All categories

2 years ago

HELP Which equations represent hyperbolas?

Mathematics

2 answers:

MissTica2 years ago

7 0

An elliptical equation is in the form
Ax^2+Bx+Cy^2+Dy+E=0
the equation is a Hyperbola. When x and y are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is positive.
1-49x^2-98x-64y^2+256y-2831=0
2-4x^2+32x-25y^2-250y+589=0
3-81x^2+512x-64y^2-324y-3836=0

Hoochie [10]2 years ago

5 0

Answer: The required equations of hyperbolas would be

$49x^2-98x-64y^2+256y-2831=0\\\\4x^2+32x-25y^2-250y+589=0\\\\81x^2+512x-64y^2-324y-3836=0$

Step-by-step explanation:

Since we know that

The general equation for a conic section:

$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$

In case of hyperbola, we get that

$Discriminant=B^2-4AC>0$

According to this, both x and y are squared.

And one of the coefficient of x and y must be positive and one of the coefficient of x and y must be negative.

So, the required equations of hyperbolas would be

$49x^2-98x-64y^2+256y-2831=0\\\\4x^2+32x-25y^2-250y+589=0\\\\81x^2+512x-64y^2-324y-3836=0$

You might be interested in

Inessa [10]

Answer:

0.05, 0.5, 0.507, 0.57, 0.577

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Can i get some help :

Charra [1.4K]

Answer:

b = $\frac{7}{12}$

Step-by-step explanation:

b + $\frac{2}{3}$ = 1 $\frac{1}{4}$ ← change to an improper fraction

b + $\frac{2}{3}$ = $\frac{5}{4}$

Multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions

12b + 8 = 15 ( subtract 8 from both sides )

12b = 7 ( divide both sides by 12 )

b = $\frac{7}{12}$

5 0

2 years ago

Read 2 more answers

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hir

Ede4ka [16]

Answer:

Explained below.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}= p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

(a)

The sample selected is of size <em>n</em> = 450 > 30.

Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.

The mean and standard deviation are:

$\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{450}}=0.0204$

So, the sampling distribution of sample proportion is $\hat p\sim N(0.75,0.0204^{2})$ .

(b)

Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:

$P(p-0.04$

$=P(-1.96$

Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.

(c)

The sample selected is of size <em>n</em> = 200 > 30.

Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.

The mean and standard deviation are:

$\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{200}}=0.0306$

So, the sampling distribution of sample proportion is $\hat p\sim N(0.75,0.0306^{2})$ .

(d)

Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:

$P(p-0.04$

$=P(-1.31$

Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.

(e)

The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.

And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.

So, there is a gain in precision on increasing the sample size.

6 0

2 years ago

The radius of a cylinder is 3 cm and the height is 6 cm.

Ratling [72]

Answer

Step-by-step explanation:

A=2πrh+2πr2=2·π·3·6+2·π·32≈169.646

5 0

2 years ago

Read 2 more answers

Write a model for the statement V varies jointly as h and the fifth power of r. Group of answer choices LaTeX: V=khr^5 V = k h r

hjlf

Answer:

Option A)

$V = khr^5$

Step-by-step explanation:

We are given the following in the question:

V varies jointly as h and the fifth power of r.

$V\propto h\\V\propto r^5$

Combing the two equations, we get,

$V\propto hr^5$

Now, removing the sign of proportionality and adding the constant of proportionality, we get,

$V = khr^5$

where k is the constant of proportionality.

Thus, the correct answer is

Option A)

$V = khr^5$

7 0

3 years ago