185 is the sum of the first part if the question
Answer:
x = {nπ -π/4, (4nπ -π)/16}
Step-by-step explanation:
It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:
cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)
= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)
= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))
= (sin(x) +cos(x))·(sin(4x) +cos(4x))
Each of the sums in this product is of the same form, so each can be simplified using the identity ...
sin(x) +cos(x) = √2·sin(x +π/4)
Then the given equation can be rewritten as ...
cos(3x) +sin(5x) = 0
2·sin(x +π/4)·sin(4x +π/4) = 0
Of course sin(x) = 0 for x = n·π, so these factors are zero when ...
sin(x +π/4) = 0 ⇒ x = nπ -π/4
sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16
The solutions are ...
x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n
Answer:
Percent of rise of a new truck on a used truck = 15%
Step-by-step explanation:
Let x be the percentage of saved money if Jason buying a used truck.
Given:
Price of the used truck = $34,000
Price of the new truck = $40,000
We need to find the percent of rise Jason saves on a used truck rather than buying a new truck
Solution:
Using a percentage formula.
Substitute Percentage cost = 34,000 and Original cost = 40,000 in above formula.
(
)
Using cross multiplication rule.
x = 15%
Therefore, Jason used 15% rise of a new truck for a used truck.
No, it’s not correct. The y-axis on the graph represents the profits p(x) so the minimum number of units produced should be when the a horizontal line at y = 590 first intersects the parabola drawn left to right, and not a vertical line at x = 590 because that represents the profit as 590 units are produced.
