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3 years ago

Which expression represents three minus the quotient of five divided by x?

Mathematics

1 answer:

STALIN [3.7K]3 years ago

5 0

Answer:

the correct answer is b) 3-5/x

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Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V b

Westkost [7]

Explanation:

Let $f(x) = \sqrt{25x}$ and $g(x) = \frac{x^2}{25}$ . The differential volume dV of the cylindrical shells is given by

$dV = 2\pi x[f(x) - g(x)]dx$

Integrating this expression, we get

$\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx$

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

$\sqrt{25x} = \dfrac{x^2}{25}$

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

$25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1$

$x^3 =(25)^3 \Rightarrow x = \pm25$

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

$\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx$

$\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx$

$\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}$

$\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2$

4 0

3 years ago

Let f ( x , y )=5 x and let C be the segment of the parabola y = 2 x squared joining O( 0 , 0 ) and P( 1 , 2 ). a. Find a parame

taurus [48]

a. We can parameterize $C$ by

$x=t$

$y=2t^2$

with $0\le t\le1$ . Then

$\displaystyle\int_C5x\,\mathrm dS=\int_0^15t\sqrt{1+16t^2}\,\mathrm dt=\dfrac5{48}(17^{3/2}-1)$

b. We can parameterize the opposite direction by instead setting

$x=1-t$

$y=2(1-t)^2$

with $0\le t\le 1$ . Then

$\displaystyle\int_C5x\,\mathrm dS=\int_0^15(1-t)\sqrt{1+16(1-t)^2}\,\mathrm dt=-\int_1^05u\sqrt{1+16u^2}\,\mathrm dt=\int_0^15u\sqrt{1+16u^2}\,\mathrm du$

which gives the same value as in part (a).

5 0

3 years ago

Find the solution(s) of the system of equations.

jasenka [17]

Dfyujb. Hgdgyyf hedge. 4+9-(/4)

4 0

3 years ago

Work out the values of a and b in the following identity

jeka57 [31]

Answer:

a = - 2 and b = - 3

Step-by-step explanation:

Distribute the parenthesis on the left side then compare like terms on both sides.

4(3x - 6) - 7(2x + b)

= 12x - 24 - 14x - 7b

= - 2x - 24 - 7b

Compare to right side ax - 3

For the 2 sides to be equal then

- 2x = ax ⇒ a = - 2

and

- 24 - 7b = - 3 ( add 24 to both sides )

- 7b = 21 ( divide both sides by - 7 )

b = - 3

7 0

4 years ago

Point O is the center of the circle in the diagram. What is m∠BCA ?

netineya [11]

The sum of angle around a point equal 360°
so (BOA) = 360-250=110°
and the sum of angle in the shape CAOB = 360°
so BCA = 360-(110+90+90)= 70°
THE ANSWER IS C.70°

7 0

4 years ago