Answer:
.
Step-by-step explanation:
This is a geometric sequence that means there is a common ratio. That means there is a number you can multiply over and over to get the next term.
The first term is 27.
The second term is (1/3)(27)=9.
The third term is (1/3)(9)=3.
So the common ratio is 1/3.
That means you can keep multiplying by 1/3 to find the next term in the sequence.
The explicit form for a geometric sequence is 
where 
is the first term and 
is the common ratio.
We are given 
and 
.
So the explicit form for the given sequence is .
Since this is a fairly small equation, it's pretty easy to plug in a few points to get ordered pairs and sketch a graph:
when x = 0...
f(0) = 2(0)^2
f(0) = 0
(0, 0)
when x = 1...
f(1) = 2(1)^2
f(1) = 2
(1, 2)
when x = -1...
f(-1) = 2(-1)^2
f(-1) = 2
(-1, 2)
from there, you can get a rough sketch of the graph just by plotting those points. essentially, it just looks "skinnier" than your typical parabola because the 2 out front makes the curve steeper.
Is the shape for H
lolololololol
Answer:
sinA = 0.79 tanA = 1.3
Step-by-step explanation:
Step1:
Find the length of the line going through the middle from A to C by using pythagorean theorem.
a = 13
b = 12
c= ?
c = sqrt(a^2 + b^2)
c = sqrt(13^2 +12^2)
c = 17.69
Step 2:
Use pythagorean theorem again to find the length of the line going from A to D.
a = ?
b = 14
c = 17.69
c^2 = a^2 + b^2
Now solve for a.
a^2 = c^2 - b^2
a = sqrt(c^2 - b^2)
a = sqrt(17.69^2 - 14^2)
a = 10.81
Step 3:
Use trignometry to find the values of sinA and tanA
sinA = opposite/hypotenuse = 14/17.69 = 0.79
tanA = opposite/adjacent = 14/10.81 =1.3
Answer:
r = 6 mph and f = 11 mph
Step-by-step explanation:
Representations:
1) speed of faster cyclist: f = r + 5
2) speed of slower cyclist: r
Distances covered:
(r + 5)(5 hr) + r(5) = 55 mi (total distance covered)
Then 5r + 25 + 5r = 55, or, after reducing this equation:
r + 5 + r = 11, or
2r = 6
Then r = 6 mph and f = 11 mph
