sputneyoh

2021-12-18

Locate the centroid x of the area.

usaho4w

Beginner2021-12-19Added 39 answers

Area

$dA=ydx$

$dA=4-(4-\frac{{x}^{2}}{16}dx)$

$dA=\frac{{x}^{2}}{16}dx$

$A={\int}_{0}^{8}4-(4-\frac{{x}^{2}}{16}dx)$

$={\left(\frac{{x}^{3}}{48}\right)}_{0}^{8}$

$=10.667\text{}{m}^{2}$

Cleveland Walters

Beginner2021-12-20Added 40 answers

Centroid

$\stackrel{\u2015}{x}=\frac{\int \stackrel{\u2015}{x}dA}{\int dA}$

$=\frac{{\int}_{0}^{8}x\left(\frac{{x}^{3}}{16}dx\right)}{10.667}$

$=\frac{{\left(\frac{{x}^{4}}{64}\right)}_{0}^{8}}{10.667}$

$=\frac{64}{10.667}$

$\stackrel{\u2015}{x}=6\text{}m$

$\stackrel{\u2015}{y}=\frac{\int \stackrel{\u2015}{x}dA}{\int dA}$

$={\int}_{0}^{8}\frac{\frac{y}{2}\left(\frac{{x}^{2}}{16}\right)dx}{10.667}$

$={\int}_{0}^{8}\frac{\frac{1}{2}[4+(4-\frac{{x}^{2}}{16})]\left(\frac{{x}^{2}}{16}\right)dx}{10.667}$

$={\int}_{0}^{8}\frac{\left(\frac{128-{x}^{2}}{16}\right)\frac{{x}^{2}}{16}dx}{21.334}$

$=\frac{{\int}_{0}^{8}(12{x}^{2}-{x}^{4})dx}{256\times 21.334}$

$=\frac{{(\frac{128{x}^{3}}{3}-\frac{{x}^{5}}{5})}_{0}^{8}}{256\times 21.334}$

$=\frac{15291.733}{256\times 21.334}$

$\stackrel{\u2015}{y}=2.8\text{}m$

nick1337

Expert2021-12-28Added 699 answers

why is

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

How to expand and simplify $2(3x+4)-3(4x-5)$?

Find an equation equivalent to ${x}^{2}-{y}^{2}=4$ in polar coordinates.

How to graph $r=5\mathrm{sin}\theta$?

How to find the length of a curve in calculus?

When two straight lines are parallel their slopes are equal.

A)True;

B)FalseIntegration of 1/sinx-sin2x dx

Converting percentage into a decimal. $8.5\%$

Arrange the following in the correct order of increasing density.

Air

Oil

Water

BrickWhat is the exact length of the spiraling polar curve $r=5{e}^{2\theta}$ from 0 to $2\pi$?

What is $\frac{\sqrt{7}}{\sqrt{11}}$ in simplest radical form?

What is the slope of the tangent line of $r=-2\mathrm{sin}\left(3\theta \right)-12\mathrm{cos}\left(\frac{\theta}{2}\right)$ at $\theta =\frac{-\pi}{3}$?

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Use the summation formulas to rewrite the expression $\Sigma \frac{2i+1}{{n}^{2}}$ as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000.

How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]?