Question

What does 4cosΘ^2 simplify to?? help

Answer 1

The question was (cos Θ + cos Θ)2 + (cos Θ + cos Θ)2

and my options are
sin2 Θ

4

8cos2 Θ

cos2 Θ

Answer 2

the 2 in the question are exponents

Answer 3

\(\normalsize\color{blue}{ (\cosθ+\cosθ)^2+(\cosθ+\cosθ)^2 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ (2\cosθ)^2+(2\cosθ)^2 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 4\cos^2θ+ 4\cos^2θ \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 8\cos^2θ \LARGE\color{white}{ \rm │ }}\)

Answer 4

@SolomonZelman ahh i made a dumb mistake thank you sooo much!! can u help me with one more? its on graphing sequences

Answer 5

wait, for the one you just answered why does it go from 2cos(theta)^2 to 4cos(theta)^2?

Answer 6

graphing sequences? Well... you can write them as coordinates and graph. Geometric sequences are curves (exponential functions), Arithmetic sequences are lines, (Linear functions).

Answer 7

Because you raise all the parenthesis to the second power, and the `2` is being raised to the second power also.

Answer 8

@SolomonZelman oh okay! i was a bit confused

Answer 9

x coordinate is the number of terms, and the y coordinates are the terms themselves.

Answer 10

Can you find the common ratio ?

Answer 11

but theres no zeroth term?

Answer 12

one sec i think i can get it

Answer 13

2 right? @solomonzelman

Answer 14

yes there is no zeroth term, and you have no intercepts...

Answer 15

the common ratio can not be 2, because the terms get smaller.

10, 5, 1.25 ...

Answer 16

oh is it 1/2?

Answer 17

I mean
10, 5, __, 1.25

Answer 18

Yes it is 1/2

Answer 19

So, can you find the average rate ?

Answer 20

but from what? like between what two points

Answer 21

@SolomonZelman

Answer 22

Like you find the overall rate, between the 4 points, and since you have 3 distances

from 1st term to the second
from second to the 3rd
(and) from 3rd to the 4th

you divide the overall distance by 3 to get the average rate.

Answer 23

ohh okay one sec ill do that

Answer 24

I got:
-5
-2.5
-.125

Answer 25

ive narrowed down the choices to b and d since 10 is the first term of the sequence

Answer 26

i just don't know if the average rate of change is negative or not. i think it is because the numbers i just got are all negative

Answer 27

\(\normalsize\color{blue}{ d=\sqrt{(10-1.25)^2+(1-4)^2} \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ d=\sqrt{(8.75)^2+(-3)^2} \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ d=\sqrt{85.5625 } \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ d=9.25 \LARGE\color{white}{ \rm │ }}\)

Answer 28

\(\normalsize\color{blue}{ 9.25=9\frac{1}{4} \LARGE\color{white}{ \rm │ }}\)

Answer 29

is 9.25 the average rate of change?

Answer 30

that is the distance (in a straight line) from x=1 to x=4.

Answer 31

oh okay. but how do i determine if the average rate of change is 15/2 or -15/2?

Answer 32

@SolomonZelman

Answer 33

What do you think? is it a negative or a positive rate of change ?

Answer 34

(x → ∞, y→0 )

Answer 35

negative

Answer 36

Yes

Answer 37

yay!! thank you so much i appreciate it

Answer 38

you answer, is choice ?

Answer 39

( just to verify )