I.the difference between two numbers is 5. their product is 36.
a. write two equations that model this situation.
b.what are the two numbers?

Equ 1: X-Y=5
equ 2: x∗y=36
from Equ 1
     X=5+Yequ 3
substitute x=5+y in equ 2
(5+y)∗y=36
5y+y^2=36
y^2+5y-36=0
factorize by substitution
(y^2+9y)-(4y-36)=0
y(y+9)-4(y+9)=0
(y-4)(y+9)=0
y=4 or y=-9

substitute y=4 or -9 in equ 1
x-4=5
x=5+4
x=9 OR

x-(-9)=5
x+9=5
x=5-9
x=-4

since -4∗-9=36
therefore y=-9 and x=-4

Approximately 1038 mph

The more accurate value is 1037.51097384802

Round that however you need to.

Explanation:

We need the circumference of the equator. Think of the equator as the largest possible circle (or belt) to fit around the earth.

C = pi*d

C = pi*7926

C = 7926pi

C = 24,900.2633723527

In 24 hours, a person at the equator travels roughly 24,900.2633723527 miles since the earth does a full rotation in this timespan.

Divide the two quantities distance over time to get the speed

rate = distance/time

rate = (24,900.2633723527 miles)/(24 hours)

rate = ( (24,900.2633723527)/(24) ) miles per hour

rate = 1,037.51097384802

rate = 1038 mph

I'm rounding to 4 sig figs since the diameter is given to be in four sig figs.

This speed of roughly 1038 mph is a linear speed and not an angular speed.

Extra info (optional section)

Upon further research, I found an article from NASA JPL (jet propulsion laboratory) which states quote:

"To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr)"

Their figure of 1000 mph seems to be a rough estimate, more or less. It's fairly close to the 1038 figure we got earlier.