Misaki

Which is oppistie which is adjacent and which is the hyptounuse

Mark them like this O for oppisite A for adjacent and H for hypotonuse.

First solve the indefinite integral

\(\int 4-2x dx=4x-x^2+c\)

Find boundaries 

\(\int_{0}^{a}4-2xd=-(a-4)a-0\)

Simplify 

\(-(a-4)a\)

\(-(a-4)a=4 \)Solve for a

\(a^2=8\)

\(a=\sqrt{8}\)

\(a=2\sqrt{2}\)

The grid is where?

Use binet's formula to find the 1995th term of the series hint: it's the fibonnacia series

so \(F(n)=\frac{\phi^n-(-\phi)^n}{\sqrt5}\)Let n=1995

\(F(1995)=\frac{\phi^{1995}-(-\phi)^{1995}}{\sqrt{5}}\)

Let Phi=1.6 \(F(1995)=23668326.9616766279790584\) divided by 8 it equals

\(=2958540.8702095784973823\)

Oh ok thanks!

\(\frac{6csc(20)}{13csc(0)-5}=0\)

Let's simplify  \(6csc(20)=17.5\)to 3 significant figures

\(csc(0-5)=csc(-5)\)

\(13csc(-5)=-149\)to 3 significant figures

\(\frac{17.5}{-149}\neq 0 \)Maybe if you wrote the whole decimal out it might equal zero but if we're simplifiying to 3 significant figures, it does not equal zero. 

The exact value is -2. 

A ray is a straight line therefore the boundry between the water  and the air will be a semi circle (180 degrees)

Hence the angle of refranction is 180-35=145 degrees.