Answer:
x = 13
Step-by-step explanation:
Note that the side length x is opposite of the right angle, which means that it is the hypotenuse, which will usually be denoted as c.
Set the equation:
a² + b² = c²
let:
a = 5
b = 12
c = x
Plug in the corresponding numbers (& x) to the corresponding variables:
(5)² + (12)² = (x)²
Simplify. First, solve for the power, and then add:
x² = (5²) + (12²)
x² = (5 * 5) + (12 * 12)
x² = 25 + 144
x² = 169
Next, root both sides of the equation:
√x² = √169
x = √169 = √(13 * 13) = 13
x = 13
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Note the rules, and it should be easier:
30-60-90° = 1 , √3 , 2
45-45-90° = 1 , 1 , √2
Any other measurements use the equation: a² + b² = c²
Answer:
7. Mean = 48
Median = 47.5
Mode = 72
Range = 66
8. Mean= 59.625
Median = 61
Mode = 90
Range = 79
9. Mean = 31.57
Median = 32
Mode = 46
Range = 34
10. Mean = 42.11
Median = 36
Mode = 51
Range = 51
Step-by-step explanation:
Mean is the average. Mode is the number that appears the most. Median is the middle number. Range is the biggest number minus the smallest number.
Hope this helps.
Replace x with π/2 - x to get the equivalent integral
but the integrand is even, so this is really just
Substitute x = 1/2 arccot(u/2), which transforms the integral to
There are lots of ways to compute this. What I did was to consider the complex contour integral
where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be
which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit
and it follows that
The coordinate (5,-6) lies in the fourth coordinate, because the first is x positive y positive, the second is x negative and y positive, the third is x negative and y negative, and the fourth is x positive y negative. This is x positive y negative, so it is in the fourth quadrant.
