Problema Solution

Terrance and Jesse are training for a long-distance race. Terrance trains at a rate of 6 miles every half hour, and Jesse trains at a rate of 2 miles every 15 minutes.

How long will each person take to run a total of 50 miles at the given rates?

Answer provided by our tutors

d = 50 mi the distance
t1 = the time of Terrance
t2 = the time of Jesse
Terrance trains at a rate of 6 miles every half hour thus his rate is:
v1 = 6/0.5 = 12 mph
Jesse trains at a rate of 2 miles every 15 minutes thus his rate is:
v2 = 2/(15/60) = 8 mph
since speed = distance/time follows time = distance/speed:
t1 = d/v1
t1 = 50/12
t1 = 4 1/6 hr
t1 = 4 hr 10 min
t2 = d/v2
t2 = 50/8
t2 = 6 1/4 hr
t2 = 6 hr 15 min
Terrance will run 4 hours and 10 minutes.
Jesse will run 6 hours and 15 minutes.

6 0

3 years ago

Find the inverse of the following function.

Naddik [55]

For this case we must find the inverse of the following function:

$f (x) = 8 \sqrt {x}$

For this, we follow the steps below:

We change f (x) to y:

$y = 8 \sqrt {x}$

We exchange the variables:

$x = 8 \sqrt {y}$

We solve for y:

$8 \sqrt {y} = x$

We divide between 8 on both sides of the equation:

$\sqrt {y} = \frac {x} {8}$

We raise both sides of the equation to the square to remove the root:

$y = (\frac {x} {8}) ^ 2\\y = \frac {x ^ 2} {64}$

So, the inverse is: $f ^ {- 1} (x) = \frac {x ^ 2} {64}$

ANswer:

Option C

3 0

3 years ago

Which of the following is the correct formula for distance?(1 point) d=(x2−x1)+(y2−y1)−−−−−−−−−−−−−−−−−√, where d is the distanc

Afina-wow [57]

Answer:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

6 0

3 years ago

Which graph shows the solution to the system of linear inequalities?<br> y< 2x-5<br> y>-3x + 1

trapecia [35]

Answer:

See explanation

Step-by-step explanation:

Plot the solution sets to both inequalities.

1. For the inequality $y$ First, plot the dotted line $y=2x+5$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$2\cdot 0-5=-5$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality $y>-3x+1.$ First, plot the dotted line $y=-3x+1$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$-3\cdot 0+1=1>0$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.

5 0

3 years ago