tayfaulk123

02.12.2020 •

Mathematics

The total fees for the high school play are $250. Tickets to the play cost $5 for students and $8
for nonstudents.

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Ответ:

katieleeisaacs8976

11.07.2020

Mathematics

a) The coordinates of the rest stop is $C(x,y) = \left(5, \frac{5}{2} \right)$ .

b) The approximate distance between the high school and the stadium is 32 miles.

Step-by-step explanation:

a) The rest stop is located in the midpoint of the line segment between the high school and the stadium. Vectorially speaking, we use the following formula:

$C(x,y) = \frac{1}{2}\cdot A(x,y) + \frac{1}{2}\cdot B(x,y)$ (1)

Where:

A(x,y) - Coordinates of the high school.

B(x,y) - Coordinates of the stadium.

C(x,y) - Coordinates of the rest stop.

If we know that A(x,y) = (3, 4) and B(x,y) = (7,1) , then the coordinates of the rest stop are, respectively:

$C(x,y) = \frac{1}{2}\cdot (3, 4) + \frac{1}{2}\cdot (7, 1)$

$C(x,y) = \left(\frac{3}{2}, 2 \right) + \left(\frac{7}{2}, \frac{1}{2} \right)$

$C(x,y) = \left(5, \frac{5}{2} \right)$

The coordinates of the rest stop is $C(x,y) = \left(5, \frac{5}{2} \right)$ .

b) The approximate distance between the high school and the stadium (), in miles, is the product of the Length Equation of the Line Segment and the scale factor:

$d = r\cdot \sqrt{(\Delta x)^{2} + (\Delta y)^{2}}$ (2)

Where:

- Scale factor, in miles.

$\Delta x$ , $\Delta y$ - Horizontal and vertical distances between the high school and the stadium, no unit.

If we know that $r = 6.4\,mi$ , $\Delta x = 4$ and $\Delta y = -3$ , then the distance between the high school and the stadium is:

$d = r\cdot \sqrt{(\Delta x)^{2} + (\Delta y)^{2}}$

$d = (6.4\,mi)\cdot \sqrt{4^{2}+(-3)^{2}}$

$d = 32\,mi$

The approximate distance between the high school and the stadium is 32 miles.

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The total fees for the high school play are $250. Tickets to the play cost $5 for students and $8 for nonstudents.