Will85237

Use the formula:

\(v^2=u^2+2as\)

Where v is final velocity, u is intitial velocity, a is acceleration, and s is distance.

v = 0 because the ball will stop moving upwards as it reaches it's peak height.

u = 12m/s as given in the question.

a = -9.81m/s/s because gravity is the force acting against the ball.

s is what we want to find.

\(0^2=12^2+2\times-9.81\times s\)

\(s=7.3m\)

This question may have been a joke, but it takes extensive proof to prove simply sums like this. For example, in Russel and Whitehead's "Principia", it took over 360 pages to prove 1+1=2.

\(f(x)=-3x+5\)

Take the function g(x) and substitute it in for x in f(x).

\(f(g(x))=-3(x-4)+5\)

\(f(g(x))=-3x+12+5\)

\(f(g(x))=-3x+17\)

(copy, paste, and change from answer to almost identical question)Using this handy binary to decimal converter, 001010101010101001010101010010101010101001 in base 2 is 732,985,371,305 in base ten.

Let the daughter's age be equal to x and the mother's age be equal to y. This means we know two things which are true.

\(y=3x\)

\(y+12=2(x+12)\)

Put the equations equal to x.

\(\frac{y}{3}=x\)

\(\frac{y+12}{2}-12=x\)

And then put them equal to each other and solve for y.

\(\frac{y+12}{2}-12=\frac{y}{3}\)

\(y+12-24=\frac{2y}{3}\)

\(3y+36-72=2y\)

\(y=36\)

The mother is 36 years old.

\(sin2\theta=cos\theta \)

Apply the double angle identity to sin2θ.

\(2sin\theta cos\theta=cos\theta \)

\(2sin\theta cos\theta-cos\theta=0\)

\((cos\theta)(2sin\theta-1)=0\)

\(cos\theta=0\)

\(\theta=90°,270°\)

\(2sin\theta-1=0\)

\(\frac{1}{2}=sin\theta\)

\(\theta=30°,150°\)

Therefore, θ can be equal to 30°, 90°, 150°, 270°

\(a^2=b^2+c^2\)

\(a^2=17^2+8.5^2\)

It's a function. You choose a number for x, and it gives you a number back, called y.

It looks kind of nice if you graph it.