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AleksandrR [38]
3 years ago
9

Can a real number be both rational and irrational?

Mathematics
1 answer:
Alexeev081 [22]3 years ago
8 0
Nope, it can only be one or the other
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Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x
PIT_PIT [208]

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

5 0
3 years ago
Can someone help me with this problem?
pashok25 [27]
No, it is not a solution.

Let's plug 5 into the equation where p is.

10(5) - 2 > 97

50 - 2 > 97

48 > 97

This is false, 48 is less than 97.
7 0
3 years ago
Read 2 more answers
Find the area A of polygon ABCDEFG with the given vertices.
zhuklara [117]
Ffhgfdhjehhdjdbdrvddjdbfb
5 0
3 years ago
1/5,0,-1/5,what two answers comes next?
jenyasd209 [6]
The next 2 answers are: -2/5 and -3/5
4 0
3 years ago
A steamer going downstream traveled the distance between two ports in 3 hours. The return trip took 3 hours 40 minutes. Find the
lapo4ka [179]

Answer:

1.8 mph

Step-by-step explanation:

Speed of the steamer in still water is 18 mph.

Speed of the current = x mph.

1. The steamer going downstream traveled the distance between two ports in 3 hours. Traveling downstream the current "helps" the steamer, then the speed is 18 + x mph.

The distance traveled downstream = 3(18 + x) miles.

2. The steamer going upstream traveled the distance between two ports in 3 hours 40 minutes that is 3\frac{2}{3} hours. Traveling upstream the current "interferes" the steamer, then the speed is 18 - x mph.

The distance traveled upstream 3\dfrac{2}{3}(18-x) miles.

3. The distances are the same, so

3(18+x)=3\dfrac{2}{3}(18-x)

Solve this equation:

3(18+x)=\dfrac{11}{3}(18-x)\\ \\9(18+x)=11(18-x)\\ \\162+9x=198-11x\\ \\9x+11x=198-162\\ \\20x=36\\ \\x=1.8\ mph

6 0
3 years ago
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