MaxWong

\(f(x)=\frac{3}{x}+2-\sqrt{x}-2\)

\(f(7)=\frac{3}{7}-\sqrt7\approx-2.22\)

32) \(3\sqrt[3]{5y^3}\times2\sqrt[3]{50y^4}\)

= \(3y \sqrt[3]{5}\times 2\sqrt[3]{5\times5\times2\times y^3\times y}\)

= \(6y\sqrt[3]{5}\times y \sqrt{50y}\)

= \(6y^2 \sqrt[3]{250y}\)

= \(6y^2 \sqrt[3]{5^3\times 2y}\)

= \(6y^2\times 5 \sqrt[3]{2y}\)

= \(30y^2\sqrt[3]{2y}\)

\(6^3 \times 6^{-2}= \frac{6^3}{6^2}= 6\)

Oops sorry wrong answer :( Had to do it all over again.

Just realized angle AEB = angle DEB = 90 degrees.

BD = \(\sqrt{3^2 + \sqrt{11}^2} = \sqrt{20}\)

BC = \(\frac{5\sqrt{2}}{2}=\frac{5}{\sqrt{2}}\)

BC² = \(\frac{25}{2}\)

X = 25+2 = 27

For Y, I admit that I am wrong and it should be a fruit which is cashew apple which makes 1 + 16 + 16 + 12 + 5 = 50

Now testing numbers between 275011 and 275098

Why 275011 and 275098? It is because the digits can't repeat and 275000 to 275010 and 275099 does not satisfy the conditions.

No such numbers satisfys such conditions.

Lesson taught: Don't even try that lock and quickly get back to water surface 

X is hard to solve but you can draw a perpendicular line from E to meet the diameter of the circle and name the intersection point F. Then you can prove that triangle BEF is congruent to triangle BED. Then BD = \(\sqrt{11}\) and BC²= \((\frac{\sqrt{11}}{2})^2 = \frac{11}{4}\)

Therefore X = 11+4 = 15.

For Y, the source of cashew. I don't think it's a fruit but I think it's a country. India? China? we will figure out.

India = 9 + 14 + 4 + 9 + 1 = 37

China = 3 + 8 + 9 + 14 + 1 = 35

As the clue of Z stated that all of the digits in the combination are unique. So we'll use India which is 37.

For Z, 8 not necessarily distinct prime factors for all digits...... the hardest of all. Now the number's 1537**  

Using a website factorizing numbers, the number is 153720 = 2³ × 3² × 5 × 7 × 61

geno3141 : However, if the ratios are not that nice: if you assume that the ratio of Lev's age to Mina's age is a / b and you assume that the ratio of Mina's age to Naomi's age is c / d, then: since a / b = a·c / b·c and c / d = b·c / c·d, the three-way ratio is: a·c : b·c : c·d.

You did the last part wrong. c / d = b·c / b·d So the three-way ratio is a·c: b·c: b·d

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables.

Source: Wolfram Mathworld

5(x+3)-3(x+2)

= 5x+15-3x-6

= 2x+9

1, 16 , 49 , 100 , 169

6em+5e+\(\frac{7}{6}\)

most simplified form.