Convert the following equations to its standard form and identify the vertex and focus. displaystyle{3}{y}^{2}+{8}{x}+{24}{y}+{40}={0}

To calculate: The value of expression ${\displaystyle y=4x^{\frac{1}{3}}}$ for x equal to 8

Determine whether the statement If ${\displaystyle D\ne 0\text{or}E\ne 0}$,
then the graph of ${\displaystyle y^2-x^2+Dx+Ey=0}$ is a hyperbolais true or false. If it is false, explain why or give an example that shows it is false.

How do you find the eccentricity, directrix, focus and classify the conic section ${\displaystyle r=\frac{14.4}{2-4.8\cos \theta }}$?

Graph the lines and conic sections ${\displaystyle r=\frac{8}{4+\sin \theta }}$

Write the following equation in standard form and sketch its graph
${\displaystyle 9x^2+72x-64y^2+128y+80=0}$

To simplify the given expression.

A conical surface (an empty ice-cream cone) with surface charge density ? has height h.Radius of the top is R.Find potential difference between vertex & center of the top.