So the ratio 3:9 can be added together to make twelve. Add the number set together 3 times to get 36. Now you have 3+9 3+9 3+9. 3=blue so you will need nine blue pens and 27 red pens.
Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is f
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The Jacobian for this transformation is
with determinant , hence the area element becomes
Then the integral becomes
where is the unit circle,
so that
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
Then
Answer:
Part 1)
Part 2)
Step-by-step explanation:
Part 1) What is the measure of AC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
substitute the values and solve for x
Find the measure of arc AC
Part 2) What is the measure of BC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
substitute the values
The height of the trapezoid is
Explanation:
AKLM is a trapezoid.
The measurements of the trapezoid are AK=13, LM=14, KL=5, AM=20
We need to find the height of the trapezoid.
Let M' be a point on AM that is 5 units toward point A from M.
Let B be a point on AM such that KB⊥AM. Let x = AB; then BM' = 15 -x.
Using Pythagorean theorem, we have,
--------(1)
-----------(2)
Subtracting the two equations, we have,
Simplifying, we get,
Subtracting both sides of the equation by 225, we get,
Dividing by 30, we get,
Substituting in the equation
, we get,
Thus, the height of the trapezoid is