How many planes appear in the figure?
2 answers:
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This is the solution hope you can understand, i apologize for the bad handwriting
Hi there!
To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:
Answer: the x-intercept is (-10,0), the y-intercept is (0,45/2)
Explanation:
First, we need to determine the function describing the line.
From the table, it is obvious that the y values increase by 9 every increase of 4 of the x values. So, the slope is 9/4 and the function looks like this:
with the y-intercept (or bias) b still unknown. This can be determined by using one of the point from the table, like so:
The above function form makes it easy to read off the y-intercept, which is (0,45/2) or (0,22.5). The x-intercept is obtained by setting y = 0 and solving for x:
The x-intercept is (-10,0)