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# help plz

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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?

Jun 6, 2022

#1
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t = (17± √209)/4

I hope this isn't too confusing. I dont know how to use LaTeX

Jun 6, 2022
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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 $$\color{brown}\boxed{{17 - \sqrt {209}} \over 4}$$

Jun 6, 2022
#3
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Thats the answer I got but how did you get it to display like that?

Jun 6, 2022
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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}).

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

BuilderBoi  Jun 6, 2022
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You did great! thank you so much

Elijah  Jun 6, 2022