The solution is (6, -8) (solved by graphing with Desmos.com/calculator)
The power symbols are missing.
I can infere that the product intended to simplify is (7^8) * (7^-4)., because that permits you to use the rule of the product of powers with the same base.
That rule is that the product of two powers with the same base is the base raised to the sum of the powers is:
(A^m) * (A^n) = A^ (m+n)
=>(7^8) * (7^-4) = 7^ [8 + (- 4) ] = 7^ [8 - 4] = 7^4, which is the option 3 if the powers are placed correctly.
We have to calculate the fourth roots of this complex number:
We start by writing this number in exponential form:
Then, the exponential form is:
The formula for the roots of a complex number can be written (in polar form) as:
Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.
To simplify the calculations, we start by calculating the fourth root of r:
<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>
Then, we calculate the arguments of the trigonometric functions:
We can now calculate for each value of k:
Answer:
The four roots in exponential form are
z0 = 18^(1/4)*e^(i*π/8)
z1 = 18^(1/4)*e^(i*5π/8)
z2 = 18^(1/4)*e^(i*9π/8)
z3 = 18^(1/4)*e^(i*13π/8)
Since we will be completing the square we need to isolate the x
y-5 = 2x^2 -4x
now we the coefficient of the x^2 to equal 1 so we take 2 as common factor
y-5 = 2(x^2 -2x)
now we'll make it perfect square by adding 2 to both sides
y-5+2=2(x^2-2x+1)
now simplify and convert the right side to squared expression
y-3 = 2(x-1)^2
now isolate the y
y = 2(x-1)^2 +3 that's it
Answer:
8 hours
Step-by-step explanation:
14 + 3x =38
-14 -14
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3x = 24
---- ----
3 3
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x = 8