1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tanzania [10]
2 years ago
13

Please help and thank you!

Mathematics
1 answer:
Lynna [10]2 years ago
6 0

Since polar coordinates are made up in this way

(r, \theta )

we need to solve for r and then find the angle. In our rectangular coordinate given,

(-4,-4\sqrt{3})

x = -4 and y=-4\sqrt{3}

We will use this fact to first find the angle then r, which might seem backwards but I am going to do it in this order. The formula to find the angle measure uses the tangent identity

tan\theta=\frac{y}{x}.

Filling in our y and x from the rectangular coordinate we have

tan\theta=\frac{-4\sqrt{3}}{-4} or

tan\theta =\frac{\sqrt{3}}{1}.

The tangent identity is the side opposite the reference angle (theta) over the side adjacent to it. Since in our rectangular coordinate both x and y are negative, we will be in QIII where x and y are negative. The side across from the reference angle is the square root of 3, which should tell us at this point in our math careers that the reference angle is a 60 degree angle. But in the third quadrant, the angle is 180+60 which is 240 degrees. Converting that to radians we get \frac{4\pi}{3}. That's our angle. In order to solve for r now, we will need the cosine of that angle. In our 30-60-90 right triangle we can solve for the length of the missing side which is the hypotenuse. If our Pythagorean triple is

(x, x\sqrt{3},2x)

and x = -4, then the length of the hypotenuse is 2(-4) which is -8 but since a hypotenuse is never negative, it's just 8. That's also the value for r! That means that the polar coordinates that are the same as the rectangular ones we were given are

(8,\frac{4\pi}{3})

first choice above.

You might be interested in
Can someone please help me I really need help it’s my last question
Svetach [21]

Answer:

x^2+11x+30

Step-by-step explanation:

This is a parallelogram.

Area of a parallelogram can be found with:

A=bh

Plug our values in.

A=(x+6)(x+5)

FOIL-

First: x*x=x^2

Outside: x*5=5x

Inside: 6*x=6x

Last: 6*5=30

x^2+5x+6x+30

Combine like terms.

x^2+11x+30

7 0
2 years ago
The points (-5, -6) and (-8, 9) fall on a particular line. What is its equation in point-slope
Lyrx [107]

Answer:

y = 1m - 1

Step-by-step explanation:

6 0
3 years ago
The following graph describes function 1 and the equation below it describes function 2:
Tanya [424]
Function 1: 
f(x) = -x² + 8(x-15)f(x) = -x² <span>+ 8x - 120
Function 2:
</span>f(x) = -x² + 4x+1
Taking derivative will find the highest point of the parabola, since the slope of the parabola at its maximum is 0, and the derivative will allow us to find that.
Function 1 derivative: -2x + 8 ⇒ -2x + 8 = 0 ⇒ - 2x = -8 ⇒ x = -8/-2 = 4

Function 2 derivative:  -2x+4 ⇒ -2x + 4 = 0 ⇒ -2x = -4 ⇒ x = -4/-2 ⇒  x= 2
Function 1: f(x) = -x² <span>+ 8x - 120 ; x = 4
f(4) = -4</span>² + 8(4) - 120 = 16 + 32 - 120 = -72
<span>
Function 2: </span>f(x) = -x²<span> + 4x+1 ; x = 2
</span>f(2) = -2² + 4(2) + 1 = 4 + 8 + 1 = 13

Function 2 has the larger maximum.
8 0
3 years ago
There is a bag with 50 popsicles inside. 5
Allisa [31]

Answer:

25%

Step-by-step explanation:

We know that there are ten purple popsicles. Together without the purple popsicles, there are 40 popsicles in total. Therefore there is a 10/40 chance to get purple. We need to turn this into a percentage so we do (10 / 40) x 100. This would equal to 25%, therefore, there is a 25% probability to get a purple popsicle.

8 0
2 years ago
What number is less than -2 4/5 and greater than -31/5
IgorC [24]

Using a calculator, you should find that

-2 & 4/5 = -(2 + 4/5) = -(2+0.8) = -2.8

-31/5 = -6.2

So the unknown number is between -6.2 and -2.8

<h3>Possible whole number answers could be: -6, -5, -4, -3, or -2</h3>

If your teacher allows decimal answers, then there are infinitely many possible ways to answer.

8 0
3 years ago
Other questions:
  • How many 5 digit numbers are there whose digits sum to 39?
    13·2 answers
  • What’s the answer to 3/4 +5/8
    7·1 answer
  • Which graph represents a quadratic function with a vertex at (0,0)
    7·1 answer
  • Sarah takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut she makes is
    11·1 answer
  • 1. 35,12 2. 24,5 3. 10,14???
    7·1 answer
  • What is 6s + 18t + 3w =
    10·1 answer
  • PLS I REALLY NEED HELP HEL HELP HELP HELP HELP
    13·2 answers
  • If T is the centroid of ∡MNP, TN = 16, MQ = 23, and RP = 18, find each missing measure.
    15·1 answer
  • I neeeeee helpppp asappppppp
    12·1 answer
  • The homeowners association for a residential community is selecting a committee of 7. There are 24 candidates for positions. How
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!