Answer 1 and 2 Solve the following. Show the step-by-step solution.1. Find the equation of the tangent line and normal line to the curve y = √x-3 andwhose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph.2. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is thesurface area increasing when the length of an edge is 12 cm? (V= e³ and SA = 6e²)3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if theradius of the tank is 4 ft, how fast is the surface rising? (Hint: V = πr²h)4. An object is moving along a horizontal line according to the position functions(t) = 2t³ - 21t² + 60t + 3, where t≥ 0.a. When is s increasing, when is it decreasing?b. When is v increasing, and when is it decreasing?c. Find the total distance traveled in the first 5 seconds of motion.

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Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = √x-3 and whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph.

Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and normal line to the curve y = √x-3 and whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time

Section: Chapter Questions

Problem 44A: Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN Seven brass...

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Question

Answer 1 and 2

Solve the following. Show the step-by-step solution.
1. Find the equation of the tangent line and normal line to the curve y = √x-3 and
whose normal line is parallel to the line 6x + 3y -4 = 0. Sketch the graph.
2. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the
surface area increasing when the length of an edge is 12 cm? (V= e³ and SA = 6e²)
3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the
radius of the tank is 4 ft, how fast is the surface rising? (Hint: V = πr²h)
4. An object is moving along a horizontal line according to the position function
s(t) = 2t³ - 21t² + 60t + 3, where t≥ 0.
a. When is s increasing, when is it decreasing?
b. When is v increasing, and when is it decreasing?
c. Find the total distance traveled in the first 5 seconds of motion.

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