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2 years ago

Please help 100 points if correct answer!

Mathematics

1 answer:

Alex Ar [27]2 years ago

8 0

Answer:

D. The base is a positive number greater than 1

Step-by-step explanation:

The formula for exponential growth and decay is

y =a b^x

where a is the initial value

b = 1 + the growth (or decay rate)

b will be greater than 1 if we have growth and between 0 and 1 if we are decaying

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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

2 years ago

1. John’s age is three times that of his sister. When you add John’s age to his sister's age, you get 36. How old are John and h

iren [92.7K]

Answer:

sister = 6 years

John=18 years

Step-by-step explanation:

A(S) + 12 = 3 * A(S), subtracting A(S) from both sides one gets 12 = 2 * A(S). Now dividing both sides by 2 we get A(S) = 12/2 = 6 . Therefore, the age of the sister is 6 years when her brother John is three times as old, that is 18 years.

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2 years ago

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2 please answer this question

Fittoniya [83]

B. End of the reconstruction.

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3 years ago

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A rocket is launched from a tower what time will the rocket reach its max

Lena [83]

Answer:

Step-by-step explanation:

A science class designed a ball launcher and tested it by shooting a tennis ball up and off the top of a 15-story building. They determined that the motion of the ball could be described by the function: h(t) = -16t2 + 144t + 160, where ‘t’ represents the time the ball is in the air in seconds and h(t) represents the height, in feet, of the ball above the ground at time t.

a) Graph the function h(t) = -16t2 + 144t + 160 (see below)

b) What is the height of the building?

The height of the building is also the height of the tennis ball before it is launched into the air. This occurs when t=0 so substitute 0 for t and you get:

H(0) = -16(0)2 + 144(0) + 160

The height of the building is 160 feet.

c) At what time did the ball hit the ground?

The ball hits the ground when the height is 0. Therefore, we are looking for a solution to: -16t2 + 144t + 160 = 0

Use the quadratic formula or put this into a calculator. The solution is t=10 and -1, but only 10 makes sense. Therefore, the ball hits the ground at 10 seconds.

d) At what time did the ball reach its maximum height?

You can put this into the calculator or you can realize that the maximum height is also

− the vertex. The x-value (‘t’ in this case) is 2

−144

which is (2)(−16) = 4.5.

Therefore, the ball reached its maximum height at 4.5 seconds.

e) What is the maximum height of the ball?

We calculated the time of the maximum height (4.5 seconds). Therefore, substitute 4.5 into the function to find the maximum height.

-16(4.5)2 + 144(4.5) + 160

The maximum height is 484 feet.

5 0

2 years ago

Which statement is sometimes true will give brainlist if righ and 10 extra points

arlik [135]

A rectangle is a square.

4 0

3 years ago

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