Question

3x-4y=7;5x+2y=3 equating coefficients variables, solve equation

Answer 1

Step-by-step explanation:

here multiplicating the the equations with other equation's coefficients, and subtracting the both newly formed equation's gives the value and y and x.

Answer 2

Step-by-step explanation:

Answer:

h=-\frac{1}{6}x^2+2xh=−61x2+2x

Step-by-step explanation:

The height of the tunnel is modeled by:

h=rx^2+txh=rx2+tx

Where r and t are constants.

We know that the maximum height of the tunnel h is 6 meters.

And at ground level, the width is 12 meters.

And we want to determine the equation of the parabola.

First, since this is a quadratic, our maximum height h will occur at the vertex of our equation.

The vertex is given by:

(-\frac{b}{2a}, f(-\frac{b}{2a}))(−2ab,f(−2ab))

In our case, we have the function:

h=(r)x^2+(t)xh=(r)x2+(t)x

Hence, a=r; b=t; and c=0.

Therefore, our vertex is:

\Rightarrow -\frac{t}{2r}⇒−2rt

Thus, if we substitute this back into our equation, we should get 6 since 6 is the maximum height which is determine by the vertex. In other words:

(6)=r(-\frac{t}{2r})^2+t(-\frac{t}{2r})(6)=r(−2rt)2+t(−2rt)

Simplify:

6=r(\frac{t^2}{4r^2})-\frac{t^2}{2r}6=r(4r2t2)−2rt2

Simplify:

6=\frac{t^2}{4r}-\frac{t^2}{2r}6=4rt2−2rt2