Відео

Wrong, m cannot be 5.14... Clearly: m⋅sin(x) = 4, m⋅cos(x) = 3 ➡ m²⋅sin²(x) = 16, m²⋅cos²(x) = 9 ➡ m²⋅(sin²(x) + cos²(x)) = 16 + 9 ➡ m² = 25 ➡ |m| = 5

30

How many squares are here?

x⁴-10x²+9=0 (x²-1)(x²-9)=0 (x+1)(x-1)(x+3)(x-3)=0 x+1=0 x=-1 ❤ x-1=0 x=1 ❤ x+3=0 x=-3 ❤ x-3=0 x=3 ❤

Completing The Square 10x²-x-3=0 400x²-40x-120=0 400x²-40x+1=121 (20x-1)²=121 |20x-1|=11 20x-1=11 20x=12 x=⅗ ❤ 20x-1=-11 20x=-10 x=-½ ❤

Quadratic Formula 10x²-x-3=0 a=10, b=-1, c=-3 ax²+bx+c=0; a≠0 x=(-b±√∆)/(2a) ∆=b²-4ac ∆=(-1)²-4•10•-3 ∆=1+120 ∆=121 x=[-(-1)±√121]/(2•10) x=(1±√121)/20 x=(1±11)/20 x=(1+11)/20 x=12/20 x=⅗ ❤ x=(1-11)/20 x=-10/20 x=-½ ❤

Factoring 10x²-x-3=0 10x²+5x-6x-3=0 5x(2x+1)-3(2x+1)=0 (5x-3)(2x+1)=0 5x-3=0 5x=3 x=⅗ ❤ 2x+1=0 2x=-1 x=-½ ❤

Domain: x≠{1, 2, 3, 4} Numerator: a=x²+5x+4 (x+1)(x+2)(x+3)(x+4) (x²+5x+4)(x²+5x+6) (x²+5x+4)(x²+5x+4+2) a(a+2) Denominator: b=x²-5x+4 (x-1)(x-2)(x-3)(x-4) (x²-5x+4)(x²-5x+6) (x²-5x+4)(x²-5x+4+2) b(b+2) [a(a+2)]/[b(b+2)]=1 a(a+2)=b(b+2) a²+2a=b²+2b a²-b²+2a-2b=0 (a-b)(a+b)+2(a-b)=0 (a-b)(a+b+2)=0 a+b+2=0 x²+5x+4+x²-5x+4+2=0 2x²+10=0 x²+5=0 x²=-5 |x|=i√5 x=±i√5 ❤❤ a-b=0 a=b x²+5x+4=x²-5x+4 5x+4=4-5x 5x+5x=4-4 10x=0 x=0 ❤

[(k+2)!]/[(k-2)!]=1680 Domain: value must be positive, cannot be fraction, cannot contain complex roots. [(k+2)(k+1)(k)(k-1)(k-2)!]/[(k-2)!]=1680 k(k+1)(k+2)(k-1)=1680 (k²+k)(k²+k-2)=1680 Let x=k²+k x(x-2)=1680 x²-2x=1680 x²-2x+1=1681 (x-1)²=1681 |x-1|=41 x-1=-41 x+40=0 k²+k+40=0 ∆=b²-4ac ∆=1²-4•1•40 ∆=1-160 ∆=-159<0 ∅ x-1=41 x-42=0 k²+k-42=0 (k+7)(k-6)=0 k+7=0 k=-7 ∅ k-6=0 k=6 ❤

XX -X - 6 = 0 *. 6 = 1x6=1,5x4=2x3 3 - 2 = 1 = (b) **. 3: 3x3 - 3 - 6 9 - 3 - 6 = 0 **. 2: 2x2 - 2 - 6 4 - 2 - 6 # 0 -2: (-2x-2) -(-2) - 6 4 + 2 - 6 = 0 *** X' = 3, X" = -2./.

XX - 7X + 12 = 0 *. 12 = 1,5x8=2x6=3x4 3 + 4 = 7 = (b) **. 3: 3x3 - 7x3 + 12 9 - 21 + 12 = 0 **. 4: 4x4 - 7x4 + 12 16 - 28 + 12 = 0 *** X' = 3, X" = 4./.

XX - 2X - 15 = 0 * 15 = 2x7,5 = 3x5 5 - 3 = 2 = (b) ** 5: 5x5 - 2x5 - 15 25 - 10 - 15 = 0 **. 3: 3x3 - 2x3 - 15 9 - 6 - 15 # 0 -3: (-3x-3) -2(-3) - 15 9 + 6 - 15 = 0 *** X' = 5, X" = -3./.

XX + YY = 29, Y - X = 3 *. XX + YY = 29 = 25 + 4 = (5x5) + (2x2) ** Y - X = 3 = 5 - 2 *** X = 2, Y = 5./.

XX - 10X + 9 = 0 *. 9 = 1x9 = 1,5x6 = 2x4,5 9 + 1 = 10 = (b) ** 9: 9x9 - 10x9 + 9 81 - 90 + 9 = 0 ** 1: 1x1 - 10x1 + 9 1 - 10 + 9 = 0 *** X' = 9, X" = 1./.

Without even going through all your calculations, one can see it is 1/2. You just need to know your exponential rules.

65

1/2

Alright

❤ Thank you

XX - 3X - 28 = 0 * 28 = 2x14= 4x7 = 8x3,5 ... 7 - 4 = 3 = (b) ** 7: 7x7 - 3x7 - 28 49 - 21 - 28 = 0 ** 4 : 4x4 - 3x4 - 28 16 - 12 - 28 # 0 -4 : (-4x-4) - 3(-4) - 28 16 + 12 - 28 = 0 *** X' = 7 , X" = -4 ./.

44

D?

_25

How do I only use 1 expression

XX - 8X + 15 = 0 * 15 = 3x5 , 3+5 = 8 =(b) ** 5 : 5x5 - 8x5 + 15 25 - 40 + 15 = 0 ** 3 : 3x3 - 8x3 + 15 9 - 24 + 15 = 0 *** X' = 5 , X" = 3 ./.

XX - X - 6 = 0 * 6 = 1x6 = 2x3 ** 1 : 1x1 - 1 - 6 # 0 6 : 6x6 - 6 - 6 # 0 ** 2 : 2x2 - 2 - 6 # 0 -2 : (-2x-2) -(-2) - 6 4 + 2 - 6 = 0 3 : 3x3 - 3 - 6 9 - 3 - 6 = 0 *** X' = 3 , X" = -2 ./.

33 - go around the circle clockwise starting at 5 and note the difference between the next number. 6-5=1; 8-6=2; 11-8=3; 15-11=4; 20-15=5; 26-20=6; therefore ?-26=7 and ?=33

33

11.0

😮😮 its 5

3pq

Dgh

72

Better to avoid unnecessary music as it disturbs the concentration.

D. 2^-3 X 2^24 = 2^-3+24 = 2^21

11•0

✓(125^x) = 25^(✓x) 125^(x/2) = 25^(x/2) 5^(3x/2) = 5^(x) 3x/2 = x x = 0

4

D

D

C

D

11.0 cm