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Ostrovityanka [42]
3 years ago
5

Identify the graph of x^2-8y=0 for theta=90º and write and equation of the translated or rotated graph in general form.

Mathematics
2 answers:
vredina [299]3 years ago
7 0

Answer:

The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 8y = 0

∵ A = 1 , B = 0 , C =

∴ B² - 4AC = (0)² - 4(1)(0) = 0

∵ B² - 4AC = 0

∴ it will be a parabola.

∵ Ф = 90°

* The point (x , Y) will be (x' , y')

∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ

∵ cos(90) = 0 and sin(90) = 1

∴ x = -y' and y = x'

* lets substitute x and y in the first equation

∴ (-y')² - 8(x') = 0

∴ (y')² - 8x' = 0

* We notice that the x' took the place of y and y' took the place of x

∴ The parabola rotated around the origin by 90°

∴ The equation of the parabola is (y')² - 8x' = 0

* The answer is parabola, with angle of rotation 90°

* The equation is (y')² - 8x' = 0

* Look to the graph

- The blue is x² - 8y = 0

- The green is (y')² - 8x' = 0

dybincka [34]3 years ago
7 0

Answer:

the correct answer is D)

parabola

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(very urgent) will gave 20 pts
kakasveta [241]

Answer:

a. 45/1024

b. 1/4

c. 15/128

d. 193/512

e. 9/256

Step-by-step explanation:

Here, each position can be either a 0 or a 1.

So, total number of strings possible = 2^10 = 1024

a) For strings that have exactly two 1's,

it means there must also be exactly eight 0's.

Thus, total number of such strings possible

10!/2!8!=45

Thus, probability is

45/1024

b) Here, we have fixed the 1st and the last positions, and eight positions are available.

Each of these 8 positions can take either a 0 or a 1.

Thus, total number of such strings possible

=2^8=256

Thus, probability is

256/1024 = 1/4

c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string.

Also, it means there must also be exactly three 0's

Thus, total number of such strings possible

10!/7!3!=120

Thus, probability

120/1024 = 15/128

d) Following are the possibilities :

There are six 0's, four 1's :

So, number of strings

10!/6!4!=210

There are seven 0's, three 1's :

So, number of strings

10!/7!3!=120

There are eight 0's, two 1's :

So, number of strings

10!/8!2!=45

There are nine 0's, one 1's :

So, number of strings

10!/9!1!=10

There are ten 0's, zero 1's :

So, number of strings

10!/10!0!=1

Thus, total number of string possible

= 210 + 120 + 45 + 10 + 1

= 386

Thus, probability is

386/1024 = 193/512

e) Here, we have fixed the starting position, so 9 positions remain.

In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.

Thus, total number of such strings possible

9!/2!7!=36

Thus, probability is

36/1024 = 9/256

5 0
3 years ago
La media aritmética de los siguientes datos son respectivamente: 1, 4, 1, 1, 4, 2, 3, 1, 4, 2Respuesta necesaria. Opción única.
AlekseyPX

Answer:

<em>La media aritmética es 2.3</em>

Step-by-step explanation:

<u>Average o Promedio</u>

El promerio, average, o valor medio es un valor representativo de un conjunto de datos y se calcula según la fórmula:

\displaystyle \bar x=\frac{\sum x_i}{n}

Donde xi es el valor de cada dato, y n es el número de datos.

Los datos presentados son:

1, 4, 1, 1, 4, 2, 3, 1, 4, 2

Nótese que hay un total de n=10 datos. Aplicamos la fórmula recordando que el símbolo Σ significa <em>sumatoria</em>:

\displaystyle \bar x=\frac{1+ 4+ 1+ 1+ 4+ 2+ 3+ 1+ 4+ 2}{10}

\displaystyle \bar x=\frac{23}{10}=2.3

La media aritmética es 2.3

8 0
3 years ago
3x + 7 = 9x + 3<br> No solution one solution or infinite
AlexFokin [52]

Answer:

One solution.  

Step-by-step explanation:

X=2/3 or x=2.6666

4 0
3 years ago
Read 2 more answers
What is the best mechanical advantage that you can obtain for any door that you simply push open?
Komok [63]

Answer:

  2

Step-by-step explanation:

The best mechanical advantage you can get is obtained by pushing the door at its edge. If the door's center of mass is halfway from the hinge to the edge, then the advantage you get (in terms of force reduction) is ...

  1/(1/2) = 2

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3 years ago
Sketch the region R defined by 1≤ x≤ 2 and 0≤ y≤ 1/x^3
steposvetlana [31]
On the attachment, there is the graph for the region "R" and the calculations for the value a and b. 

the theory is that you have to choose a value that is between the range and assume that this value will divide the area into two equal parts. This is done for x = a

For
"y" you have to change the integral from dx to dy and you have to divide the region into 2 parts, given that the area cannot be calculated by 1 integral equation, so you proceed to calculate the rectangular area and take this area into consideration, for the same procedure as before. 

Then you calculate again the value y = b and that's it.

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3 years ago
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