Given the polar coordinates (4,-pi/3) which of the following rectangular coordinate pairs represents the same point?
a) (-2,2sqrt3)
b) (2,-2sqrt3)
c) (2sqrt3,-2)
d) (2sqrt3, 2)
Answers
The rectangular point that represents (4, - pi/3) is the one in option b: (2, -2√3).
How to change the coordinates?
For a point (x, y), the polar coordinates are:
R = √(x^2 + y^2)θ = atan(y/x).Then we must have:
R = 4 = √(x^2 + y^2)
Notice that for all the given points we have the radius equal to 4, so the only part that we care is the angle one:
-pi/3 = Atan(y/x)
tan(-pi/3) = y/x = -1.73
So, y and x must have different signs, and because the angle is negative, we will say that the y-component must be negative.
So the correct option will be b: (2, -2√3)
y/x = -2*√3/2 = √3 = -1.73
If you want to learn more about polar coordinates, you can read:
https://brainly.com/question/14965899
Answer: Quiz answer Unit 4 lesson 6
all answers are right
Step-by-step explanation:
1.) Given the polar coordinates (4,-pi3)which of the following rectangular coordinate pairs represents the same point?
Answer is B: (2,-2sqrt3)
2.) Given the rectangular coordinates (-5 5) which of the following polar coordinate pairs in, radians, represent the same points?
the correct option is D. (5√2,3π4)
3.)Rewrite in rectangular form: r=8 sin theta -2 cos theta.
Answer:
The equation in rectangular form is:
4.)Rewrite in polar form: x^2+y^2-6y-8=0
the Answer is B. r^2=6r sin 0+8
5.)The graph of r=-9 cos theta has which of the following characteristics?
Answer:
"circle; diameter of 9; center at (-4.5,0)"
6.)Which conic section is represented by the polar equation r=1/4-6 cos theta?
Answer:
Option 2 - Hyperbola
7.)Identify the horizontal and vertical intercepts of the limaçon represented by the equation r=7+3 cos theta ?
Answer:
vertical intercepts: (7, pi/2) and (-7, pi/2)
horizontal intercepts: (10,0) and (-4,0)
8.) Classify the limaçon represented by the equation r=1/2-1/2 sin theta.
A. Cardioid
9.)Write the equation for the graph of the rose curve.
answer C: r=9 sin 4 theta
10.) Write the equation for the graph of the lemniscate.
answer D: r^2=-49 sin 2theta
(pls don't report for me not explain it took a lot of time typing this and im just trying to help people have less stress on their shoulders :p )
Related Questions
So what are the chances of getting a 100% effort out of someone who never tries than someone who does??
Answers
Answer:
someone who doesn't try would have a lower chance of 100% effort and someone who dose try would have a much higher chance of 100% effort
Step-by-step explanation:
i hope this helps!!
Rebecca has $128 to spend. She
spends $78 on a running shoes.
Tank tops cost $12.50 each. Write and
solve an inequality to find how many
tank tops she can buy.
Answers
Answer:
12.5x =10x+10
12.50x=x10+10
subtract 10x from both sides
2.5x=10
divide by 2.5
x=4
1. Find the slope of a line
that passes through (3,-2)
and (7,5)
Answers
=7/4 is the slope
Answer:
m= [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
[tex]m=\frac{y2-y1}{x2-x1} \\\\m=\frac{5--2}{7-3} \\m=\frac{5+2}{4}\\ m=\frac{7}{4}[/tex]
First, define what equation needs to be used. We need to use the slope formula to find the answer.
Next, we substitute the x and y values into their respective places.
Last, simplify the equation!
Write the polar equation 0= pi/3
Answers
Answer:
1
(
π
3
)
)
Step-by-step explanation:
Explanation:
Substitute
tan
(
y
x
)
for
θ
tan
(
y
x
)
=
π
3
Obtain
y
x
on the left by using the inverse tangent on both sides:
tan
−
1
(
tan
(
y
x
)
)
=
tan
−
1
(
π
3
)
y
x
=
tan
−
1
(
π
3
)
Multiply both sides by x:
y
=
(
tan
−
1
(
π
3
)
)
x
Multiplication and __are inverse operations. addition subtraction O division
Answers
Answer:
Division is the opposite of multiplication
Step-by-step explanation:
Opposites:
Addition and subtraction
multiplication and division
differentiation and integration.
