heureka

Exponentialgleichungen, Lösungsweg

\(\begin{array}{|rcll|} \hline 8\cdot 2^{x^2-2x} &=& 8 \quad & |\quad :8 \\ 2^{x^2-2x} &=& 1 \quad & |\quad 2^0 = 1 \\ 2^{x^2-2x} &=& 2^0 \\ x^2-2x &=& 0 \\ x(x-2) &=& 0 \\\\ \mathbf{ x_1 }&\mathbf{=}& \mathbf{0} \\\\ x_2 - 2 &=& 0 \\ \mathbf{ x_2 }&\mathbf{=}& \mathbf{2} \\ \hline \end{array}\)

How can I divide 10^9.7 to 1000 and have the result as 10^x format?

\(\begin{array}{|rcll|} \hline \dfrac{10^{9.7}}{1000} &=& 10^x \\\\ \dfrac{10^{9.7}}{10^3} &=& 10^x \\\\ 10^{9.7-3} &=& 10^x \\\\ 10^{6.7} &=& 10^x \\\\ \mathbf{ 6.7 } & \mathbf{=} & \mathbf{ x } \\ \hline \end{array}\)

how do you find the angle after doing dot product?

Formula:

\(\begin{array}{|rcll|} \hline \vec{a}\cdot \vec{b} &=& a\cdot b \cdot \cos(\varphi) \quad & | \quad |\vec{a}| = a \qquad |\vec{b}| = b \\ \cos(\varphi) &=& \dfrac{ \vec{a}\cdot \vec{b} }{a\cdot b} \\ \hline \end{array} \)

Hi Alan,

that's great, thanks

What does it mean, that cosine, sine, tangens etc, is hyperbolic?:)

Hummingbirds lay eggs that are nearly spherical and about 1 centimeter in diameter.

Find the volume of an egg.

The volume enclosed by a sphere is given by the formula:
( Let d = diameter )

\(\begin{array}{|rcll|} \hline \frac16 \pi d^3 \\ \hline \end{array}\)

\(\begin{array}{rcll} V &=& \frac16 \pi d^3 \quad & | \quad d=1\ \text{cm} \\ V &=& \frac{1}6 \pi 1^3\ \text{cm}^3 \\ V &=& \frac{\pi}6 \ \text{cm}^3 \\ V &=& 0.52359877560 \ \text{cm}^3 \\ \end{array} \)

(0.0167 cm^-1)^-1

\(\begin{array}{|rcll|} \hline && (~0.0167\ \text{cm}^{-1} ~)^{-1} \\ &=& (~0.0167^1\cdot \ \text{cm}^{-1} ~)^{-1} \\ &=& (0.0167^1)^{-1}\cdot \ (\text{cm}^{-1})^{-1} \\ &=& 0.0167^{1\cdot(-1)} \cdot \ \text{cm}^{(-1)\cdot(-1)}\\ &=& 0.0167^{-1} \cdot \ \text{cm}^{1}\\ &=& 0.0167^{-1} \cdot \ \text{cm} \\ &=& \frac{1}{0.0167} \cdot \ \text{cm} \\ &=& 59.8802395210\ \text{cm} \\ \hline \end{array} \)

What is 2/3 x 15

\(15\cdot \frac{2}{3} \\ = \frac{3\cdot 5\cdot 2 }{3} \\ = 5\cdot 2 \\ = 10\)

1/3 of 18

\(18\cdot \frac{1}{3} \\ = \frac{3\cdot 6 }{3} \\ = 6\)

(x-4)^2+8*(x-2)

\(\begin{array}{|rcll|} \hline && (x-4)^2+8\cdot (x-2) \\ &=& x^2-8x+16 +8x-16 \\ &=& x^2 \\ \hline \end{array}\)