Mathematics, 15.07.2019 12:30, juansebas35

On a steeper slope, the jogger can run at an average speed of 5.3 miles per hour up the slope and 6.7 miles per hour going down the slope. how long, in hours, the full trip will take (1 mile uphill and 1 mile downhill). give an exact answer expressed as a fraction in simplest terms and then give a decimal approximation correct to three decimal places. (hint: use the same method as in #1.) reduced fraction: decimal approximation:

Answers: 1

Show answers

Answers

On a steeper slope, the jogger can run at an average speed of 5.3 miles per hour up the slope and 6.7 miles per hour going down the slope.

distance = rate times time.

In this problem, distance = 1 mile = rate times time

In the first case, the rate is 5.3 mph, so 1 mile= (5.3 mph)(time), and (time) =

1 mile
= 0.189 hour
5.3 mph

In the second case, the rate is 6.7 mph, and

1 mile
= 0.149 hour
6.7 mph

The total transit time (up and down) is 0.189 hour plus 0.149 hour, or

0.338 hour, or 20.3 minutes.

answered: Guest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

answered: Guest

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number $c\in[0.5,0.75]$ that satisfies the conclusion of the mean value theorem, that is, a number $c\in[0.5,0.75]$ such that

$f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},$

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.