The two pairs of polar coordinates for the point (3, -3) when x² - y² = 4 in polar coordinates are (3√2, -45°) or (3√2, 315°) and (-3√2, 135°).
Given the Cartesian coordinate (3, -3), and the equation x² - y² = 4.To convert Cartesian coordinates to polar coordinates, we use the formula:r = sqrt(x² + y²)θ = tan⁻¹(y/x)
The first step is to substitute the given Cartesian coordinates into the formula:
r = sqrt(3² + (-3)²)r = sqrt(18)r = 3√2
To determine the angle θ, we first look at the sign of both the x and y coordinates. Since x is positive and y is negative, the angle θ is in the fourth quadrant.
To determine the angle θ, we use the formula:θ = tan⁻¹(y/x)θ = tan⁻¹(-3/3)θ = -45°Alternatively, we can add 360° to get the angle in the fourth quadrant:θ = 315°
Therefore, one pair of polar coordinates is (3√2, -45°) or (3√2, 315°).To determine the second pair of polar coordinates, we can add 180° to the angle and negate the radius,
since this will give us the same point but in the opposite direction.θ = -45° + 180° = 135°r = -3√2
Therefore, the second pair of polar coordinates is (-3√2, 135°).
To learn more about : coordinates
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Mrs. Wilson Shared 63 stickers equally among 4 girls and 5 boys.How many stickers were in each share?
Answer:
7 stickers for each kid
Step-by-step explanation:
Given the following information, find the length of the missing side. Leave your answer as a simplified radical.
Answer:
Long= [tex]2\sqrt{3}[/tex]
Step-by-step explanation:
This is a 30-60-90 right triangle, which has a special rule that would be very useful to memorize for the future. Take a look at the attached image.
From this, we can deduce that
hypotenuse=2*2=4, and
long= [tex]2\sqrt{3}[/tex]
3. The third side of a triangle measures (3x-5) cm. If the length of the midline is 14 m,
what is ?
A 8
C. 10
B. 9
D. 11
Answer:
The correct answer is D, 11 cm.
Step-by-step explanation:
Given that the third side of a triangle measures (3x-5) cm, if the length of the midline is 14 m, to determine the length of the third side and the correct option, the following calculations must be performed:
X (third side) = midline x 2
X = 14 x 2
X = 28
3X - 5 = 28
3X = 28 + 5
3X = 33
X = 33/3
X = 11
Therefore, the correct option is D: 11 cm.
What number should be added to both sides of the equation to complete the square? x^2-40x=0
Answer:
+40
Step-by-step explanation:
Answer:
400
Step-by-step explanation:
When completing the square, all you need to do is take half the coefficient of x, and square it.
In this case the coefficient of x is -40, and half of that is -20. -20 squared is 400, and that is what you need to add to both sides.
Note that when completing the square, you'll always be adding a positive number unless coefficient you're working with is an imaginary or complex number.
Jen needs to save $180 for a new camping tent. She is able to save $9 each week. How many weeks will Jen need to save to reach her goal? Write an equation to solve the problem. Explain how you found your answer.
Answer:
i got 20 weeks. i divided 180 by 9 and i got 20. i'm not sure if it's what you're looking for, but i hope it helps.
Step-by-step explanation:
Find The distance between the pair of points
G(0, - 5) and H(0, - 10
Answer:
5
Step-by-step explanation:
What value of x makes this equation true?
12x - 15 = 6 - 36
PLEASE HELP ME! I AM NOT SURE OF MY ANSWERS.
(Only correct or possible answers. I am on Edmentum.)
Answer:
Your answers are correct
guys thank you for everyone who has helped me im almost done
Answer:
y = 4
y = 7
x = 6
Hope that helps! :)
Step-by-step explanation:
Find the volume of the cylinder below. Leave your answer in terms of pi.
GEOMETRY find the angle of PRQ NO LINKS!!
