A population of insects increases at a rate 290+10t+0.3t^2 insects per day (t in days). Find the insects population after 3 days assuming there are 30 insects at t=0.

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A: Given,         A 13-foot ladder leaning against a wall is pulled away from the wall at a constant…

Q: two legs of a right triangle are reach 70 cm. if one leg grows at the rate of 5cm/min and the other…

A: The solution is given below in the next step:

Q: A cell culture contains 7 thousand cells, and is 0.12t thousand cells growing at a rate of r(t) per…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

A:

Q: A 16-foot ladder rests against a vertical wall. The bottom of the ladder begins sliding at a rate of…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Volume of a sphere of radius r isV=43πr3

Q: A helicopter is rising vertically from the ground at a constant rate of 6 m/s. When it is 75 m off…

A: Let x be the vertical distance travelled by helicopter and y be the horizontal distance travelled by…

Q: tion, what is the longest time within whic at the predator will have to spend more t

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Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A:

Q: volume

A:

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at a…

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Q: Initially 50 pounds of salt is dissolved in a tank holding 300 gallons of water. A brine solution is…

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Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given: Rate of increase in length of a rectangle, dldt=5 cm/s Rate of decrease in width of a…

Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: Oil from an uncapped well is radiating outward in the form of a circular film on the surface of the…

A: Let r and A be the radius and area of the circle respectively at time t. The radius of the circle is…

Q: A ball is thrown vertically upward with a speed of 15 m/s. Determine the maximum height and the time…

A: Find maximum height and time to reach that's height

Q: A cylindrical tank 24 inches in radius and 2 meters tall initially contains 100 gal of cane juice. A…

A: Please check step 2 for solution.

Q: At a certain instant, the radius of a right circular cylinder is 6 inches and is increasing at the…

A: The volume of a right circular cylinder is given by V=πr2h where r is the radius of the circular…

Q: 9) Sand falls from an overhead bin, accumulating in a conical pile with a radius that is always…

A:

Q: A cell culture contains 12 thousand cells, and is growing at a rate of r(t) = 2e0.17t thousand cells…

A:

Q: data point at x1= 1, x2=4, x3=6 and x4=5 were used to estimate ln 2 with a third-order newtons…

A: To obtain the required polynomial equation, use the following Newton's divided difference…

Q: A hollow cone of base radius 20 cm and height 10 cm is held with its vertex downwards. Oil is poured…

A: BC and BV are the base  radius  and height of the cone        BC=20        BV=10…

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

A: Rate of change

Q: A patient's blood is traveling at a rate of 16 mL/sec while conveying a medicine into the liver and…

A: so, initially, liver is full at t = 0, but has no medicine,  medicine rich blood comes in, mixes…

Q: A container contains 80 liters of pure water. A brine solution with 2 kg/L of salt enter at 2 L/min,…

A:

Q: The average annual increment in the horn length (in centimeters) of bighorn rams born in recent…

A:

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Let x be the length, y be the width and A be the area of the rectangle. Then we get, A = xy The rate…

Q: A rectangle's length is increasing at the rate of 5 inches/sec, its width at 2 inches/sec. At what…

A:

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given a rectangle whose length is increasing at rate of 5cm per second and width is decreasing at…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A: 1. givendrdt=0.1 cm/minr=8 cmdvdt=?volume of sphere (v)=43πr3diffrentiate with respect to…

Q: A truck moves along a straight road starting from rest with an acceleration 0.6 m/s. After 3…

A: Given that, A truck moves along a straight road starting from rest with an acceleration 0.6 m/s2.…

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

A:

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at…

A: Given :- The length of a rectangle is increasing at a rate of 5 cm per second and its width is…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is…

A:

Q: A piece of wire of length 12 cm was cut into two pieces. The first was folded to form an equilateral…

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Q: A particle is moving along the curve y=4sqrt(2x+3). As the particle passes through the point (3,12),…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A:

Q: A bacteria grows proportional to the square root of its current population. Starting at an initial…

A:

Q: A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with å rope…

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Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

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Q: A conical tank with the vertex down measures 10 meters in height and 9 meters in diameter of its…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cmminwhile the area of the triangle is…

A: Givendhdt=1cm/mindAdt=2cm2/minA=100cm2h=10cm

Q: A ladder 10 meters long leans against a vertical wall. The lower end of the ladder is pulled away…

A: Let x= distance of the lower end from the wall y= height of the top of the ladder Given that dx/dt=…

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.2 cm/min.…

A:

Q: A leaky 10kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope…

A:

Q: A leaky 10-kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope…

A:

Q: Give examples of basic integration using exponential rule

A: Give examples of basic integration using exponential rule Let us integrate an exponential function.…

Q: (a) Water flows from a storage tank at a rate of 900 – 6t liters per minute. Find the amount of…

A: This question is related to calculus . solve in step 2.

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.