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Dovator [93]
2 years ago
8

Which table can be created using the equation below?

Mathematics
1 answer:
mafiozo [28]2 years ago
5 0

Answer:

h

Step-by-step explanation:

h

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Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.
inna [77]

Answer:

First part

The answer is (5 square root 2, 45°), (-5 square root 2, 225°) ⇒ answer (d)

Second part

The equation in standard form for the hyperbola is y²/81 - x²/19 = 1 ⇒ answer(b)

Step-by-step explanation:

First part:

* Lets study the Polar form and the Cartesian form

- The important difference between Cartesian coordinates and

  polar coordinates:

# In Cartesian coordinates there is exactly one set of coordinates

  for any given point.

# In polar coordinates there is an infinite number of coordinates

   for a given point. For instance, the following four points are all

   coordinates for the same point.

# In the polar the coordinates the origin is called the pole, and

  the x axis is called the polar axis.

# The angle measurement θ can be expressed in radians

   or degrees.

- To convert from Cartesian Coordinates (x , y) to

  Polar Coordinates (r , θ)

# r = ± √(x² + y²)

# θ = tan^-1 (y / x)

* Lets solve the problem

- The point in the Cartesian coordinates is (5 , 5)

∵ x = 5 and y = 5

∴ r = ± √(5² + 5²) = ± √50 = ± 5√2

∴ tanФ = (5/5) = 1

∵ tanФ is positive

∴ Angle Ф could be in the first or third quadrant

∵ Ф = tan^-1 (1) = 45°

∴ Ф in the first quadrant is 45°

∴ Ф in the third quadrant is 180 + 45 = 225°

* The answer is (5√2 , 45°) , (-5√2 , 225°)

Second part:

* Lets study the standard form of the hyperbola equation

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the y-axis is

  y²/a² - x²/b² = 1, where

• the length of the transverse axis is 2a

• the coordinates of the vertices are (0 , ±a)

• the length of the conjugate axis is 2b

• the coordinates of the co-vertices are (±b , 0)

•      the coordinates of the foci are (0 , ± c),  

• the distance between the foci is 2c, where c² = a² + b²

* Lets solve our problem

∵ The vertices are (0 , 9) and (0 , -9)

∴ a = ± 9 ⇒ a² = 81

∵ The foci at (0 , 10) , (0 , -10)

∴ c = ± 10

∵ c² = a² + b²

∴ (10)² = (9)² + b² ⇒ 100 = 81 + b² ⇒ subtract 81 from both sides

∴ b² = 19

∵ The equation is  y²/a² - x²/b² = 1

∴  y²/81 - x²/19 = 1

* The equation in standard form for the hyperbola is y²/81 - x²/19 = 1

3 0
3 years ago
What is the value of the expression below when x = 5 and y = 2?<br>X + 6y​
Vedmedyk [2.9K]
Instead of X put 5 and instead of y put 2
5+6(2)
5+12= 17
7 0
3 years ago
a cell phone company offers two different monthly plans.plan a charges $41 for unlimited cell phone minutes plus $0.10 per text
tiny-mole [99]

41+0.10x = 31+0.15x

10 +0.10x=0.15x

10=0.05x

x=10/.05

x= 200 text messages


check 200*0.10 = 20 +41 =61

200*0.15 = 30+31 = 61

 they equal each other so number of texts is 200

6 0
3 years ago
The volume of a gift box is 972 in. The height of the gift box is 12 inches
Serggg [28]

Answer:

The length of each side of the 9 in

Step-by-step explanation:

The volume of the gift box is 972 in. The height of the gift box is 12 inches

and the area of the base is 81 in².

We want to determine the length of each side of the square base if the base shape is a square.

Recall that, the area of a square is

{l}^{2}

It was given that, the area of this base is 81 in²

{l}^{2}  = 81

Take positive square root:

l =  \sqrt{81}  = 9in

5 0
3 years ago
Solve the equation :<br>-3 • ( 2 - x ) + 4 = 2 • ( 1 - 2x) + 3<br>thanks :) ​
kakasveta [241]

Isolate the variable by dividing each side by factors that don't contain the variable.

x  =  1

-6+3x+4=2-4x+3

-8+7x+1=0

7x=7

x=1

4 0
3 years ago
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