Answer:
a transformation happen when the shape changes. There are four transformations
translation
rotation
reflection
dilation
translation, rotation and reflection do not change the shape or the size of the shape and are known as rigid motions
Tom bought 768 pounds of candy because 333 + 435 = 768
Answer:
$265.65
Step-by-step explanation:
Given :
WACC: 9.00%
Year 0 1 2 3 Cash flows (-$1,000) $500 $500 $500
The NPV is calculated thus :
Initial cashflow + Σ additional cash flows / (1 + r)
Rate, r = 9% = 0.09
(1 + r) = (1 + 0.09) = 1.09
NPV = - 1000 + (500 / (1.09)¹ + (500 / 1.09)² + (500 / (1.09)³
NPV = - 1000 + 458.71559 + 420.83999 + 386.09174
NPV = 265.64732
NPV = 265.65 (2 DECIMAL PLACES)
Answer:
Anything in the form x = pi+k*pi, for any integer k
These are not removable discontinuities.
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Explanation:
Recall that tan(x) = sin(x)/cos(x).
The discontinuities occur whenever cos(x) is equal to zero.
Solving cos(x) = 0 will yield the locations when we have discontinuities.
This all applies to tan(x), but we want to work with tan(x/2) instead.
Simply replace x with x/2 and solve for x like so
cos(x/2) = 0
x/2 = arccos(0)
x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k
x = pi + 4pi*k or x = -pi + 4pi*k
Where k is any integer.
If we make a table of some example k values, then we'll find that we could get the following outputs:
- x = -3pi
- x = -pi
- x = pi
- x = 3pi
- x = 5pi
and so on. These are the odd multiples of pi.
So we can effectively condense those x equations into the single equation x = pi+k*pi
That equation is the same as x = (k+1)pi
The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).