A picture of graph of g(x) = (1/5x)^2 .
Answer:
y = -4x + 1
Step-by-step explanation:
The line passes through points (-5,21) and (-4,15)
Slope(m) = change in y ÷ change in x
m = 
m = 
= -36/9 = -4
Taking another point (x,y) on the line and comparing it with point (4,-15):
-4 = 
Cross multiplying gives:
y + 15 = -4x + 16
y = -4x + 1
Y=3x-(1/4)
To find the inverse, flip x and y and solve for y.
x=3y-(1/4)
x+(1/4)=3y
(x+ 1/4)/3= y
Final answer: y= (x+1/4)/3
The x+ 1/4 should have both terms over 3.
Answer:
f(x + 1) = -(3/4)*f(x)
(second option)
Step-by-step explanation:
Here we have the sequence:
64, -48, 36, -27, ...
First, we can notice two things:
Each term has a different sign than the previous term, so the relation is something like:
f(x + 1) = -k*f(x)
Now to find the value of k, we can just replace some of the values (for example, the first and the second one)
-48 = -k*64
48/64 = k
3/4 = k
Now, if we use any pair of consecutive terms we should get the same value of k, now let's try to use the second and third terms to see if we get the same value of k:
36 = -k*(-48)
36 = k*48
36/48 = k
3/4 = k
We got the same value, so we can conclude that k = (3/4)
Then the relation that describes this sequence is:
f(x + 1) = -(3/4)*f(x)
You will need to use the Pythagorean Theorem and plug in the varibles. The rope is the hypotenuse of the right triangle formed, and the 40ft water is the vertical leg, which leaves the ocean floor to be the horizontal leg.[a^{2}+b^{2}=c^{2}\] \[a^{2}+40^{2}=140^{2}\] Then solve for a. \[a^{2}=18000\] \[a=134.164\]