A teacher of a dance class collected data and created a histogram as shown.
Which statement accurately describes the information in the graph?
A.
The data describes the ages of the teachers of an art class.
B.
The data describes the ages of the students in an art class.
C.
The data describes the ages of the students in a dance class.
D.
The data describes the ages of the teachers of a dance class.
Answers
Answer:
C
Step-by-step explanation:
this was quite the toungue twister
I have a recipe to make 48 cupcakes. The recipe says that I need 8 eggs . I only need to make 12 cupcakes . how many eggs will I need
Answers
Answer:
2 eggs
Step-by-step explanation:
Use a proportion.
48 cupcakes is to 8 eggs as 12 cupcakes is to x eggs.
48/8 = 12/x
Reduce the left fraction.
6 = 12/x
Multiply both sides by x.
6x = 12
Divide both sides by 6.
x = 2
Answer: 2 eggs
18. Find the surface area of the prism.
Answers
Step-by-step explanation:
the total surface area is the sum of the individual areas on the surface.
we have
2 triangles (top and bottom)
1 front rectangle
2 rectangles in the back
the area of a triangle is
baseline × height / 2
1.7 × 0.5 / 2 = 0.425 in²
both triangles together : 2×0.425 = 0.85 in²
the area of a rectangle is
length × width
so, the front is
1.7 × 1.5 = 2.55 in²
one back rectangle is
1 × 1.5 = 1.5 in²
both back areas are 2×1.5 = 3 in²
so, the total surface area is
0.85 + 2.55 + 3 = 6.4 in²
Solve and show the answer in simplest terms 1 over 8 + 1 over 2 + 1 over 4
Answers
Answer:
7 over 8
Step-by-step explanation:
Change all the numerators over the least common denominator. 1+4+2 over 8.
Miranda's heart beats 3 times every 2 secounds. At that rate, how many times does her heart beat in 1 minute?
Answers
30 x 3 = 90
Answer is 90
100 BRAINLY POINTS!!!!!!
A cell phone company charges its customers a flat fee of $60 each month for calls and texts, plus an additional $5.00 for each gigabyte of data used. What does the y-intercept of the function represent?
A. the flat fee for calls and texts
B. the cost for each gigabyte of data used
C. the total amount of a monthly bill with 1 gigabyte of data used
D. the total amount of a monthly bill with 2 gigabytes of data used
PLS HELP CUH
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
JUST HELP ME PLSSS
Answers
Now
Equation in slope intercept form
y=mx+bIf each GB be x
y=5x+60Here
yintercept=b=60Option A is correct
The area of a rectangle is 45 m squared, and the length is 6 m less than three times the width. Find the dimensions of the rectangle.
Answers
Answer:
Step-by-step explanation:
Mrs. o'brien used a compass to draw two circles on a coordinate plane. circle a is centered at (3,-1)
and has a radius of 4 units. circle b is centered at (4, 5) and has a
radius of 3 units. select all of the
transformations that can be performed on circle a to prove that it is similar to circle b.
Answers
To prove that circle A is similar to circle B, it needs to be moved 1 unit right and 6 units up and then dilated by a scale factor of 3/4
What is transformation?
Transformation is the movement of a point from its initial location to a new location.
Types of transformation are rotation, translation, dilation and reflection.
To prove that circle A is similar to circle B, it needs to be moved 1 unit right and 6 units up and then dilated by a scale factor of 3/4
Find out more on transformation at: https://brainly.com/question/4057530
I need helppppppppppppppppppp
Answers
Answer:
See explanation
Step-by-step explanation:
look at the photo
I hope it will help you <3
Answer:
Step-by-step explanation:
*The other person that answered may be correct, but this was my way of solving the functions.
