladder 25 feet long leans against a vertical wall. The bottom of the ladder slides away from…

A:

Q: The length of a rectangle is increasing at a rate of 4 meters per day and the width is decreasing at…

A:

Q: Bacteria in a certain culture increase at the rate proportional to the number umber? bacteria…

A: The rate of increase dNdt in number of bacteria is proportional to the number of bacteria present N…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Given data is : dhdt=+3cm/min and dAdt=+3cm2/min h=7cm , A=86cm2 where A is area of triangle, h is…

Q: The altitude of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A:

Q: solve the problem. A ladder is slipping down a vertical wall. if the ladder is 20 ft long and top of…

A: Use pythagorous theorem and differentiation to solve

Q: A box is partially filled with sand. The length of the box is 12 mm. The width of the box is 18 mm.…

A:

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: In this we are going to use formula for area of triangle and then differentiation of that. So I'm…

Q: b. One airplane is approaching an airport from the north at 206 km/hr. A second airplane approaches…

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Q: 5) A thin sheet of ice on a lake is in the shape of a circle. If the ice is melting such that the…

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Q: The population of a city is 50,000. The city grows continuously by 4% per year. this trend…

A: Given query is to find the rate of change after 11 years.

Q: (6) A person 2 meters tall walks directly away from a streetlight that is 8 meters above the ground.…

A: At first we draw the diagram  AC  is the street light, DE is the person. Let distance between…

Q: The radius of a sphere, initially zero, increases at rate 6 ft per seconds. Find how fast the volume…

A: By using differentation and integration and rate of change

Q: Zakiya, a biologist is observing the growth pattern of a virus. she starts with 140 of the viruses…

A:

Q: A.) A. Converting Doubling Time to Tripling Time. The number of bacteria in a colony increases at a…

A: To find the time it takes to triple the bacteria.

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Let height of altitude=h ,Base=b and Area=A  Given dh/dt=3cm/minutes And dA/dt=4cm2/minutes

Q: The area of a square is increasing at the constant rate of 16 sq. ft./min. When the perimeter of the…

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Q: 95. At a certain point on a heated plate, the greatest rate of temperature increase, 5°C per meter,…

A: (95) Let , f = f(x,y) be the temperature at any point. We know the greatest rate of temperature…

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

A:

Q: 2.) An underwater drone is being used to explore ancient ruins at the bottom of the ocean. begins at…

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Q: Part A. The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing…

A: Volume of sphere =(4/3)πr3   surface Area of sphere =4πr2

Q: 6) A cat is running straight toward a 8 foot tall brick wall at a rate of 4 feet per second.…

A:

Q: 3. A snowball is rolling down a hill, getting bigger as it goes. Assume the snowball remains a…

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Q: An assortment of 100 fish is put into a fish tank; the fish population grows at a continuous rate of…

A: