Answer:
MEEEE ME ME ME ME ME ME ME ME MEEEE
Let C represent the temperature in Celsius, and let F represent the temperature in Fahrenheit.
F=1.8C+32
Using that equation, plug in the numbers. F=1.8*25+32. F=77
Answer:
a) 217
b) 1351
c) 5403
Step-by-step explanation:
Given that:
confidence interval (c) = 0.95
The Z score of 
is from the z table is given as:
Range = $45000 - $30000 = $15000
The standard deviation (σ) is given as:
Sample size (n) is given as:
a) E = $500
≈ 217
b) 
≈ 1351
c) 
≈ 5403
It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
First things first, write the equations!
- Word problems can be intimidating because of all information given, so all you need to focus on, is the information about the variables you are solving, everything else, like the story line is irrelevant!
- Writing Equations from Word Problems:
pull the good stuff (information about the variables) so you can see the information needed, without having to mess your brain up with a bunch of irrelivance!
Equation 1:
3 donuts and 2 coffees is $3.94
Equation 2:
2 donuts and 6 coffees is $7.20
Now it is simply reading the equation...
Knowing these "terms" when writing Equations from a word problem is VERY IMPORTANT;
IS: =
and, more than, etc: +
less than, etc: -
Knowing the terms makes Writing the Equations THE EASIEST PART! Most of the time students get these problems wrong because of wrong equations!
So Equation 1 IS ( = ) ;)
3 Donut + 2 Coffee = 3.94
Equation 2:
2 donut + 6 coffee = 7.20
Now, to make things simple I personally find it easier to "let Donuts = d" and "let Coffee = c"
so...
3d + 2c = 3.94
2d + 6c = 7.20
in order to solve, we have to ELIMINATE one of the variables by making one of them equal 0.
I chose to eliminate c by multiplying the first equation by 3.
3 (3d + 2c = 3.94)
--> 9d + 6c = 3.94
and then the 2nd equation by -1
-1 (2d + 6c = 7.20)
---> -2d + -6c = -7.20
9d + 6c = 11.82
-2d + -6c = -7.20
--- Now we can add the 2 equations, doing so will cancel out c!
9d + 6c = 11.82
+
-2d + -6c = -7.20
= 7d + 0c = 4.62
= 7d = 4.62
now it is simple algebra to figure out d!
- you want to get d by itself so we need to get rid of the 7 and take it to the other side by division!
so-- 7d/7 = 4.62/7
= d = .66
Now that we know d, we just plug it into the original equations to find c!
- you can choose either one to plug it intl , but I chose equation 2:
2(.66) + 6c = 7.20
* MUST DO ORDER OF OPERATIONS- PEMDAS (parentheses, exponemts, multiplication, division, addition and then lastly subtraction)
so first we multiply 2 and .66
1.32 + 6c = 7.20
Now we want to get c by itself, so we subtract 1.32 by both sides-
6c = 5.88
now divide to get c
c = .98
ALWAYS CHECK
BOTH
EQUATIONS AFTER FINDING THE VARIABLES TO ENSURE YOU HAVE THE CORRECT ANSWER (:
I hope that helped (:
