An anchor chain has 32 links lying on a ship's deck, while the rest of the chain is below deck height. each time the raise-anchor control is activated, 9 more links come over the edge to lie on the deck

write a linear function that models the number of chain links on deck after n activations of the raise-anchor control.

*hint:

common difference is the slope (m)
initial value is the y-intercept (b)
function notation:

  f(n) = 9n +32

Step-by-step explanation:

The problem statement and hint tell you how to fill in the values of the form ...

  y = mx + b

Here, you have "n" (not "x") as the independent variable, and you want functional form (f(n) =, not y =). So the form you're filling in with m=9, b=32 is ...

  f(n) = mn +b

After the substitution, you have ...

  f(n) = 9n +32

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.