A group of hikers walked 8 and 7/10 miles. And then 5 and 1/5 miles. How far did they walk altogether?

A drone is monitoring the atmospheric conditions above a farm field.

Viefleur [7K]

Answer:

$y=5 \ \ \ x x_o + 1.9s$

Step-by-step explanation:

This situation can be considered as a piecewise function. First, you take xo as the time in which the drone goes upward. Before this time the height of the drone is constant with a value of 5 m. Next, you take into account that during 1.9 s after xo the drone accelerates. Finally, the drone flies again with a constant height of 5.9m. Hence, this function has three parts:

For the first part you have:

y = 5 for x < xo

For the second part you first calculate vertical speed (which means the slope of the linear function) by using the following kinematic equation:

$y=vx\\\\v=\frac{y-y_o}{x}=\frac{5.9m-5.0m}{1.9s}=0.47m/s$

Then you have:

y = 0.47x for xo < x < xo + 1.9s

And for the third part:

y = 5.9 for x > xo + 1.9s

Summarizing you obtain:

$y=5 \ \ \ x x_o + 1.9s$

4 0

2 years ago

Find the equation of the line between the points (10, – 5) and ( - 2,0).

Natali5045456 [20]

Answer <u>(assuming it can be in slope-intercept form)</u>:

$y = -\frac{5}{12} x-\frac{5}{6}$

Step-by-step explanation:

1) First, find the slope of the line between the two points by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}$

Thus, the slope of the line is $-\frac{5}{12}$ .

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute values for $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{12}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

$y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}$