heureka

(i) ratio among their surface areas is 4:1.

(ii) the ratio among their volumes is 8:1.

A Spherical water tank is of 7.7m radius. How many liters of water can it contain

I. The Volume of the Sphere in m^3:

$$\small{\text{ $ \begin{array}{rcl} V &=& \frac{4}{3}\pi r^3 \\\\ V &=&\frac{4}{3}\pi (7.7)^3\\\\ V &=&\frac{4}{3}\pi * 456.533\ m^3\\\\ V &=& 1912.32095856 \ m^3 \end{array} $ }}$$

II. The Volume of the Sphere in liters:

$$\small{\text{ $ 1\ m^3 = 1000\ liters $ }}$$

$$\small{\text{ $ V=1912.32095856\not{m^3} *\frac{1000\ liters}{1\ \not{m^3}}=1912320.95856\ l $ }}$$

18-3.8x=7.36-1.9x

$$\small{\text{ $ \begin{array}{rcll} 18 - 3.8x &=& 7.36-1.9x \\ 7.36-1.9x &=& 18-3.8x & \quad | \quad +3.8x\\ 3.8x -1.9x +7.36 &=& 18\\ 1.9x +7.36&=& 18 & \quad | \quad -7.36\\ 1.9x &=& 18-7.36 \\ 1.9x &=& 10.64 & \quad | \quad :1.9\\\\ x &=& \frac{10.64}{1.9}\\\\ x &=& 5.6 \\\\ \end{array} $ \\ }}$$

$$\boxed{x = 5.6}$$

g(x)=2^-x find x

$$\begin{array}{rcl} g(x) &=& 2^{-x} \quad | \quad \ln() \\\\ \ln{(g(x))} &=& -x\ln{(2)} \\\\ \boxed{x = - \frac{ \ln{(g(x))} } {\ln{(2)} }} \end{array}$$

tan A = 0.58384

$$A = 30.2780919731\ensurement{^{\circ}}$$

Thank you CPhill

Expand this binomial power (x^2+2/x)^4

What is the formula of this sequence?

1, 8, 27, 256, 3125, 46656, 823543

$$a_n=n^{ \left[ n+integerPart\left(\dfrac{2}{n}\right) \right]} \quad \text{ and } \quad n > 0$$

dumm + dumm = 2 * dumm

1298cosx=2770sinx+325.8

$$\begin{array}{rcl} 1298*cos(x) &=& 2770*sin(x)+325.8\\ \underbrace{1298}_{x_p}*\underbrace{cos(x)}_{n_x} -\underbrace{2770}_{y_p}*\underbrace{sin(x)}_{n_y} &=& \underbrace{325.8}_d \qquad \text{line: } \vec{p}*\vec{n}=d \quad \vec{p}=(x_p,y_p)=(1298,-2770) \\ \tan{(\alpha)} &=& \frac{y_p}{x_p} = -\frac{2770}{1298}\\\\ cos(x-\alpha) &=& \frac{d}{ \sqrt{x_p^2+y_p^2} } \\\\ sin(x-\alpha) &=& \frac{ \sqrt{x_p^2+y_p^2-d^2}}{\sqrt{x_p^2+y_p^2} }\\\\ tan(x-\alpha) &=& \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 )} \\\\ x_{1,2} -\alpha &=& tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& \alpha + tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& tan^{-1} { \left( \frac{y_p}{x_p} \right) } + tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& tan^{-1} { \left( \frac{-2770}{1298} \right) } + tan^{-1} { \left( \pm \sqrt{\frac{ (1298)^2+(-2770)^2 }{(325.8)^2} -1 \right) } }\\\\ x_{1,2} &=& ( -64.8925847874\ensurement{^{\circ}} \pm n*\pi) +(\pm 83.8861674476\ensurement{^{\circ}} \pm n*\pi)\\\\ x_1 &=& -64.8925847874\ensurement{^{\circ}} + 83.8861674476\ensurement{^{\circ}} \pm n*2\pi\\\\ x_2 &=& -64.8925847874\ensurement{^{\circ}} - 83.8861674476\ensurement{^{\circ}} \pm n*2\pi\\\\ x_1 &=& 18.9935826602\ensurement{^{\circ}} \pm n*2\pi\\\\ x_2 &=& -148.778752235\ensurement{^{\circ}} \pm n*2\pi \end{array}$$