6. Expand the left side:
Recall the Pythagorean identity,
which leaves us with
Recall the angle sum formula for cosine:
which gets us to where we need to be:
and we're done.
7. A. The formulas you need are
This gives
7. B. Solving for gives
which holds for
where is any integer.
7. C. Factorize as
From here, we have
which hold for
where is any integer.
Answer:
x = 2 is the solution of the given equation
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given equation
squaring on both sides , we get
⇒ x + 2 = x²
⇒x² - x -2 =0
<u><em>Step(ii)</em></u>:-
Given x² - x -2 =0
⇒ x² - 2x + x - 2 =0
⇒ x ( x-2) + 1(x - 2) =0
⇒ (x + 1) ( x-2) =0
⇒ x = -1 and x =2
x = 2 is the solution of the given equation
<u><em>Verification</em></u>:-
Put x= 2
2 = 2
Answer:
Jim's claim is correct
Step-by-step explanation:
Total survey=100 people
Morning exercise=35 people
Afternoon exercise=45 people
Night exercise=20 people
Morning exercise : Total survey
=35 : 100
Afternoon exercise : Total survey
=45 : 100
Night exercise : Total survey
=20 : 100
Jim's claim is correct because in finding the ratio, one has to relate it with the total people involved in the survey.
Tara's claim however seems to relate one variable with two other variables
Example:
35 : 55
Morning exercise : (morning exercise + night exercise)
35 : (35+20)
35 : 55
Answer:
each band can perform 1 way assuming that they get 1 turn