The sides of a cube are increasing at a rate of 1cm/s. How fast is the diagonal of the cube changing when the side length is 1cm?

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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Q: Car A leaves a parking lot at 9 am and travels eastward at the rate of 60 kph. Another vehicle, car…

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Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that  The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: It would be best to express length, width, and area as functions of time. I’ll set x = width, y =…

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

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Q: A screen saver displays 3 cm x 5 cm and then expands it in such a way that the length of the longer…

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

A: Let the length be: l Let the width be: w

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: A ship moving 8 mph sails north for 30 minutes then turns east. If a searchlight at the point of…

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Q: the

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Q: If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast (in…

A: We will find the rate of increase of side of cube.

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: We have to find the area of rectangle increasing

Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

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Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: The radius of the circle is increasing at a rate of 3 meters per minute and the sides of the square…

A: Since the circle is enclosed inside the square, the area between the circle and the square will be…

Q: Two people start from the same point. One walks east at 2 km/h and the other walks northeast at 3…

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Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

Q: The length of a rectangle is increasing at a rate of 5 meters per hour and the width is decreasing…

A: The length of a rectangle is 11 meters and the width is 20 meters. The length is increasing at a…

Q: wo cars start moving from the same point. One travels south at 16 mi/h and the other travels west at…

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Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: A 3-m long steel pipe has its upper end leaning against a vertical wall and the  lower end on a…

A: Given that: Length of steel pipe=3mLower end moves away from the wall at a speed = 2cm/s

Q: The length of a rectangle is increasing at the rate of 2 feet per second, while the width is…

A: Let length = x feet and width = y feet  Given that dx/dt= 2 and dy/dt= 1

Q: The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of…

A: The length of a rectangle is increasing at a rate, dldt = 4 cm/s The width of a rectangle is…

Q: A man 2 m tall walks toward a lamppost on level ground at a rate of 0.5 m/s. If the lamp is 5 m high…

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

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Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

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Q: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline…

A: Given a lighthouse which is located on a small island 3 km away from the nearest point P

Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline…

A: Let y be the distance of lighthouse from nearest point on the shoreline and at time t, the beam…

Q: Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west…

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

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Q: Sand is accumulating in a conical pile with a radius that is always 3 times its height. If the sand…

A: Given: A conical pile with radius 3 times its height. r=3h Rate of change of velocity of sand…

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

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Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

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Q: The volume of a cube is increasing at the rate of 1200 cm3/min at the instant its edges are 20 cm…

A: Let the length of the sides of the cube = xAnd the volume of the cube = V = x^3

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface…

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

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Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline…

A:

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

A:

Q: A man, running 3 meters per second in an open field, runs east for 30 seconds, then turns north.  If…

A: Since the man ran 3m/s east for 90 sec so he is 90 m from the searchlight. Consider the diagram…

Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

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Q: A rectangle’s length is growing at 3 inches per second, while its width is shrinking at 5 inches per…

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Q: Each side of a square is increasing at a constant rate of 4 centimeters per second. At what rate is…

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Q: A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12 feet above…

A: dx/dt​=4.  given.    Distance of tip= y+x…

Q: Two people start from the same point. One walks east at 3mi/h and the other walks northeast at…

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Q: Ship A is 70 km west of ship B and is sailing south at the rate of 25 kph. Ship B is sailing north…

A: At t = 0 { initial position } , distance between ships.Let the distance between ship A and ship B be…

Q: A 80 foot ladder leaning against a wall is being pushed so that the bottom of the ladder is sliding…

A: Here dydt=6feet/secondx=48 feety=64feet

Q: A 22-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Leader is leaning against wall at AC=22 ft. Distance of the ladder from the wall is x=15 ft. Let the…