Melody

450000

2(2x x y)

I will interpret this as

2(2x * y)

2*2xy=4xy

6 - - 4 = 6 + 4 = 10

Hello  :)

How do you get the answer 20

\((\pm 2 \sqrt5)^2\\=(\pm 2 \sqrt5)\times(\pm 2 \sqrt5)\\=2*2*\sqrt5*\sqrt5\\=4*5\\=20\)

a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64

I noticed that the differentces in the numerator were  2, 4, 8, 16    and these are powers of 2. So...

\(\displaystyle\sum_{n=1}^{n=5}\;\frac{2^n-1}{2^{n+1}}\)

b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64

\(\displaystyle\sum_{n=1}^{n=6}\;\frac{n!}{2^n}\)

An instructor gives a pop quiz consisting of 10 multiple choice questions, where each question has 5 choices, (a) through (d). What is the probability of passing the pop quiz if you guess the answers? Passing means getting 8 out of 10 questions correct.

p = 0.2   q=0.8

P(at least 8 correct)

= P(8 correct)+P(9correct)+P(10 correct)

=  10C8*0.8⁸*0.2²   +    10C9*0.8⁹*0.2¹     +     10C10*0.8¹⁰*0.2⁰

=  45  *0.8⁸ * 0.04   +    10  *0.8⁹ * 0.2     +     0.8¹⁰

^{=      You can finish it :)}

Find Dy/Dx (X=pi) when y = sin(x) + sec(x).

I will change the question to:    Find Dy/Dx     of    y = sin(x) + sec(x)       at the point where x=pi

\( y = sin(x) + sec(x) \\  y = sin(x) + [ cos(x) ]^{-1}\\  y' = cos(x) +-1 [ cos(x) ]^{-2}*-sin(x)\\  y' = cos(x) +\frac{sin(x)}{cos^2(x)}\\  y'(\pi) = cos(\pi) +\frac{sin(\pi)}{cos^2(\pi)}\\  y'(\pi) = -1+\frac{0}{1}\\  y'(\pi) = -1\)

I don't think that you can make the calc do it.  ://

Yes Max I used Google too  but it did not make full sense.  

Maybe your interpretation is correct or maybe not :))