4 years ago

Out of 45 times at bat, Raul got 19 hits. Find Raul's batting average as a decimal rounded to the nearest thousands

Mathematics

1 answer:

svetoff [14.1K]4 years ago

3 0

Out of 45 times at bat, Raul got 19 hits. Find Rauls batting average as a decimal rounded tothe nearst thousandth.

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Use the arc length formula to find the length of the curve y = 4x − 5, −1 ≤ x ≤ 3. Check your answer by noting that the curve is

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Answer:

$4\sqrt{17}$

Step-by-step explanation:

Let's find the answer by using the arc length formula which is:

$\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^{2} } } \, dx$

First, let's find dy/dx which is:

y=4x-5

y'=4*(1)-0

y'=4, now let's use the formula:

$\int\limits^3_{-1} {\sqrt{1+4^{2}} } \, dx=\sqrt{17} *(3-(-1))=4\sqrt{17}$

Now, using the distance formula we have:

$d=\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }$

$y(-1)=4*(-1)-5=-9 \\y(3)=4*(3)-5=7$

So we have two points (-1, -9) and (3, 7) so:

$d=\sqrt{(3-(-1))^{2} +(7-(-9))^{2} }=4\sqrt{17}$

Notice both equations gave the same length $4\sqrt{17}$ .

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