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3 years ago

What is the discontinuity of (x^2 + 3x - 4)/(x^2 + x - 12)?

2 answers:

5 0

Firstly, factorise both the numerator and denominator to simplify it.

Let y = (x^2 + 3x - 4) / ( x^2 + x - 12)

y = (x^2 + 3x - 4) / ( x^2 + x - 12)
= (x - 1)(x + 4) / (x - 3)(x + 4)
= (x - 1) / (x - 3)

Then, by long division,

(x - 1) / (x - 3) = 1 + [2 / (x - 3)]

For vertical asymptote, when y tends to infinity, (x - 3) will tend to 0. Hence, x = 3.

For horizontal asymptote, when x tends to infinity, y = 1.

zvonat [6]3 years ago

4 0

The discontinuity occurs when the denominator is equal to zero, as it has "infinite" slope, and thus is not a real value or point.

x^2+x-12

x^2+4x-3x-12

x(x+4)-3(x+4)

(x-3)(x+4)

So discontinuities occur when x=-4 and x=3

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Reva is playing a bean-bag toss game. For each bag that misses the board, the player scores -8 points. Reva misses the board 4 t

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Answer:

The answer is -32.

Step-by-step explanation:

Since there is no detailed information given about the game or the total tosses in the question, i will assume that the game is concluded when each player has had 4 tosses.

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3 years ago

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

$df=n-1=10-1=9$

Since is a one-side upper test the p value would be:

$p_v =P(t_9>10.349)=1.34x10^{-6}$

Conclusion

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3 years ago

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Firlakuza [10]

10 x 3 x 2 = the volume
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