Answer:
55
Step-by-step explanation:
Remark
This is a really good question to know the answer to. <PRQ = 1/2 POQ (the central angle. )
The central angle for this question is 110o. So any angle that has its vertex on the circumference is 1/2 110 = 55. The central angle and the angle on the circumference must be related as they are as this question is. (Both are on the same side of PQ which is not drawn but you can draw it).
Evaluate the expression x + 23, when x = 17
Answer:
40
Step-by-step explanation:
If we have to evaluate an expression, we spsolve for whatever variable there is, and simplify. Here, we know x is 17, so we can plug it into the original expression.
17 + 23 = 40
What is the solution to the inequality 7x + 2 < 3x + 1?
Ο Α. α
<
1
10
OB.
<
3
4
O C.
3
>
O D. I
>
- 1 금
10
Know
Answer:
x < -1/4
Step-by-step explanation:
7x + 2 < 3x + 1
4x + 2 < 1
4x < -1
x < -1/4
01:11:1
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The population, P, of six towns with time t in years are given by the following exponential equations:
(0) P - 1000(1.08)'
(ii) P-600(1.12)
(iii) P - 2500(0.9)'
(iv) P - 1200(1.185)
(V) P - 800(0.78)
(vi) 2000(0.99)
Which towns are decreasing in size?
i, ii, and iv
c. i, ii, and iii
b. iii, v, and vi
d. vi, i, and ii
a.
Please select the best answer from the choices provided
А
B
е с
D
9514 1404 393
Answer:
b. iii, v, and vi
Step-by-step explanation:
We assume your equations are intended to be P=(something) where the something has a final factor of ( )^t.
The final factor is called the "growth factor". Subtracting 1 from it gives the "growth rate". When that value is negative, the population is declining.
Equations (iii), (v), and (vi) have growth rates that are negative, so those represent towns decreasing in size.
Find the measurement indicated. Round to the nearest tenth.
9514 1404 393
Answer:
22.015.030.0°137.0°Step-by-step explanation:
These are all Law of Cosine problems. A generic expression for the length of side 'c' opposite angle C, which is defined by sides 'a' and 'b' is ...
c² = a² +b² -2ab·cos(C)
The square root of this gives the side length:
c = √(a² +b² -2ab·cos(C))
Rearranging the equation, we can obtain an expression for the angle C.
C = arccos((a² +b² -c²)/(2ab))
These two formulas are used to solve the offered problems.
__
1) AC = √(13² +14² -2·13·14·cos(109°)) ≈ √483.506
AC ≈ 22.0
__
2) BC = √(7² +10² -2·7·10·cos(123°)) ≈ √225.249
BC ≈ 15.0
__
3) ∠B = arccos((24² +28² -14²)/(2·24·28)) = arccos(1164/1344)
∠B ≈ 30.0°
__
4) ∠B = arccos((6² +9² -14²)/(2·6·9)) = arccos(-79/108)
∠B ≈ 137.0°
7. The area of a triangle is 2.1 square feet. Its base is 2 feet. What is its height
Step-by-step explanation:
area of a triangle is (bh)/2
b=base
h=height
2.1=(2h)/2
2.1=height
Hope that helps :)
Answer:
4.2
Step-by-step explanation:
Multiply 2.1 and 2 to get 4.2
Which set of shapes could you use to form a net for a
triangular prism?
O 5 triangles
О 4 triangles, 1 rectangle
O 3 triangles, 2 rectangles
O 2 triangles, 3 rectangles
Amar and his friends went to a movie at 3:55 P.M. The movie ended at 5:30 P.M.
How long was the movie?
The movie was
hour(s) and
minutes.
Amar got home 45 minutes after the movie ended.
What time did Amar get home?
Complete the explanation for how you found your answer.
You need to find
minutes after 5:30 P.M.
5:30 to 6:00 is
minutes, so 15 minutes more is
:15.
Answer: the movie was 1 hour and 35 minutes and Amar got home at 6:15 P.M.
Step-by-step explanation:
to find out how long the movie was you have to find the distance between the time frames 3:55 and 5:30.
3:55+1 hour= 4:55
4:55+5 minutes= 5:00
5:00+30 minutes= 5:30
Add the times to find how long the movie was.
