![Arealbot](/avatars/42254.jpg)
Arealbot
11.02.2020 •
Mathematics
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. yequals=StartRoot sine Superscript negative 1 Baseline x EndRootsin−1x, yequals=StartRoot StartFraction pi Over 2 EndFraction EndRoot π 2, y equals StartRoot StartFraction pi Over 3 EndFraction EndRoot comma and nbspy= π 3, and xequals=0
Solved
Show answers
More tips
- H Health and Medicine How to Treat Styes: Causes, Symptoms, and Home Remedies...
- C Computers and Internet How to Learn to Type Fast?...
- F Food and Cooking Delight for Gourmets: How to Prepare Liver Pate...
- S Style and Beauty How to braid friendship bracelets?...
- H Health and Medicine Mercury Thermometer Danger: What to do when a thermometer breaks?...
- F Food and Cooking Which Calamari Salad is the Most Delicious?...
- S Society and Politics 10 Tips for Boosting Your Self-Esteem...
- F Food and Cooking The Most Delicious and Simple Fish in Batter Recipe...
- H Health and Medicine What is Autism? Understanding the Basics of This Neurodevelopmental Disorder...
- P Philosophy How to Develop Extrasensory Abilities?...
Answers on questions: Mathematics
- M Mathematics Two of the angles in a triangle measure 169 and 1. what is the measure of the third angle...
- M Mathematics In 15 words or fewer, describe what happens to the coordinates when a graph is stretched vertically....
- M Mathematics Pete is making decorations for a dinner party the instructions tell him to use 9 flowers for a medium sized decoration...
- M Mathematics Lois and clark own a company that sells wagons. the amount they pay each of their sales employees (in dollars) is given by the expression 12h+30w12h+30w where hh is the number...
- M Mathematics Simplify. write the expression using only postive exponents. m^-4*n^3...
- M Mathematics Write a function for p(x), the profit from selling x hats...
- M Mathematics If de = 37 cm and ef = 16 cm, then what are the possible lengths for df so that de,ef, and df can form a triangle? explain your reasoning....
- M Mathematics The perimeter of a regular octagon is 24a + 48 inches.(a) write an expression for the length of any one side of the octagon. the perimeter of a regular octagon is 18 feet.(b)what...
- M Mathematics Cody was 165cm y’all on the first day of school this year, which was 10% taller than he was on the first day of school last year. how tall was cody on the first day of school...
- M Mathematics Write your answer in simplest form. 11 2/16 - 8 3/16...
Ответ:
Volume = 1.535
Step-by-step explanation:
The region R is bounded by the equations:
y = √sin⁻¹x
y = √(π/2)
y = √(π/3)
x = 0
R is revolved around the x-axis so we will need f(y) for finding out the volume. We need to make x the subject of the equation and then replace it with f(y).
f(x) = √sin⁻¹x
y = √sin⁻¹x
Squaring both sides we get:
y² = sin⁻¹x
x = sin (y²)
f(y) = sin (y²)
Using the Shell Method to find the volume of the solid when R is revolved around the x-axis:
The limits a and b are the equations y = √(π/2) and y = √(π/3) which bound the region R. So, a = √(π/2) and b = √(π/3).
V = 2π![\int\limits^\sqrt{\frac{\pi }{2}}](/tpl/images/0506/2100/843a2.png)
sin (y²) dy
Integrating sin (y²) dy, we get:
-cos(y²)/2y
So,
V = 2π [-cos(y²)/2y] with limits √(π/2) and √(π/3)
V = 2π [(-cos(√(π/2) ²)/2*√(π/2)] - [(-cos(√(π/3) ²)/2*√(π/3)]
V = 2π [(-cos(π/2)/ 2√(π/2)) - ((-cos(π/3)/ 2√(π/3))]
V = 2π [ 0 - (-0.5/2.0466)]
V = 2π (0.2443)
V = 1.53499 ≅ 1.535
Ответ:
2) 24
Step-by-step explanation:
(-5/4)x-5= -35
(-5/4)x-5+5= -35+5
(-5/4)x= -30
-1.25x/-1.25= -30/-1.25
x=24