Simplify. 8 · 3 · x 13x 24x 22x 48x

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = 4x and y = x2/4 . Find V by slicin

aliya0001 [1]

Answer:

Step-by-step explanation:

Consider the graphs of the $y = 4x$ and $y = \frac{x^{2} }{4}$ .

By equating the expressions, the intersection points of the graphs can be found and in this way delimit the area that will rotate around the Y axis.

$4x = \frac{x^{2} }{4} \\ x^{2} = 16x \\ x^{2} - 16x = 0 \\ x(x-16) = 0$ then $x=0$ o $x=16$ . Therefore the integration limits are:

$y = 4(0) = 0$ and $y = 4(16) = 64$

The inverse functions are given by:

$x = 2 \sqrt{y}$ and $x = \frac{y}{4}$ . Then

The volume of the solid of revolution is given by:

$\int\limits^{64}_ {0} \, [2\sqrt{y} - \frac{y}{4}]^{2} dy = \int\limits^{64}_ {0} \, [4y - y^{3/2} + \frac{y^{2}}{16} ]\ dy = [2y^{2} - \frac{2}{5}y^{5/2} + \frac{y^{3}}{48} ]\limits^{64}_ {0} = 546.133 u^{2}$

6 0

3 years ago

Assuming x > 0, which of these expressions is equivalent to 11 times the square root of 245 x to the third plus 9 times the s

ehidna [41]

The answer is 104 x times the square root of 5 x

11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third is:
 $11 \sqrt{245 x^{3} } +9 \sqrt{45 x^{3} } =11 \sqrt{245} *\sqrt{ x^{3} } +9 \sqrt{45} *\sqrt{ x^{3} }= \\ \\ =11 \sqrt{5*49} * \sqrt{ x^{2} *x} +9 \sqrt{5*9} * \sqrt{ x^{2} *x}= \\ \\ =11* \sqrt{5} * \sqrt{49} * \sqrt{ x^{2}} * \sqrt{x} +9* \sqrt{5} * \sqrt{9} * \sqrt{ x^{2} }* \sqrt{x} = \\ \\ 
=11* \sqrt{5} *7*x* \sqrt{x} +9* \sqrt{5} *3*x* \sqrt{x} = \\ \\ 
=77x* \sqrt{5*x} +27x* \sqrt{5*x} = \\ \\ 
=77x \sqrt{5x} +27x \sqrt{5x} = \\ \\ 
=104x \sqrt{5x}$

4 0

2 years ago

Read 2 more answers

Please answer the questions in my profile. There's plenty of points there

Shtirlitz [24]

Answer:

ok

Step-by-step explanation:

3 0

3 years ago

at noon on jan 7, the temperature in buffalo ny was 1 degree below of?. the temp in pittsbug, p at the same time was 10 degrees

Bumek [7]