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danessaporter
31.08.2019 •
Mathematics
Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (4, 80), and the x-axis.
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Ответ:
The required area of the region bounded by the parabola is
units.
Given that,
The parabola is bounded by
,
And tangent of the line to parabola (4,80).
We have to find,
The area of the region bounded by the parabola.
According to the question,
Parabola,![y = 5x^{2}](/tpl/images/0214/3395/17254.png)
To find the tangent line,
Differentiate the equation with respect to x,
At x = 4 slope of line tangent of parabola,
Then, the slope m = 40 .
The tangent line to this parabola at (4, 80), and the x-axis and slope m = 40.
The equation of tangent,
At point (4,80) at m = 40
y - 80 = 40(x - 4)
y - 80 = 40x - 160
y = 40x- 80
Total area of the region bounded by parabola is ,
Hence, The required area of the region bounded by the parabola is
units.
For more information about Area under Curve click the link given below.
link
Ответ:
At the point when
This line intercepts the x-axis at
To do so, first write
Now in terms of
Ответ:
7*7=49
7*8=56
7*9=63
7*10=70
7*11=77
7*12=84
7*13=91
the only number that "matches" is 84