Krysta knit a total of 16 centimeters of scarf over 8 nights. How many nights will Krysta have to spend knitting in order to knit a total of 46 centimeters of scarf? Assume the relationship is
directly proportional.
nights

23 nights

Step-by-step explanation:

What does "Proportional" Mean? Proportional means that the ratio is the same throughout.

Step One: First, to set this up, we will put the 16 centimeters for the numerator and then the 8 nights on the bottom. The bottom is the independent variable because we can't physically change the number of nights. 16/8.

Step Two: Now, we have to scale this up to 46. Because the 46 is the centimeters, we have to do 46/16 to see how much we need to scale it by: 46/16= 2.875.

Step Three: Lastly, we can multiply 8 by 2.875 to see how many nights it took: 8 times 2.875 is 23 nights.  

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.