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2 years ago

Which condition must be satisfied in order to use the arc length formula L = the integral from a to b of sqrt(1 + f'(x)^2) dx?

Mathematics

1 answer:

ivanzaharov [21]2 years ago

6 0

Looking through my old calc notes, I am reading that f(x) needs to be continuous on [a,b] and f ' (x) also needs to be continuous on [a,b]. Both conditions are needed. If you had to pick just one, then I'd say f(x) being continuous is much more important. Though I'm not 100% sure on this one. My thinking is that if there was any discontinuities on f(x), then the arc length would be distorted and overblown. The arc length should not account for any piece that isn't on the curve.

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What is the slope of the line that is perpendicular to the line that passes through (-2, 7) and (4, 9)? Type a numerical answer

kodGreya [7K]

Answer:

Therefore $m_{2}$ = -3.

Step-by-step explanation:

i) let us say the slope of the line passing through (-2,7) and (4,9) is $m_{1}$ .

ii) to find the slope of the line passing through two points ( $x_{1}$ , $y_{1}$ ) and ( $x_{2}$ , $y_{2}$ ) we use the formula m = $\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }$ . Therefore we can say that $m_{1}$ = $\dfrac{9 - 7}{4 - (-2)}$ = $\dfrac{1}{3}$ .

iii) let us say the slope of the perpendicular line to the line passing through (-2,7) and (4,9) is $m_{2}$

iv) from the formula for the slopes of a line and the line perpendicular to it which is given by $m_{1}$ × $m_{2}$ = -1, therefore $m_{2}$ = -1 ÷ $m_{1}$ = -3. Therefore $m_{2}$ = -3

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Tanzania [10]

Answer:

40 2/5Ibs or $40\frac{2}{5}$ lbs

Step-by-step explanation:

Let weight of object on the moon be represented = Wm

weight of object on the Earth = We

In the above question, we are told:

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5 of its weight on Earth.

Hence, mathematically, this is represented as:

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