A traveler is driving home. He is currently 500 miles from home and he drives 75 miles each hour. Find a function for the traveler's distance from home after x hours.

f(x) = 500 - 75x

Step-by-step explanation:

Since he drives 75 miles each hour, his distance driven can be represented by 75x.

To represent his distance from home, 75x needs to be subtracted from 500.

So, the function will be f(x) = 500 - 75x

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).