Answer:
Infinite many solutions
Step-by-step explanation:
All real numbers
The total cost for plumber number 1 expressed as a function of x is
c1(x)=45x+90
That is, the charge per hour times the number of hours plus the fixed charge for a visit.
Using the same pattern, write the function for the second plumber. Then set the two functions equal to each other and solve for
(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)
… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)
… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))
… = (2 - 2√3 <em>i</em> ) / 4
… = 1/2 - √3/2 <em>i</em>
… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))
… = exp(<em>i</em> arctan(-√3))
… = exp(-<em>i</em> arctan(√3))
… = exp(-<em>iπ</em>/3)
By DeMoivre's theorem,
[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1
Answer:
a) y = 2x +4
b) y = 1/2x +4
c) y = -2x +11
Step-by-step explanation:
The given equations are in slope-intercept for, so we can read the slope directly from the equation. It is the x-coefficient.
We can then write an equation of a parallel line using the point-slope form of the equation of a line:
y -k = m(x -h) . . . . for a line with slope m through point (h, k)
If you like, you can rearrange this to "slope-intercept" form. Add k and simplify.
y = mx +(k -mh)
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a) m = 2, (h, k) = (3, 10)
y = 2x +(10 -2·3)
y = 2x +4
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b) m = 1/2, (h, k) = (0, 4)
y = 1/2x +(4 -(1/2)·0)
y = 1/2x +4
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c) m = -2, (h, k) = (4, 3)
y = -2x +(3 -(-2)(4))
y = -2x +11
Conversion from degree to radian ~
Conversion from radians to degree ~
