asinus

What is the value of 4^{10} * 8^{20} * 16^4?

Hello Guest!

\({\color{blue}4^{10} \cdot8^{20} \cdot 16^4}=2^{2\cdot 10}\cdot2^{3\cdot 20}\cdot 2^{4\cdot 4}=2^{20+60+16}\color{blue}=2^{96}\)

\(=79228162514264337593543950336\)  !

Trigonometric subtraction

Доброе утро русский друг!

\(cos\ (x)-sin\ (x)=\sqrt 2\ sin(\frac{\pi}{4}-x)\\ (cos\ (75^\circ)-sin\ (75^\circ))^2=(\sqrt 2\ sin(\frac{\pi}{4}-\frac{75^\circ \cdot\pi}{180^\circ}))^2\\ \color{blue}=(-0,5\sqrt{2})^2=0,5\)

  !

When will the object hit the ground? 

Hello Guest!

h(t)=-16t^2 +198+64t=0

t = 6,047 sec

  !

\(How \ do \ I \ get \ better \ at \ latex?\)

Hello friend!

solve this

Hello Guest!

\({\color{blue}\int_1^2 \frac{(x+3)^2}{3}\ dx}=\int_1^2\frac{1}{3}(x^2+6x+9)\ dx=\frac{1}{3}\left[\frac{x^3}{3}+3x^2+9x\right]_{1}^{2}\\ = \frac{1}{3}(\frac{8}{3}+12+18-\frac{1}{3}-3-9)\color{blue}=6\frac{7}{9}\)

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The domain of
\(f(x) = (x - 1)(x - 2)(x - 3)/(x(x - 1)(x - 2) \)

is

\(x\in \mathbb R \ |\ x \in \{0,1,2\}\\ \color{blue}0+1+2=3\)

The sum of those three numbers is 3.

  !

Hello Guest!

\(presently\\j=2b=s+6\\ b=\frac{j}{2}\\ s=j-6\\ after\ x\ days\\ j+x=\frac{1}{2}(b+x+s+x)\)

\(2j+2x=\frac{j}{2}+x+j-6+x\\ 2j-\frac{j}{2}-j=-6\\ \frac{j}{2}=-6\\ \color{blue}j=-12\)

That means Jerry will be born in 12 years.

Therefore:

At no time will Jerry be half the age of his brother and sister combined.

  !

Simplify the expression.

Hello Guest!

\((x^2/5)^{10}=(\dfrac{x^2}{5})^{10}=\color{blue}\dfrac{x^{20}}{9765625}\)

Or, it is meant like this:

\((x^{2/5})^{10}=x^{\frac{20}{5}}=\color{blue}x^4\)

  !

Determine where f is continuous:

Hello Guest!

1. f(x) = sin-1 (2x)\(f(x)=sin^{-1}(2x)\)

    f(x) is continuous if:   \(\color{blue}x\in \mathbb R\ |\ x\notin \{n\cdot \pi /2\}.\)

2. \(f(x) = \sqrt{arctan\ x} / (x^2 - 9)\)

   \(\sqrt{arctan\ x}/(x^2-9)\)  is continuous if: \(\color{blue}x\in \mathbb R\ |\ 0\le x< \infty\ and\ x\ne 3.\)

  !

Richtig geschrieben \((35000cm)^3.\) Zahl und Einheit sind Faktoren eines Produktes.