MaxWong

\(\quad \cos\left(6x\right)\\ =\cos(2\cdot3x)\\ =2\cos^2(3x)-1\\ \text{Know: }\cos(3x) = 4\cos^3(x) - 3 \cos (x)\\ =2\left(4\cos^3(x)-3\cos(x)\right)^2 - 1\\ =2\left(16\cos^6(x)-24\cos^4(x)+9\cos^2(x)\right)-1\\ =32\cos^6(x)-48\cos^4(x)+18\cos^2(x)-1\)

\(\dfrac{111}{\frac{33}{\frac{-22}{-2}}\cdot(-5^2)+(-4)}\\ =\dfrac{111}{\frac{33}{11}\cdot(-25)-4}\\ =\dfrac{111}{-75-4}\\ =\dfrac{-111}{79}\)

I guess you are trying to ask what is the values of m and a.

\(8x + 1 \equiv 5\pmod{12}\\ 8x\equiv4\pmod{12}\\ 8x\equiv16\pmod{12}\\ x\equiv2\pmod{12}\)

Thank you. This is helpful.

It's the 4th option.

Observing the oblique straight line for x < -2, we see its slope is 1.

Extend the straight line, and it meets y-axis at (0,5).

Therefore when x < -2, f(x) = x + 5.

On the other hand, when x >= -2, it is a horizontal straight line with y-intercept 4. 

Therefore when x >= -2, f(x) = -4.

This is why the 4th option is the answer.

Fraction of red paint = (3/5)/(16/3) = 9/80.

First thing we know BC = BK + CK = 14.

Then we use Pythagorean theorem twice to get:

\(AB = \sqrt{AK^2 + BK^2} = 10\)

\(AC = \sqrt{AK^2+CK^2} = 6\sqrt2\)

Therefore,

Perimeter = AB + AC + BC = 14 + 10 + 6√2 = 24 + 6 √ 2

\(\sin A = \dfrac{a}{c}\\ \cos A = \dfrac{b}{c}\\ \tan A = \dfrac{a}{b}\\\)

:)

Because F = ma, if the acceleration is 0, then the forces are in equilibrium.

First, the man have weight(of course!), so there is a force pointing downwards labeled W(stands for weight).

And then, there is tension in the string, so there is a force pointing upwards labeled T(stands for tension).

Also, there is normal force, so there is another force pointing upwards labeled N(stands for normal force).

Finally, the normal force and tension balances the weight, so it should be in equilibrium.

P.S.: I am not specifically good at Physics, but I tried my best to help. If anyone sees mistake in my solution, please teach me. Thank you.

"The interior acute angles are congruent" tells you it is a regular pentagram, so the measure of interior acute angle = 180/5 = 36 degrees. (I divided by 5 because it is a pentagram(5-gram) .)

Now you draw a straight line like this:

Calculate the angles in the triangle formed:

the base angles of the isosceles triangle is 72 degrees.

As the line drawn is a straight line, so the exterior angle is 108 degrees.

Measure of internal reflex angle = 72 * 2 + 108 degrees = 252 degrees