3.

Mathematics

1 answer:

navik [9.2K]2 years ago

3 0

Answer: 12.5

Step-by-step explanation:

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1) the form of the equation may be written as y = A(X - Xo)(X - X1)

Where Xo and X1 are the two roots of the equation.

2) We can fix the system of coordinates so that the vertex is in the middle of the gate => Xo = - 40 and X1 = +40

=> y = A (X + 40) (X - 40) = A (X^2 - 1600)

3) The height, at X = 0 is 25

=> A(0 - 1600) = 25

=> -1600A = 25 => A = -25 / 1600 = - 1/64

4) The equation is y = - [1/64] (X^2 - 1600)

5) You can present it in different equivalent forms.

Some of those other forms are:

1) - 64y = (x^2 - 1600)

2) x^2 = - 64y + 1600

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$\bf 5n^2+6n+7=n^2-4n\implies 5n^2+6n+7-n^2+4n=0
\\\\\\
4n^2+10n+7=0\\\\
-------------------------------\\\\
\begin{array}{llccll}
&{{ 4}}x^2&{{ +10}}x&{{ +7}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\\\\\\
discriminant\implies b^2-4ac=
\begin{cases}
0&\textit{one solution}\\
positive&\textit{two solutions}\\
negative&\textit{no solution}
\end{cases}$

if you get a positive value, that means 2 real solutions
if you get 0, means 1 real solution only
if you get a negative value, is an imaginary root solution, same as saying no solution.

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