This is how I found how long the movie was.
To find out when Amar got home you have to do the same thing as well.
5:30+30 minutes= 6:00
6:00+15 minutes= 6:15
Hope this helps!
Given f(x) = -x^2 - 2x + 4, find each of the following,
Symmetric point:
Minimum of f:
Maximum of f:
Is f a one-to-one
Does f have an inverse?
Increasing on
Decreasing on
Answer:
Symmetric point: x = -1; (-1, 5)
Minimum of f: None; approaches -∞.
Maximum of f: y = 5.
Is f(x) a one-to-one: No, it fails the horizontal line test and is not injective.
Increasing from: -∞ to -1; (-∞, -1)
Decreasing from: -1 to ∞. (-1, ∞)
Answer:
Given f(x) = -x^2 - 2x + 4, find each of the following,
Step-by-step explanation:
f(x) = -x²-2x+4
f(2) = (-2)²-2×2+4
f(2) = 4-4+4
f(2) = 4
Select all of the given trigonometric equations that are true statements. sin(180°) = cos(0°) cos(74°) = sin(16°) sin(20°) = cos(70°) sin(A°) = cos(90° - A°) sin(A°) = cos(180° - A°) cos(140°) = sin(40°)
Answer:
Cos 74°= Sin 16°
Sin 20°= Cos 70°
Sin A°=Cos (90°- A°)
Step-by-step explanation:
This is because the three pairs are complementary i.e they add up to 90° and in trigonometric ratios, complementary ratios are equal.
multiplicative identity
multiplication property of zero
addition property of zero
multiplicative inverse
additive inverse
communicative
reflexive
distributive
symmetric
Factor out the greatest common monomial factor from polynomial. Show your work or explain your reasoning
Answer:
7(1 +3x)
Step-by-step explanation:
The simplest monomial is a constant that is a prime number. That constant is a factor of the coefficient of the only other monomial in the expression, so it can factored from both terms.
= 7 + 7·3x
= 7(1 +3x)
NEED HELP ASAP FREE BRAINLIST
Answer:
the correct answer is 904.78 cubic. inches
Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.
Answer:
1st
Step-by-step explanation:
Two closets can store 16
chairs. How many chairs
can 8 closets store?
Answer:
64
Step-by-step explanation:
Use the distributive property to simplify 3 + 5c(2 + 6c) completely.
Answer:
Distributive property says that:
(A + B)*C = A*C + B*C
Now let's try to use it in our expression:
3 + 5*c*(2 + 6*c)
Here we can take the two terms inside the parentheses as A and B, and the term that multiplies them as C, then distributing we get:
3 + (5*c)*2 + (5*c)*(6*c)
Now remember that the multiplications are associative and commutative, then we can write this as:
3 + (2*5)*c + (5*6)*(c*c)
3 + 10*c + 30*c^2
And we can't simplify it anymore.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each division expression with the correct quotient. (These are the answers)
18x^(2)+39x+15 over 3x+5 -----> 6x+3
35x^(2)-5x-30 over 5x-5 -------> 7x+6
15x^(2)-44x+21 over 5x-3 ------> 3x-7
Answer:
18x^(2)+39x+15 over 3x+5 -----> 6x+3
35x^(2)-5x-30 over 5x-5 -------> 7x+6
15x^(2)-44x+21 over 5x-3 ------> 3x-7
Step-by-step explanation:
Plato Gang
what is one-tenth of 0.90?
Answer:
0.09
Step-by-step explanation:
Two families are saving money for a vacation. The Juarez family has saved $1000 and will save $50 more each week. The Kim family has saved $500 and will save $75 more each week. Write a system of equations to represent how much money each family will save.
Answer:
There are many ways you could put this let me demonstrate.
Step-by-step explanation:
If they were to do this for a year (52 weeks) that would be 50x52=2600+1000=3600. Then 75x52=$3900+500=$4400. but if you were to cut that time in half to 6 months it would go something like this. 50x26=1300+1000=2300. Then 75x26=1950+500=2450. It all has to do with the time. I hope this helped.
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