Genius Mug - result

Check your results!

1) 2, 5, 9, 16, 27, 45, ?

5+2+2=9
9+5+2=16
16+9+2=27
27+16+2=45
45+27+2=74

2) 1, 5, 13, 29, 61, ?

125

(5-1)*2+5=13
(13-5)*2+13=29
(29-13)*2+29=61
(61-29)*2+61=125

3) 5, 10, 15, 20, 25, ?

5+5=10
10+5=15
15+5=20
20+5=25
25+5=30

4) 3, 9, 18, 54, 108, ?

324

3*3=9
9*2=18
18*3=54
54*2=108
108*3=324

5) a, d, g, j, ?

a b c d e f g h i j k l m

6) 3, 7, 15, ?, 63, 127

3*2+1=7
7*2+1=15
15*2+1=31
31*2+1=63
63*2+1=127

7) 1, 1, 2, 3, 5, 8, ?

Fibonacci Sequence - the next number is found by adding up the two numbers before it.
Ciąg Fibonacciego - każdy następny wyraz jest sumą dwóch poprzednich.
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13

10)

3^{2 x + 2} - 40 = -13

x = \frac{1}{2}

3^{2 x + 2} - 40 = -13

3^{2 x + 2} = 27

3^{2 x + 2} = 3^{3}

2 x + 2 = 3

2 x = 1

x = \frac{1}{2}

11) (0!+1!+2!)!= ?

(0!+1!+2!)!=(1+1+1*2)!=4!=1*2*3*4=24

12)

\frac{6}{2} * (2 + 2 * 4) =

\frac{6}{2} * (2 + 2 * 4) = 3 * (2 + 8) = 3 * 10 = 30

13) C+M-L= ?

1050

C=100, M=1000, L=50
100+1000-50=1050

14)

\sqrt{2} * (\sqrt{2} + \sqrt{8}) =

\sqrt{2} * (\sqrt{2} + \sqrt{8}) = \sqrt{2} * \sqrt{2} + \sqrt{2} * \sqrt{8} = \sqrt{4} + \sqrt{16} = 2 + 4 = 6

15)

\frac{2}{3} + 1 \frac{1}{2} =

2 \frac{1}{6}

\frac{2}{3} + 1 \frac{1}{2} = \frac{2}{3} + \frac{3}{2} = \frac{4}{6} + \frac{9}{6} = \frac{13}{6} = 2 \frac{1}{6}

16)

\frac{21!}{19!} =

420

\frac{21!}{19!} = \frac{19! * 20 * 21}{19!} = 20 * 21 = 420

17)

5*6-10=20
8*6-15=33

18)

19)

\log_{3} 81

3^{4} = 81

20)

\log 100

10^{2} = 100

21)

4^{2} + 2^{3} =

16+8=24

22)

\sqrt[3]{27} =

23)

\cos 0^{º} =

24)

\frac{2 x}{8} = \frac{1}{4}

x = 1

\frac{2 x}{8} = \frac{1}{4}

2 x * 4 = 8

8 x = 8

x = 1

25)

4^{\frac{3}{2}} =

4^{\frac{3}{2}} = \sqrt{4^{3}} = \sqrt{64} = 8

26)

27)

28)

\cos 60^{º} + ctg 45^{º} - \sin 30^{º} + tg 45^{º} =

\cos 60^{º} + ctg 45^{º} - \sin 30^{º} + tg 45^{º} = \frac{1}{2} + 1 - \frac{1}{2} + 1 = 2

29) 2x+5*(7x-8)-10=3x+1

x=1,5

2x+5*(7x-8)-10=3x+1
2x+35x-40-10=3x+1
2x+35x-3x=1+40+10
34x=51
x=1,5

30)

| -2 * | 5 - 8 | - | -3 - 6 | | =

| -2 * | 5 - 8 | - | -3 - 6 | | = | -2 * 3 - 9 | = 15

31) (7x)'+(2)'= ?

(7x)'+(2)'=7+0=7

32)

\sqrt[3]{(8 * 27 * 64)} =

\sqrt[3]{(8 * 27 * 64)} = 2 * 3 * 4 = 24

33)

\int x^{2} dx =

\frac{x^{3}}{3} + c

\int x^{2} dx = \frac{1}{2 + 1} * x^{2 + 1} + c = \frac{x^{3}}{3} + c

34) 9+8+7+6+5+4+3+2+1= ?

9+8+7+6+5+4+3+2+1=(1+9)+(2+8)+(3+7)+(4+6)+5=10+10+10+10+5=45