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3 years ago

The base of a rectangular fish tank measures 18 inches long by 10 inches wide. If it is filled with 1,080 cubic

Mathematics

1 answer:

Oxana [17]3 years ago

5 0

Answer:

Volume = length x width x height

V = 18 x 8 x 12 = 1728 cm3 = 1728 ml = 1.729 liters

Step-by-step explanation:

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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

Watch help video Determine if the sequence below is arithmetic or geometric and determine the common difference ratio in simples

Helen [10]

Answer:

arithmetic

Step-by-step explanation:

common difference because -6

7 0

3 years ago

Read 2 more answers

Why do you think triangular structures are so stable?

BabaBlast [244]

They are balanced more evenly than other shapes

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3 years ago

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Having troubles with inequalities.. 3.8x + 14.5 < 32

ryzh [129]

$3,8x + 14.5 < 32\\
3,8x$

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3 years ago

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Suppose a normally distributed set of data with 4800 observations has a mean of 195 and a standard deviation of 12. Use the 68-9

Artemon [7]

Answer:

The number of observations in the data set expected to be below a value of 231 is of 4793.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 195

Standard deviation = 12

The normal distribution is symmetric, which means that 50% of the observations are above the mean and 50% are below.

Proportion of observations below 231:

231 = 195 + 3*12

So 231 is three standard deviations above the mean.

Of the 50% of observations below the mean, all are below 231.

Of the 50% of observations above the mean, 99.7% are between the mean of 195 and three standard deviations above the mean(231).

So, the proportion of observations below 231 is:

$P = 0.5*1 + 0.5*0.997 = 0.9985$

Out of 4800:

0.9985*4800 = 4793

The number of observations in the data set expected to be below a value of 231 is of 4793.

4 0

2 years ago