
Concept explainers
(a)
To find:The formula for height
(a)

Answer to Problem 2E
The formula of theheight
Explanation of Solution
Given information: Theheight of an equilateral triangle is
Formulaused:Pythagoras theorem - In a right angle triangle, the sum of its square of its base and height is equal to the square of the hypotenuse.
Calculation:
The height of an equilateral triangle is the perpendicular line drawn from a point to its base. So, the height is the median of the triangle.
The length of the base is
Substitute
Therefore, the formula of the height
(b)
To find:The height of an equilateral triangle with side length
(b)

Answer to Problem 2E
The height of an equilateral triangle with side length
Explanation of Solution
Given information:The length of the side of an equilateral triangle is
Calculation:
As calculated in part(a), the formula for height of an equilateral triangle as a function of its side length
Substitute
Therefore, the height of an equilateral triangle with side length
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
A First Course in Probability (10th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Basic Business Statistics, Student Value Edition
Calculus: Early Transcendentals (2nd Edition)
Elementary Statistics: Picturing the World (7th Edition)
University Calculus: Early Transcendentals (4th Edition)
- Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 3 and 7 each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where I and y are the demand functions and 0 < x,y. Then as x = y = the factory can attain the maximum profit,arrow_forwardEvaluate the following integrals, showing all your workingarrow_forwardConsider the function f(x) = 2x³-4x2-x+1. (a) Without doing a sketch, show that the cubic equation has at least one solution on the interval [0,1]. Use a theorem discussed in lectures, or see Section 1.8 of Calculus (7th ed) by Stewart. Ensure that the conditions of the theorem are satisfied (include this in your solution) (b) Now, by sketching the cubic (by hand or by computer), you should see that there is, in fact, exactly one zero in the interval [0,1]. Use Newton's method to find this zero accurate to 3 decimal places. You should include a sketch of the cubic, Newton's iteration formula, and the list of iterates. [Use a computer if possible, e.g., a spreadsheet or MatLab.]arrow_forward
- A box with a square base and open top must have a volume of 13,500 cm³. Find the dimensions that minimise the amount of material used. Ensure you show your working to demonstrate that it is a minimum.arrow_forwardConsider the equation, f(x) = x*. (a) Using the trapezoidal method with 3 columns, estimate the value of the integral f² f(x)dx. (b) Using the trapezoidal method with 10 columns, estimate the value of the integral f² f(x)dx. You many need software to help you do this (e.g. MATLAB, Excel, Google sheets). (c) Use software to accurately calculate the integral (e.g. Wolfram alpha, Matlab). Using this answer, comment on the answers you found in parts a) and b).arrow_forwardUsing the first-principles definition of differentiation, find the derivative of f(x) = = 2x²arrow_forward
- Evaluate the following integrals, showing all your workingarrow_forwardDifferentiate the following functionarrow_forwardQuestion 1. (10 points) A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by dV = 1.45V(2 In(V+1)). dt (a) (4 pts) Find all the equilibria and determine their stability using the stability condition. (b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable. (c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain in biological terms what happens to the size of each of these tumours at time progresses.arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





