11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is changing with respect to the height.

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: If the radius of a sphere is increasing at a constant rate of 2 cm/sec, then the volume 3 is…

A:

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A: Formula of volume V=43πr3 Given: Radius, r=8 mm drdt=-1mm/month

Q: 11. If a snowball melts so that its surface area decreases at a rate of 1 cm/min, find the rate at…

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Q: Suppose that a given moment, the radius of a right circular cylinder is 2 cm and increasing at a…

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Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

A:

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: 7. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

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Q: snowball melts so that its surface area decreases ata rate of 1cm^2/min, find the rate at which the…

A: Given query is to find the rate of chnage of diameter.

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

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Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

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Q: How do you solve?

A: Given, Side of square= x x(t)= 3t+1 Therefore, Area= (3t+1)*(3t+1) A(t)= 9t²+6t+1

Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at…

A:

Q: A vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Given: A drum of length : 5m The drum has a cross section of isosceles trapezoid with length of…

Q: If the rate of change in volume of a sphere is equal to its rate of change of its radius. What is…

A: if we let the radius of square = r unit then volume of the square =4/3 πr3 unit3

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Now in triangle ABC, by using Pythagorean theorem, we get

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

Q: 9. If the volume and radius of a sphere are functions of time,what is the relationship between the…

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Q: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

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Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

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Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height of the cylinder…

A: Given,         The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height…

Q: 14. If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at…

A: To find the rate

Q: A cone-shaped tank of water is leaking water at a constant rate of 2 m3/hour. If the base radius of…

A: Given that

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: here is a constant inflow of a liquid into a conical vessel 15 feet deep and 7.5 feet in diameter at…

A: The height of the conical vessel h = 15 feet.  Diameter of the lop d = 7.5 feet,  The radius of the…

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: Given: S the surface area of the cube, x the length of the cube and the length x of the cube…

Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

A:

Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…

A:

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: 4 mm/s when these three sides are 5cm, 4 cm sides x, y and z increase at 6 mm/s, 5 mm/s and Fig.…

A: we have to find rate of change of AC.

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

Q: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

Q: The volume V of a right circular cone of radius r and height h is given by V = Tr²h. Find a formula…

A: To find the instantaneous rate of change:

Q: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

A:

Q: 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm…

A: Given: 4) Question is wrong (Some values are missed) 5) dxdt=10 ft/sec, h=100 ft, and l=125 ft