MaxWong

\(\sin^2 x - \sin x = 2\\ \sin^2 x - \sin x - 2 = 0 \\\text{Let a = sin x}\\ a^2 - a - 2 = 0\\ (a-2)(a+1) = 0\\ (\sin x - 2)(\sin x + 1) = 0\\ \sin x = 2\text{(rejected) or }\sin x = -1\\ \sin x = -1\\ x = \dfrac{3\pi}{2} \text{rad}\)

\(\cos^2 x + \cos x = \sin^2x\\ \cos^2x + \cos x = 1 - \cos^2x\\ 2\cos^2x + \cos x - 1 = 0\\ \text{Let a = cos x this time.}\\ 2a^2 + a - 1 = 0\\ (2a - 1)(a + 1) = 0\\ \cos x = \dfrac{1}{2} \text{ or }\cos x = -1\\ x = \dfrac{\pi}{3}\text{ rad} \text{ or }x = \pi \text{ rad}\)

Rauhan:

Your answer for 1 is correct, it is water.

I am not too sure for Question 2...... But my answer is different with yours.

6/2(2+1)

= 3(2+1)

= 3(3)

= 9

cos(540)

= cos(360 + 180)

= cos(180)

= 1

Great cake!! Seems delicious :)

x-y = 11

x+y = 143

2x = 154

x = 77

y = 66

Part 1:

x(x + 5) = 24

Part 2:

x(x + 5) = 24

1st way: By trial and error(not recommended because in exam you will only get the marks for the answer but not the steps)

x = 3, (x+5) = 8

Therefore width = 3 inches and length = 8 inches.

x(x + 5) = 24

2nd way: By factorization(highly recommended if you are really good at factorization)

x^2 + 5x = 24

x^2 + 5x - 24 = 0

(x - 3)(x + 8) = 0

x = 3 or x = -8(rejected)

Therefore x = 3 and x + 5 = 8

Therefore width = 3 inches and length = 8 inches.

3rd way: By quadratic equation

x(x + 5) = 24

x^2 + 5x - 24 = 0

x = (- 5 +- sqrt(5^2 - 4*1*(-24)))/(2*1)

x = (-5 +- 8)/(2*1)

x = 3 or -8(rejected)

Therefore width = 3 inches and length = 8 inches

 ♪ ♪ Make the equation into slope-intercept form  ♪ ♪

0x + 6y = 35

6y = 35

y = 35/6

(You can say that the graph is a horizontal line at the height y = 35/6 already, but I will change it into y = mx + b)

y = 0x + 35/6

 ♪ ♪ Therefore the y-intercept = 35/6  ♪ ♪

Easy question. Good question though

We would use inches.

-4.5 x 10^7

= -45000000