First, some housekeeping:
cos = 12/13 is incomplete; "cos" must have an argument (input).
cos x = 12/13 is fine; here "cos" has the argument (input) x.
Given that cos x = 12/13, find sin x. To do this, we'll need to find the length of the opposite side, given that the hypo length is 13 and the adj. side length is 12.
12^2 + opp^2 = 13^2, or opp^2 = 169-144 = 25.
Then the opp side could be either 5 or -5. Let's assume that it's +5, and that angle x is in the first quadrant.
Then sin x = opp / hyp = 5/13 (answer)
cos 2 is an entirely different kind of problem. Here you are told what the argument (input) to the cosine function is (it is 2, which here means 2 radians).
Using a calculator: cos 2 = -0.416. Note that the angle 2 rad is in QII, which is why the "adjacent side" is negative and also why the cos of 2 is negative.
Answer:
18√2
Step-by-step explanation:
The smaller triangle sharing a vertex with the larger one is similar and half the area. That means its linear dimensions are √(1/2) = (√2)/2 times those of the larger triangle.
The line segment of interest has length ...
36 × (√2)/2 = 18√2
_____
The ratio of area of similar figures is the square of the ratio of their linear dimensions. Thus the ratio of linear dimensions is the square root of the ratio of area.
Answer:
f(n)=-5-3n
Step-by-step explanation:
Given the recursive formula of a sequence
f(1)=−8
f(n)=f(n−1)−3
We are to determine an explicit formula for the sequence.
f(2)=f(2-1)-3
=f(1)-3
=-8-3
f(2)=-11
f(3)=f(3-1)-3
=f(2)-3
=-11-3
f(3)=-14
We write the first few terms of the sequence.
-8, -11, -14, ...
This is an arithmetic sequence where the:
First term, a= -8
Common difference, d=-11-(-8)=-11+8
d=-3
The nth term of an arithmetic sequence is determined using the formula:
T(n)=a+(n-1)d
Substituting the derived values, we have:
T(n)=-8-3(n-1)
=-8-3n+3
T(n)=-5-3n
Therefore, the explicit formula for f(n) can be written as:
f(n)=-5-3n
This seems to be dividing by 4, so the next numbers are 20, and then 5. If there is a 3rd, it's 1.25
Answer:2
Step-by-step explanation: 5 - 3 = 2
