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Plot your graphs here

b)

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

\(12'' = \dfrac{12}{3600}^\circ = \dfrac{1}{300}^\circ\\ 6' = \dfrac{6}{60}^\circ = \dfrac{1}{10}^\circ\\ 6'12'' = \dfrac{31}{300}^\circ = 0.10\bar{3}^\circ\\ -46^\circ6'12'' = -46.10\bar{3}^\circ\\ \sec(46.10\bar{3}) \approx 1.44225\)

0.08062

That's the formula I was using but I kept calculating wrong or something. Wasn't sure what I was doing wrong.

\(p[k=42] = \dbinom{100}{42}(0.42)^{42}(1-0.42)^{100-42}\\ \text{I'll let you crunch the numbers}\)

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.

\(\tan\left(-\dfrac{13\pi}{6}\right) = \tan\left(-\dfrac{\pi}{6}\right)=\\ \dfrac{\sin \left (-\frac{\pi}{ 6} \right) }{\cos\left(-\frac \pi 6 \right)} =\dfrac{-\frac 1 2}{\frac{\sqrt{3}}{2}} = -\dfrac{1}{\sqrt{3}}\)

separate the coins into pairs.

weigh one pair against another

if they balance, the 3rd pair has the heavier coin

if they don't balance the heavier pair has the heavier coin

whichever pair it is weigh the two coins against each other to determine the heavier.

2 weighings

where do you all get these questions....

\((10a+b)\left(\dfrac 7 4 \right) = 10b+a,~a, b \in \mathbb{Z}^+\\ 70a+7b = 40b + 4a\\ 66a = 33b\\ 2a=b\\ 12+24+36+48 = 120\)

thank you!!!

s=side length of the triangle.

what does s mean?

Yep, very nice, CPhill! Infinite series!

The formula to find the area of an equilateral triangle is \(\frac{\sqrt{3}}{4}s^2\)\(\) , so the answer is    \(\sqrt{3}*16=16\sqrt{3}.\)

7^(7^7) =3.759823527 E+695,974 in base 10

Convert 7^(7^7) from base 10 to base 7 =6.666666666666..._7×7^823,542

First, let's find out what each of those expressions boils down to.

square root 0.64  -- well, this is plus or minus 0.8 but I'm going to use only the positive value =  0.8  =  8/10 

cube root –0.008  --  this equals –0.2  =  –2/10

fourth root 4/20.25  --  I had to use the calculator to determine this is 0.666666•••  =  2/3 

fifth root (16 ÷ 1/2)  --  same as fifth root of 32 which is 2 

put them together  8/10 – (–2/10) + 2/3 + 2/1 

a common denominator of 30 will work, so 24/30 + 6/30 + 20/30 + 60/30  = 110/30  = 3 20/30  = 3 2/3

????

DELETED......

Just drop the log6 from both sides

-5r-2   has to equal r-4

-5r-2 = r-4

2 = 6r

r = 1/3   but that would mean you are taking the log of a negative......not allowed       no solution

According to the graph, from rest, the pendelum swings right.....then swings back through its resting point  in 2.5 secs

According to the tire graph the tire goes through 1/2 cycle in 1 sec = 180 degrees

a  affects the amplitude and flips the graph around the x-axis if negative

h shifts the graph L if it is a neg value   and  R if it is a pos value  (there is a neg sign in front of h in your example)

k shifts the graph up if positive....down if negative