Alan

"If a plane flies from south to north with 324 km/h and the wind blows from northeast to southwest with 28.3 m/s what is the angle between the fly direction and the deviating direction if the pilot ignores the wind? "

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Google translate gives:

"There are a few cats and ducks. 48 feet, 32 eyes. How many cats and how many ducks are there?"

c = cats,  d = ducks

4c + 2d = 48

2c + 2d = 32

2c = 48 - 32   so  2c = 16   so c = 8

16 + 2d = 32   so 2d = 32 - 16  so  2d = 16  so d = 8

There are 8 cats and 8 ducks.

有8隻貓和8隻鴨子

Suppose x = 4 and f(x) = x^2 + 1/x

Enter  x=4;x^2+1/x      (i.e. separate the x and f(x) by a semicolon ";")

Then press the "=" sign to get:

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4^(7)×4^(3)÷4^(6) → 4^(7+3-6) → 4^4 → 256

(1 + x²)i/(1 + xi) + x- 6i → (1 + x²)i(1 - xi)/((1 + xi)(1 - xi)) + x - 6i

→ (1 + x²)i(1 - xi)/(1 + x²) + x - 6i → 1 - xi + x - 6i 

→ 1 + x - (x + 6)i 

Like so

\(\frac{1}{27}=3^{-y}\\ \frac{1}{27}=\frac{1}{3^y}\\ 3^y=27\\y=3\)

Here's a more general solution:

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"can you solve for z, for z+2\overline{z}=\overline{2-5iz}"

As follows:

By definition the angle in radians is given by arc length/radius, i.e. \(\theta = s/r\)

So, for 01:  \(\theta = 6/27 \rightarrow 0.222 \text{ radians}\)

See if you can now do the others (don't forget to convert degrees to radians first in 03 and 04).

The instantaneous rate of change of f(x) = 6x² - 9 at any x is f`(x) = 12x.  This is a straight line.  Its average value between x=2 and x=b is (12b + 12*2)/2 → 6b+12