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satela [25.4K]
3 years ago
10

What is the area of 71 length and 27 width of the triangle??

Mathematics
1 answer:
vazorg [7]3 years ago
8 0
The area of this triangle is 958.5 units^2
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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
Please help :( it doesnt make any sense​
melomori [17]
I’m guessing that x is the angle on the right that isn’t shown?
Anyways if that’s the case then:

We know that the sum of all the angles of a triangle add up to 180 degrees.
In this triangle we know that one angle is 55 degrees and the other is 90 degrees, so to find the last angle we do the sum of all the angles and we remove the 2 angles:

180- (55+90)= 35 degrees.

x= 35 degrees
4 0
3 years ago
-8(1 + 5b) – 2(86 – 1) = 50
kati45 [8]

Answer:

b = -57/10

Step-by-step explanation:

Let's first distribute everything out:

-8(1 + 5b) = -8 * 1 + (-8) * 5b = -8 - 40b

2(86 - 1) = 2 * 85 = 170

So, we have:

-8 - 40b - 170 = 50

-40b - 178 = 50

-40b = 50 + 178 = 228

b = -228/40 = -57/10

Thus, the answer is b = -57/10.

Hope this helps!

3 0
3 years ago
Find the output when the input x is 7
Anvisha [2.4K]
Not enough information
7 0
3 years ago
A bag contains 5 red marbles, 3 green marbles, 2 purple marbles, 2 orange marbles, and 1 blue marble.
san4es73 [151]

The answer is blue i just took the test.

7 0
3 years ago
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