asinus

Thanks Alan and Guest for the right answer!

asinus   !

Soll zeigen das beide Terme gleich sind durch umformen

1+1)+(n+1)^2+n^2 = 1/3(n+1)(2(n+1)^2+1) /3n(2n^2

\(\frac{1}{3n(2n^2+1)}+(n+1)^2+n^2\) 

gleich

\(\frac{1}{3(n+1)\times(2(n+1)^2+1)}\)   ?

\(\frac{1}{3(n+1)\times(2(n+1)^2+1)}\)= \(\frac{1}{(3n+3)\times (2n^2+4n+2+1)}\)

Später mehr, es ist heute zu spät.

 asinus :- )    !

\(\)

Hello Pearl,

The slope is = -4/3
The constant is -1

so

\(\LARGE y=-\frac{4}{3}x-1\)

Greeting asinus :- )    !

What is the variance of 67, 70, 74, 75, 77, 68, 72, 76, 69, 72?

\(\large\sigma^2=\frac{\sum\limits_{i=1}^{n} (x_i-\overline x\ )^2 }{n-1} \)  

\(n=10\)

\({\color{blue}\overline x}=\frac{\sum(67, 70, 74, 75, 77, 68, 72, 76, 69, 72)}{10}\color{blue}=72\)

\(\sum\limits_{i=1}^{10} (x_i-\overline x\ )^2 \) = (67-72)²+(70-72)²+(74-72)²+(75-72)²+(77-72)²+(68-72)²+(72-72)²+(76-72)²+(69-72)²+(72-72)²

=25+4+4+9+25+16+0+16+9+0

=108

\(\sigma^2=\frac{108}{10-1}=12\)

\(\sigma=\sqrt{12}=3.4641\)

\(The \ variance \ is \ \sigma =3.4641.\)

   !

log base 5 x=-4/3 find value of x

\(log_5(x)=\frac{4}{3}\) 

\(x=5^\frac{4}{3}=\sqrt[3]{5^4} =\sqrt[3]{5\times5^3}\)

\(x=5\times\sqrt[3]{5} \) = 8.5499     !

what is 8,569 rounded to 100

8,569 rounded to 100 is 8,570

  !

A gardener measures the height of a plant after 4 weeks to be 9.0 inches. After 6 weeks the height of the plant is 13.5 inches. In this situation, what UNITS would you use to describe the rate of change of the height of the plant?

The appropriate units are millimeters mm and hours h.

\(v=s/t\)

\(v=\frac{(13.5-9)inches}{(6-4)weeks}\)

\(v= \frac{4.5\ inches}{2\ weeks}\times\frac{25.4 \ mm}{inch}\times\frac{week}{7\times 24\ h}\)

\(\large v=0.34\frac{mm}{h}\)

   !

\(\)Hallo, hier die Herleitung:

\(\large\frac{-ln(a-x)}{((b-a)*(c-a))}+\frac{ln(a)}{((b-a)*(c-a))}\)

\(\large=\frac{-ln(a-x)+ln(a)}{((b-a)*(c-a))}=\frac{ln\frac{a}{a-x}}{((b-a)*(c-a))}\) 

\(\LARGE=\frac{1}{((b-a)*(c-a))}\times ln\frac{a}{a-x}\)

  !

Wieviel sind 10% von 59,89?

\(59,89\times 10\%=\frac{59,89\times10}{100}=5,989\)

  !

Wie rechne ich ein tan wert (0,4006) in Grad um?

\(arctan 0.4006=0.38102511452=21°49'\ 52''\)

  !