CPhill

Well explained, HSC......

Note that she needs 3 times as many ounces of beets as servings

So....for 1200 servings, the cafeteria needs 3600 ounces of beets

Here's one example  :     a function representing an automobile's speed in mph - x -  and its speed in ft per second - y

So.....some ordered pairs are :

x         y

30     44

60     88

90     132

120   176

This is a linear function    ......the slope is   [ 88 - 44] / [ 60 - 30]  = 44/30  = 22/15

And the equation of this function  is

y - 44  = (22 / 15) (x - 30)

y = (22 / 15)x

Here's the graph :  https://www.desmos.com/calculator/rjxubcceok

We know this is a function because it passes the vertical line test.....

According to the legend,Galileo (1564-1642, Italy) used the Leaning Tower of Pisa to conduct his experiments in gravity. Assume that when he dropped objects from the top of the 55 meter tower ( this is measured length, not the height of the tower), they landed 4.8 meters from the tower’s base. What was the angle that the tower was leaning from the tower’s vertical?

The angle is given by

asin(4.8 / 55)  = about 5.007°

Two roads intersect at an angle of 120 degrees as shown on the right figure. Romeo’s mailbox is 600 m from the intersection. Juliet’s mailbox, on the other hand, is 476 m from the intersection. How far is romeo’s mailbox from juliet’s mailbox?

I don't see any illustration, but we can use the Law of Cosines to find the distance, d......

d^2  = 600^2 + 476^2  - 2(600)(476)cos(120)

d^2 = 872,176

d = about 933.9 m

While viewing a statue of Superman in the wax museum, kevin noticed that when he looked up to the top of the statue, the angle of elevation was 15 degrees and when he looked down at the statue’s base, the angle of depression was 20 degrees. If his eyes were 5 ft above the floor, how tall was the statue of superman.

We need to find out how far he was from the statue.....this is given by:

5 / tan(20)   = about 13.74 ft

And the total height =

5 + 13.74*tan(15)  = about 8.68 ft

6x^2 + 17x − 3   can be factored as

(6x -1) (x + 3)

And these are the dimensions in terms of length and width

x^2 + bx + 375

The positive divisors of 375 are :

1  3  5  15  25  75  125  375

So  b could equal the following for p,q   [or vice-versa]

 [375 + 1]  =  376

 [3 + 125]  =  128

 [5 + 75] =  80

 [15 + 25 ] =  40

49 m/s * ( 1/100) s   =  0.49 m

Sphere_{surface area}   =  4 pi * r^2       where r is the radius