Find the term independent of x in the binomial expansion of (x^3 - 1/2x) ^12
1 answer:
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9514 1404 393
Answer:
252.8 cm²
Step-by-step explanation:
The missing side of the right triangle can be found from the Pythagorean theorem:
s² = 20² -16² = 400 -256 = 144
s = 12 . . . . cm
The area of a right triangle is more easily found using the traditional area formula:
A = 1/2bh
A = 1/2(12 cm)(16 cm) = 96 cm² (left-side triangle)
The area of the triangle on the right can be found from Heron's formula. The semiperimeter is ...
s = (16 +20 +23)/2 = 29.5
The area is ...
A = √(29.5(29.5 -16)(29.5 -20)(29.5 -23)) = √(29.5·13.5·9.5·6.5)
A = √24591.9375 ≈ 156.818 . . . . . cm² (right-side triangle)
Then the total area of the figure is ...
A = 96 cm² +156.818 cm² = 252.818 cm² . . . . total area
Answer:
Step-by-step explanation:
Let's break it down:
In the sinusoidal function :
represents Amplitude
represents a constant related to the Period
represents Phase Shift
represents Vertical Shift
To find Amplitude, divide the entire height of the function (from top to bottom) by two, or find the vertical distance between the horizontal line of symmetry and the highest/lowest point of the wave. In this case, Amplitude is 2.
To find , use
, where
is the period of the function. To find the period, count the horizontal distance of the length of one complete cycle. In this case, period is
and therefore
.
To find Phase Shift, find the horizontal shift from the parent function . In this case, there is no phase shift.
To find Vertical Shift, find the vertical shift from the parent function . In this case, vertical shift is -1.
Thus, we've found:
Substituting these values into , we get: