Find the length of an arc of 40° in a circle with an 8 inch radius.

2 answers:

7 0

The length of an arc is the fraction of its circumference based on the given intercepted angle. This is given by the equation,
L (arc) = (Angle / 360) x 2πr
Substituting the known values,
L (arc) = (40 / 360) x 2π(8 inch) = 16π/9 inch
Thus, the length of the arc is approximately equal to 5.585 inches.

mario62 [17]3 years ago

7 0

Answer: 8π/9 plz give brainlies.

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(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or

olasank [31]

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(Missing part of the question is attached)

$L(x)=2x+3$

Estimates are too large.

Step-by-step explanation:

Suppose the only information we know about the function is:

$f(1)=5$

where the graph of its derivative is shown in the attachment

If the function $f\\$ is differentiable at point $x=1$ , the tangent line to the graph of $f$ at 1 is given by the equation:

$y=f(1) +f'(1)(x-1)$

So we call the linear function:

$L(x)=f(1) +f'(1)(x-1)$

We know the $f(1)=5$ as it is given in the question, and $f'(1)=2$ from the graph attached. Substitute in the equation of $L(x)$ .

$L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\$

At x=1, $f'(x)$ is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve $f$ . Thus, The estimates are too large.