To explain: How to approximate to force against the end of the tank by the Riemann sum.
![Check Mark](/static/check-mark.png)
Answer to Problem 13E
The answer is:
Explanation of Solution
Given information:
The vertical end of the tank contained water weight
The figure is:
Calculation:
Let's first review the equation for a fluid force in a constant-depth surface in order to determine the force acting against the end of the tank.
Where,
Let's partition the height of the tank into k parts in order to approximate the force using the Riemann sum. The semicircle shape of the tank suggests that it has a radius of
Where,
Now, The Riemann sum formula for the force is given below.
To generate the force approximation, substitute the value from the graph into equation
To find: The force as an integral.
![Check Mark](/static/check-mark.png)
Answer to Problem 13E
The answer:
Explanation of Solution
Given information:
The vertical end of the tank contained water weight
The figure is:
Calculation:
Have a look at the graph above. The y-axis of the graph is symmetric, as can be seen. multiply by two and integrate the right side using the same strip. Put the integral together,
Now let,
New boundaries of
Upper boundary:
Lower boundary:
Put everything to the integration:
Now evaluate the integral:
Therefore, the required force as an integral is
Chapter 7 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below. Let g(x) = √ƒƒ(t) dt . 0 3 2 -2 2 4 5 6 7 8 9 10 11 12 13 14 15 1. g(0) = 2. g(2) = 3. g(4) = 4. g(6) = 5. g'(3) = 6. g'(13)=arrow_forwardThe expression 3 | (3+1/+1) of the following integrals? A Ов E + + + + 18 3+1+1 3++1 3++1 (A) √2×14 dx x+1 (C) 1½-½√ √ ² ( 14 ) d x (B) √31dx (D) So 3+x -dx is a Riemann sum approximation of which 5 (E) 1½√√3dx 2x+1arrow_forward2. Suppose the population of Wakanda t years after 2000 is given by the equation f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000 people? Show all your work, round your answer to two decimal places, and include units. (4 points)arrow_forward
- 3. Solve the equation, give the answer exactly (no calculator approximations), and show all your work. (4 points) log5 2x = 3arrow_forwardLet I = f(x) dx, where f is the function whose graph is shown. 4 2 y f X 1 2 3 4 (a) Use the graph to find L2, R2 and M2. R₂ M2 = = = (b) Are these underestimates or overestimates of I? O 42 is an underestimate. O 42 is an overestimate. ◇ R2 is an underestimate. OR2 is an overestimate. OM2 is an underestimate. ○ M2 is an overestimate. (c) Use the graph to find T2. T₂ =arrow_forwardVector u has a magnitude of 23 and vector v has a magnitude of 83. The angle between the two vectors is 126 degrees.a) Draw a fully-labelled vector diagram showing the two vectors and the resultant vector when they are added together.b) Find the magnitude of the resultant vector.c) Find the direction of the resultant vector relative to vector u. Solding by finding the x and y of the vectors and addingarrow_forward
- 3) If a is a positive number, what is the value of the following double integral? 2a Love Lv 2ay-y² .x2 + y2 dadyarrow_forward16. Solve each of the following equations for x. (a) 42x+1 = 64 (b) 27-3815 (c) 92. 27² = 3-1 (d) log x + log(x - 21) = 2 (e) 3 = 14 (f) 2x+1 = 51-2xarrow_forward11. Find the composition fog and gof for the following functions. 2 (a) f(x) = 2x+5, g(x) = x² 2 (b) f(x) = x²+x, g(x) = √√x 1 (c) f(x) = -1/2) 9 9(x) = х = - Xarrow_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
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)