P(x) = x^4 - 9x^2 - 4x + 12
P(1) = 1^4 - 9(1)^2 - 4(1) + 12 = 1 - 9 - 4 + 12 = 0
x = 1 is a root.
By dividing the polynomial by x - 1, gives other roots as 3 and -2
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:
Step-by-step explanation:
Year on is 480 dollars and year two is 960 dollars
The average would be the total yards divided by the number of carries:
Rewrite 15 3/4 as 63/4
Now divide by 7:
63/4 / 7 =
63/4 x 1/7 = 63/28 = 2 1/4
Because the total yards was a loss, which would be a negative number, the average is - 2 1/4 yards per play.
Answer:
Probability of event E = (4/10) = 0.40
Step-by-step explanation:
Note that n(E) is the number of outcomes in E
n(S) is the number of outcomes in S
And with each outcome having equal likelihood of occurring,
SetS = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
n(S) = 10
Event E = {1, 4, 7, 9}.
n(E) = 4
Probability of event E = n(E)/n(S)
Probability of event E = (4/10) = 0.40
Hope this Helps!!
