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2 years ago

Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

Mathematics

1 answer:

tester [92]2 years ago

8 0

Answer:

x^2/12 - y^2/4 = 1

Step-by-step explanation:

As the diretrices have simetrical values of x and have y = 0, the center is located at (0,0)

The formula for the diretrices is:

x1 = -a/e and x2 = a/e

And the foci is located at (a*e, 0) and (-a*e, 0)

So we have that:

a/e = 3

a*e = 4

From the first equation, we have a = 3e. Using this in the second equation, we have:

3e*e = 4

e^2 = 4/3

e = 1.1547

Now finding the value of a, we have:

a = 3*1.1547 = 3.4641

Now, as we have that b^2 = a^2*(e^2 - 1), we can find the value of b:

b^2 = 3.4641^2 * (1.1547^2 - 1) = 4

b = 2

So the equation of the hyperbola (with vertical diretrices and center in (0,0)) is:

x^2/a^2 - y^2/b^2 = 1

x^2/12 - y^2/4 = 1

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A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is 14 1/2 fe

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The net change in elevation is 72.5 feet

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2 years ago

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The value of a car is 18,500. It loses 10.3% of its value every year. Find the approximate monthly decrease in value. Round your

valentina_108 [34]

Answer:

$158.8

Step-by-step explanation:

There are 12 months in 1 year.

If in 1 year, it looses value of 10.3%, so in a month it will loose value of:

10.3%/12 = 0.8583% per month

So, to find the decreased value (in dollars) per month, we got to find 0.8583% of 18,500 dollars.

First, we need to convert percentage to decimal by dividing by 100. Then we multiply that to 18,500 to get our answer. So:

0.8583% = 0.8583/100 = 0.008583

Now,

0.008583 * $18,500 = $158.7855

Rounded to nearest tenth (1 decimal pae) = $158.8

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2 years ago

A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first sta

Akimi4 [234]

Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of women who find success with this new treatment = $\frac{7}{14}$ = 0.50

n = sample of women = 14

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the true proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ , $0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ ]

= [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

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2 years ago

A student estimates the weight of astronauts on the moon by multiplying their weight by the decimal 0.16666....what fraction can

Elden [556K]

Let $x = 1.66666...$ ....(1)

Multiply both sides of equation (1) by 10.

$10x = 1.666666....$ .... (2)

Multiply both sides of equation (1) by 100.

$100x = 16.66666....$ ... (3)

Subtract equation (2) from equation (3)

$100x - 10x = 16.66666...- 1.66666...$

$90x = 15$

$x= \frac{15}{90} = \frac{1}{6}$

Hence, the required fraction form is $\frac{1}{6}$ .... Answer.

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2 years ago

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For which function does f decrease by 15% every time x increases by 1

LenaWriter [7]

Answer:

$f(x) = 0.85^{x}$

Step-by-step explanation:

The exponential function that decrease by 15% every time x increases by 1 is given by:

$f(x) = {(1 - 0.15)}^{x}$

We simplify the parenthesis to get:

$f(x) = 0.85^{x}$

Therefore the decrease by 15% every time x increases by 1 is

$f(x) = {0.85}^{x}$

The second choice is correct.

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2 years ago