Answered: At what rate is the diagonal of a cube…

At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 12.6 cm/s? (Use decimal notation. Give your answer to three decimal places.) Rate is cm/s

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section: Chapter Questions

Problem 21T: A basketball has a volume of about 455.9 cubic inches. Find the radius of the basketball (accurate...

See similar textbooks

Related questions

Q: If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in…

Q: At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 9.9 cm/s?…

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

Q: At a certain instant the dimensions of a rectangle are 8 and 12 feet, and they are increasing at the…

A: At a certain instant the dimensions of a rectangle are: Length L=8 feetWidth W=12 feet

Q: The volume of a cube is increasing at a rate of 64 in/sec. At what rate is the length of each edge…

Q: The lengths of the edges of a cube are increasing at a rate of 1 ft/min. At what rate is the surface…

Q: If the length of the edge of a cube is increasing at a rate of 3cm/s, how fast is the volume of the…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: The volume of a cube is increasing at a rate of 60 in/sec. At what rate is the length of each edge…

A: The objective is to find the rate at which the length of each edge of the cube is changing when the…

Q: 3. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a…

A: As per our guideline we are supposed to be answer only one question you can repost other question in…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

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

Q: The lengths of the edges of a cube are increasing at a rate of 9 ft/min. At what rate is the surface…

A: Total surface area of cube S = 6x2 Where x is length of the side of cube. we have given x = 19 ft.…

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…

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

Q: At noon Person A is 15 km east of person b. person A is walking west at 3km/h, and person b is…

A: initially A and B apart 15 km apart that person A moves towards west at rate (da/dt) = 3 km/hr…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in…

Q: If the volume of a different sphere is increasing at a rate of 24 cubic inches per minutes and the…

Q: pherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At…

A: The radius of the balloon decreases at the rate of =15 cm/min let radius of balloon =r then…

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

A: (a)Given:

Q: A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm…

Q: The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

Q: 5. A trough is 6m long and its ends have the shape of isosceles triangles that are 1m across at the…

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

Q: At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 4.6 cm/s?…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

Q: At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 7.3 cm/s?…

A: As we know that; The diagonal length of the cube is: L=3a Where a is the edge of the cube. And The…

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

Q: A ladder 15 feet long leans against a vertical wall. If the bottom of the ladder is pulled away from…

A: According to Pythagorean theorem , square of the hypotenuse side is equal to sum of the square of…

Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Related rates of changes – The related rate of change is finding the rate of change…

Q: If the base h of a triangle is increasing at a rate of 3 inches per minute while its height h is…

A: Area of a triangle of base b and height h is given as, A=12bh The derivative of area with respect to…

Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

Q: Two cars start moving from the same point. One travelssouth at 60 mih and the other travels west at…

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Given data: The length of the trough is L=12 ft. The side of the isosceles triangle is b=2 ft. The…

Q: 1)A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the ground.…

A: ----------------------------------------------------------------------------------------------------…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: Given,Surface area is decreasing at rate = 3 cm2 per minDiameter of the snowball (d) = 11 cm

Q: A hypothetical square grows at a rate of 8 m^2/min. How fast are the diagonals of the square…

Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate (in cm2/s) is the area of the…

Q: paper cup has the same shape of a cone with the height of 8cm and a radius 3cm (at the top). If…

Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Given Volume of cube increasing at a rate of 68 in3/ secTo the rate of change of length of each edge…

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

Q: The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: Let the volume of the water in the trough at time be V. The rate of change of V is,

Q: A boat is pulled toward a pier by means of a taut cable. If the boat is 20 ft below the level of the…

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: The original 24 m edge length x of a cube decreases at the rate of 4 m/min. a. When x = 3 m, at what…

A: Given query is to find rate of change of surface are and volume when rate of chnage edge length is…

Q: How fast is the surface area of a cu

A: Given that : Edge of a cube = 30 cm Th edge changing at the rate of 3 mm per second.

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at…

A: Let V be the volume of the water inside the trough and h be the height of the water inside the…

Q: Consider the given isosceles triangle of base 10 inches and side lengths x inches. If is increasing…

Question

At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 12.6 cm/s?
(Use decimal notation. Give your answer to three decimal places.)
Rate is
cm/s

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A basketball has a volume of about 455.9 cubic inches. Find the radius of the basketball (accurate to three decimal places).
The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?
Compute the number of cubic centimeters of iron required for the cast-iron plate shown. The plate is 3.50 centimeters thick. Round the answer to the nearest cubic centimeter.