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Gala2k [10]
2 years ago
10

Shondra was unsure about what career to go into. Her high school counselor suggested a personal assessment to point out Shondra’

s interests. The assessment revealed that Shondra is very passionate about justice and making sure that people stay safe and treat each other fairly. Shondra also enjoys physical fitness and can handle risky high-pressure situations well.
Shondra would be well suited for which career cluster. Select three options.
Mathematics
1 answer:
sineoko [7]2 years ago
7 0

Answer:

lawer, Police officer criminal justice

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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
In the figure above if PQRS is a square, what is the value of a?
yanalaym [24]

Answer:

sino me quivoco es 1/53 espero aber ayudado

6 0
2 years ago
The longest side of a triangle is 5 inches longer than the shortest side. The medium side is 2 inches longer than the shortest s
Rom4ik [11]
If we refer to the longest side as x and the shortest side as y and the medium side as z then we come up with this formation:

x+y+z= 22

y is shorter than x by 5 inches so y= x-5

z is longer than y by 2 inches therefore z= x-5 +2

therefore:
x+(x-5)+(x-5+2)=22
x+x-5+x-5+2=22
3x-8=22
3x= 22-8
3x=14
x=
\frac{14}{3}

replace x in y and z in previous formations
5 0
3 years ago
How do you solve this for math -3/4÷(-8/5)
Natasha2012 [34]

Answer:

15/32

Step-by-step explanation:

(-3/4)÷(-8/5)

(-3/4)×(-5/8)

15/32

6 0
3 years ago
Alex can plant of his garden in hour. If he continues working at this rate, what fraction of Alex's garden can he plant in one h
Nookie1986 [14]

Answer:

89

Step-by-step explanation:

2 PLUS 3456 PLUS 687=32534

4 0
2 years ago
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