Melody

These are plug in questions (as far as checking goes) and you are just being lazy.

Here is my take :)

\(\sqrt{0.64}-\sqrt[3]{-0.008}+\sqrt[4]{\frac{4}{20.25}}+\sqrt[5]{16\div\frac{1}{2}}\\ =0.8-\sqrt[3]{-1*8*0.001}+\sqrt[4]{\frac{4}{2025\div100}}+\sqrt[5]{32}\\ =0.8-(-0.2)+\sqrt[4]{\frac{4*100}{2025}}+2\\ =0.8+0.2+\sqrt[2]{\frac{2*10}{45}}+2\\ =3+\sqrt[2]{\frac{2*10}{5*9}}\\ =3+\sqrt[2]{\frac{2*2}{9}}\\ =3+\frac{2}{3}\\ =3\frac{2}{3}\\\)

Plot your graphs here

b)

\( sin x + \sqrt2 = -sin x\\ 2sinx=-\sqrt2\\ sinx=-\frac{\sqrt2}{2}\\ sinx=-\frac{1}{\sqrt2}\qquad \text{3rd and 4th quads}\\ x=180+45,\;\;\;or\;\;\;360-45\\ x=225^\circ\;\;\;or\;\;\;315^\circ\\ \)

Where is the figure?

\(7^{7^7}\)   is not a base 7 number  (there are no 7s in a base 7 number)     so I am guessing this is in base 10

Anyway, when it is written in full in base 7 it will have the same number of digits as     \(10^{10^{10}}\)    (base 10) has

\({10^{10}} \)    has 10 zeros plus the 1 which is 11 digits  = 10 000 000 000

\(10^{10000000000}\)     has 10 billion zeros plus a 1 in the biggest spot

So altogether  \(10^{(10^{10})}\)   will have      10,000,000,001     digits.

so

\(7^{(7^7)} \;\;base\;10\\ =10^{(10^{10})} \;\;base\;7\\ =\text{1 followed by 10,000,000,000 zeros}\;\;\\ =\text{10,000,000,001 places}\)

I think that is correct but I always get confused when dealing with huge numbers so it would be good if someone could confirm it.