Describe and correct the error in finding the distance between the points (−3 −2) and (7 4)

Mathematics

1 answer:

worty [1.4K]3 years ago

8 0

Answer:

Can u show the whole question please?

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What is the quadratic formula of #0=10x^2 + 9x-1#?

natali 33 [55]

Quadratic formula is:

$x = \frac{- b +/- \sqrt{ b^{2} - 4ac} }{2a}$

Plug in:

$x = \frac{-9 +/- \sqrt{9^{2} - 4(10)(-1)} }{2(10)}$

$x = \frac{-9 +/- \sqrt{81 + 40}}{20}$

$x = \frac{- 9 +/- \sqrt{121}}{20}$

$x = \frac{- 9 +/- 11}{20}$

$x = \frac{-9 - 11}{20}$ and $x = \frac{- 9 + 11}{20}$

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3 0

3 years ago

How do I solve this?

Verdich [7]

Consider the point P where the gears meet. When the smaller gear rotates clockwise, the larger one will rotate counterclockwise.

Through one rotation of the smaller gear, P will have traveled the circumference of the smaller gear, which is $8\pi$ in.

At the same time, a point P' on the larger gear traverses the same distance along the larger gear's circumference. This point traces out an arc that is subtended by some angle $\theta$ . The arc is as long as the smaller gear's circumference.

The measure of a circle's interior angle subtended by an arc is proportional to a complete revolution, i.e. an angular displacement of $2\pi$ radians:

$\dfrac{14\pi\,\mathrm{in}}{2\pi\,\mathrm{rad}}=\dfrac{8\pi\,\mathrm{in}}\theta\implies\theta=\dfrac{8\pi}7\,\mathrm{rad}\approx205.7^\circ$

For part 2, we apply the same reasoning to the larger gear. In one full rotation of the larger gear, the point P' traverses the circumference $14\pi$ in, and so does the point P on the smaller gear.