The equation y = -6t^2 + 51t describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 30 feet in height?

Guest Jun 6, 2022

#1

#2**0 **

We can set 30 equal to y, and we have the equation: \(30 = -6t^2 + 51t\)

Subtracting 30 from both sides, we get: \(0 = -6t^2 + 51t - 30\)

Now, we can use the quadratic formula: \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\), to get \({17 \pm \sqrt {209}} \over 4\).

But, we are looking for the first time it reaches 30 ft, so the answer is \(\color{brown}\boxed{{17 - \sqrt {209}} \over 4}\)

BuilderBoi Jun 6, 2022

#3

#4**0 **

The \over function is used for fractions, so example, 1/2 is 1 \over 2

Curly brackets ({), are the equivalent of parenthesis in PEMDAS, so, for example, 1/2 = 0.5, would be {1 \over 2} = 0.5. The brackets around the fraction separate the fractions, without them, it would be \(1 \over 2 = 0.5\).

Next, the square root function is \sqrt{} (where the number is inside the bracket), so, \(\sqrt {209}\) is \sqrt{209}.

So, \({17 - \sqrt {209}} \over 4\) is {17 - \sqrt{209}} \over 4.

To box something, use the \boxed{} function, where the thing that is being boxed goes inside the curly brackets.

To make it a different color, use the /color{insert color here}{}, where the color goes in the first pair of brackets and the thing that you would like to change he color of.

Putting all these concepts together, \(\color{brown}\boxed{17 - \sqrt {209} \over 4}\) in raw form is "\color{brown}\boxed{17 - \sqrt {209} \over 4}".

/color{brown} makes everything brown, /boxed boxes the entire thing in brown, and the brackets immediately after that define the fraction that is being boxed. The \sqrt{209} makes the square root of 209, and \over 4 makes a fraction with a denominator of 4 and a numerator with everything before it ( in this case 17 - \sqrt {209}).

More info available here: https://web2.0calc.com/questions/latex-coding

Also, sorry if this isn't helpful, I'm not the best at explaining...

BuilderBoi
Jun 6, 2022