Mathematics, 21.06.2019 14:00 Cheyenneross366
Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis the volume of the solid is: (type an exact answer cubic units)
Answers: 1
![\bf \stackrel{\textit{top, f(x)}}{4\sqrt{x}}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{farthest radius}}{4\sqrt{x}-0\implies 4\sqrt{x}} \\\\\\ \stackrel{\textit{top, f(x)}}{x}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{closest radius}}{x-0\implies x} \\\\[-0.35em] ~\dotfill\\\\ 4\sqrt{x}=x\implies \stackrel{\textit{squaring both sides}}{16x=x^2\implies }16x-x^2=0](/tpl/images/0000/4491/49bd6.png)
![\bf x(16-x)=0\implies x= \begin{cases} 0\\ 16 \end{cases}\qquad \qquad \impliedby \textit{these are the bounds} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int\limits_{0}^{16}~\pi [(4\sqrt{x})^2-(x)^2]dx\implies \pi \int\limits_{0}^{16}[16x-x^2]dx\implies \pi \int\limits_{0}^{16}16x~~-~~\pi \int\limits_{0}^{16}x^2](/tpl/images/0000/4491/1f364.png)
![\bf \pi \left. 16\cdot \cfrac{x^2}{2} \right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16}\implies \left. \pi 8x^2 \cfrac{}{}\right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16} \\\\\\ \left( \pi [2048]-\pi [0] \right)-\left(\left[ \cfrac{4096\pi }{3} \right]-[0] \right)\implies 2048\pi -\cfrac{4096\pi }{3} \implies \cfrac{2048\pi }{3}](/tpl/images/0000/4491/13f80.png)
Another question on Mathematics
Mathematics, 21.06.2019 13:20
Given f(x) = 10x + 4 and g(x) = 3x - 8, what is f(x) + g(x) ? - 7x - 4 - 13x + 4 - 7x + 4 - 13x - 4
Answers: 2
Mathematics, 21.06.2019 19:40
What is the range of the function? f(x)=-2|x+1|? a. all real numbers. b. all real numbers less than or equal to 0. c. all real numbers less than or equal to 1. d. all real numbers greater than or equal to 1
Answers: 2
Mathematics, 21.06.2019 20:30
The interior angles formed by the side of a hexagon have measures of them up to 720° what is the measure of angle a
Answers: 2
Mathematics, 22.06.2019 00:00
Charlie is at an amusement park that has 18 different rides. each ride costs $1.75. the function c(r) = 1.75r represents the total amount of money that charlie will spend if he goes on r rides, but he never goes on the same one more than once. what domain and range are reasonable for the function?
Answers: 3
You know the right answer?
Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about...
Questions
Mathematics, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Social Studies, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Biology, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Social Studies, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
Mathematics, 10.12.2020 01:00
