Superman needs to save lois from the clutches of lex luther. after flying for 15 seconds, he is 2100 meters from her. then at 18 seconds he is 1980 meters from her.

a) write an equation in slope-intercept form to model this situation where m is the distance in meters and s is the time in seconds.

b) how far is superman away from lois after flying for 6 seconds?

Part A

x = time in seconds that have gone by

y = distance in meters Superman is away from Lois

"After flying for 15 seconds, he is 2100 meters from her" means we have the point (x,y) = (15, 2100)

"at 18 seconds he is 1980 meters from her" tells us we have a second point (x,y) = (18,1980)

Find the slope of the line through these two points

m = (y2-y1)/(x2-x1)

m = (1980-2100)/(18-15)

m = (-120)/(3)

m = -40

The slope is -40 which means Superman is getting 40 meters closer each second. I.e, the distance is dropping 40 meters per second

Use one of the points and the slope to find the y intercept b

y = mx+b

2100 = (-40)*15 + b

2100 = -600 + b

2100+600 = b

b = 2700

This is the starting distance Superman is away from Lois

Since m = -40 and b = 2700, we know the y = mx+b equation becomes y = -40x+2700.

Replace x with s, replace y with m. We now have m = -40s+2700

Part B

Plug s = 6 into the equation we found for part A. Then simplify.

m = -40s+2700

m = -40*6+2700

m = -240+2700

m = 2460

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}