Hi there!
We are given:
cos(7x)cos(4x) = -1 - sin(7x)sin(4x)
Begin by moving all terms with variables to one side:
cos(7x)cos(4x) + sin(7x)sin(4x) = -1
The corresponding trig identity is cos(A - B). Thus:
cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1
cos(3x) = -1
cos = -1 at π, so:
3x = π
x = π/3
We can also find another solution. Let 3π = -1:
3x = 3π
x = π
Thus, solutions on [0, 2π) are π/3 and π.
Answer:
(in step-by-step explanation)
Step-by-step explanation:
The ratio x:y is the same as the fraction x/y if that helps, so it is basically putting the coordinates into a fraction. Here is a video that might help also: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-ratio-word-problems/v/ratios-on-coordinate-plane
Coordinate planes are a way of expressing data, so if it makes it easier, put the data into a ratio! Sorry, it is a bit difficult to explain such a broad question.
Answer:
$ 0.34 or 34 cents
Step-by-step explanation:
Bill amount = $31.18
sales tax = 6% of $31.18
= 0.06 ($31.18)
= $1.8708
Bill with tax = $31.18+$1.8708
= $33.0508
value of tip = 20% of 33.0508
= 6.61016
Total payment = 33.0508+ 6.61016
= $39.66096
or $39.66
We get change of $40 - $39.66
= $ 0.34
We shall get back in cents that will be 34 cents
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