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3 years ago

While playing pool, you try to shoot the eight ball into the corner pocket.

Mathematics

1 answer:

Verdich [7]3 years ago

8 0

Answer:

Step-by-step explanation:

to go from (4, 3/4 ) to (6, 0) you need

a line with slope m= (y2-y1)/(x2-x1) = $\frac{3}{4}$ -0 / 4-6 = $\frac{3}{4} /\frac{-2}{1} =\frac{3}{4} *\frac{-1}{2} =\frac{-3}{8}$

use the quation of a line point-slope

(y-y1)=m(x-x1)

substitute m= -3/8 and (x1,y1) with (6,0)

$y=\frac{-3}{8} (x-6)$

Now does point (10,4) where is the aim is verified by this equation?

substitute x=10, y=4 in the equation to check

4= -3(10-6)/8

4= -3*4/8

4=-3/2 this is never true so you do NOT make the shot

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Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.

insens350 [35]

Answer:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

Step-by-step explanation:

Given

$p(x) = \frac{x^2-2x-3}{x+2}$ -- Missing from the question

Required

The behavior of the function around its vertical asymptote at $x = -2$

$p(x) = \frac{x^2-2x-3}{x+2}$

Expand the numerator

$p(x) = \frac{x^2 + x -3x - 3}{x+2}$

Factorize

$p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}$

Factor out x + 1

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

$x -> -2^{-}$ Say x = -3

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

$p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12$

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

$x->-2^{-}, p(x)->-\infty$

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: $x>-2$

Say x = -2.1

$p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1$

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

$x->-2^{+}, p(x)->-\infty$

So, the behavior is:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

6 0

3 years ago

Select the term that best describes the statement.. . All angles are right angles or a triangle has four sides.. 1) conjunction.

nydimaria [60]

The correct answer is:

2) disjunction.

Explanation:

A conjunction is when two statements are connected by "and." These are not, so this is not a conjunction.

A disjunction is when two statements are connected by "or." These are; this is a disjunction.

A negation is the opposite of a statement.

A conditional is an if-then statement.

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AysviL [449]

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mel-nik [20]

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miskamm [114]

x^8 ÷ x^4 · x^2
= x^4 · x^2
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4 years ago