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weqwewe [10]
3 years ago
6

Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x

Mathematics
1 answer:
PIT_PIT [208]3 years ago
5 0

Answer:

  1. x^2 = 12 y equation of the directrix y=-3
  2. x^2 = -12 y equation of directrix y= 3
  3. y^2 = 12 x   equation of directrix x=-3
  4. y^2 = -12 x equation of directrix x= 3

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

  1. x^2 = 12 y
  2. x^2 = -12 y
  3. y^2 = 12 x
  4. y^2 = -12 x

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

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(x^2−1)(3x−4)(3x+4) what is the product
Andrei [34K]

Answer:

9x^4-25x^2+16

Step-by-step explanation:

(x^2−1)(3x−4)(3x+4)=(*)

(x^2−1)((3x)^2−4^2) =

(x^2 - 1)(9x^2-16)=

x^2*9x^2 - x^2*16 - 1*9x^2 +16=

9x^4-16x^2-9x^2+16=

9x^4-25x^2+16

(*) (A-B)(A+B) =A^2 - B^2

6 0
3 years ago
Find the equation of the linear function represented by the table below in slope-
maria [59]

Answer:

y=2x+1, assuming my change in the reported data was correct.

Step-by-step explanation:

The data for x had one more entry than the values for y.  I removed the second "0" so that the x and y points line up, as shown in the attached image.  The data indicate a straight line, with a slope of 2 (y increases by 2 for every x increase of 1).  The y-intercept is 1, as per the first data point (0,1).

3 0
3 years ago
Need help
aleksandr82 [10.1K]

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

The parameters are given as follows:

\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24

Item a:

The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:

Z = \frac{X - \mu}{\sigma}

Z = \frac{984 - 959}{263}

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem:

Z = \frac{X - \mu}{s}

Z = \frac{984 - 959}{43.24}

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

8 0
2 years ago
How do you solve this??? I need it fast please help with steps.<br> (x+3)(x+1)^2(x−4)&gt;0
scZoUnD [109]

Answer:

  x < -3 or x > 4

Step-by-step explanation:

The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).

The factors tell you the following about the zeros:

  x = -3 . . . sign change from + to -

  x = -1 . . . graph touches, but no sign change. - on either side of x=-1

  x = 4 . . . sign change from - to +

__

The function will be positive for x < -3 and for x > +4.

_____

<em>Additional comments</em>

The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.

However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.

The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).

3 0
2 years ago
Please answer correctly
mrs_skeptik [129]

Answer:

y=2x-1

Step-by-step explanation:

up 2 right 1 for slope

y intercept is -1

7 0
2 years ago
Read 2 more answers
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