100 POINTS !!! Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11. x = 2; (2, −13) x = 4; (4, 11) x = −2; (−2, 83) x = −4; (−4, −11)
Answers
Let's see
[tex]\\ \rm\rightarrowtail y=6x^2-25x+11[/tex]
Graph attached
vertex(-2,-13)Axis of symmetry
x=-2Answer:
axis of symmetry: x = 2
vertex: (-2, 13)
Step-by-step explanation:
Given function
[tex]\sf y=6x^2-24x+11[/tex]
Vertex form
[tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Expand vertex form:
[tex]\sf \implies y=ax^2-2ahx+ah^2+k[/tex]
Compare coefficients of expanded vertex form with given function:
coefficient of [tex]\sf x^2[/tex]:
⇒ a = 6
coefficient of [tex]\sf x[/tex]:
⇒ -2ah = -24
⇒ ah = 12
⇒ 6h = 12
⇒ h = 2
constant:
⇒ [tex]\sf ah^2+k=11[/tex]
⇒ [tex]\sf 6 \cdot 2^2+k=11[/tex]
⇒ [tex]\sf 24+k=11[/tex]
⇒ [tex]\sf k=-13[/tex]
Vertex
Vertex = (2, -13)
Axis of symmetry
Axis of symmetry is when x = h
Therefore, axis of symmetry is x = 2
Solve for h.
2 < -19 - 7h
Answers
Answer:
h < -3
Step-by-step explanation:
2 < -19 - 7h
2 + 19 < -7h
21 < - 7h
21/7 < -h
bringing -h to the left
-h > 3
changing the sign to positive h
h < -3
solution set : {h < -3}
Hope that helps...
GIVING BRAINLIEST AND 30 POINTS TO BEST ANSWER!! REMEMBER, FOLLOW DIRECTIONS. YOU CAN DO IT! :D
Answers
Answer:
2 3 4 5 6 7 8 9 10
Step-by-step explanation:
even odd even odd even odd even odd even odd
A new car is purchased for $31,000 and over time its value depreciates by one half
every 6.5 years. How long, to the nearest tenth of a year, would it take for the value
of the car to be $3,800?
Answers
Using an exponential function, it is found that it would take 19.68 years for the value of the car to be $3,800.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^\frac{t}{n}[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal, after each n years.In this problem:
The initial value is of $31,000, hence A(0) = 31000.It depreciates by one-half every 6.5 years, hence r = 0.5, n = 6.5.Then, the equation is:
[tex]A(t) = A(0)(1 - r)^\frac{t}{n}[/tex]
[tex]A(t) = 31000(1 - 0.5)^\frac{t}{6.5}[/tex]
[tex]A(t) = 31000(0.5)^\frac{t}{6.5}[/tex]
The value would be of $3,800 at t for which A(t) = 3800, hence:
[tex]A(t) = 31000(0.5)^\frac{t}{6.5}[/tex]
[tex]3800 = 31000(0.5)^\frac{t}{6.5}[/tex]
[tex](0.5)^\frac{t}{6.5} = \frac{3800}{31000}[/tex]
[tex](0.5)^\frac{t}{6.5} = 0.12258064516[/tex]
[tex]\log{(0.5)^\frac{t}{6.5}} = \log{0.12258064516}[/tex]
[tex]\frac{t}{6.5}\log{0.5} = \log{0.12258064516}[/tex]
[tex]t = 6.5\frac{\log{0.12258064516}}{\log{0.5}}[/tex]
t = 19.68.
It would take 19.68 years for the value of the car to be $3,800.
More can be learned about exponential functions at https://brainly.com/question/25537936
Answer:
t≈19.7
Step-by-step explanation:
I do not have one, I apologize.
solve the equation 5.5g+9=2.5g+27
a. find the value of g.
b. explain how you can check that the value you found for g is correct. if your check does not work, does that your result is incorrect?
Answers
5.5g+9=2.5g+27
Or, 5.5g-2.5g= 27-9
Or, 3g= 18
Or, g= 18/3
Or, g= 6
Hope it helped you.. I have no doubt that it is incorrect.
The equation y=37.8xy=37.8x represents the number of miles, yy, that Julian can drive his car for every xx gallons of gas. Find the rate of change.
Answers
The rate of change of Julian given the equation y = 37.8x is 37.8
How to find the rate of changeThe equation:
y = 37.8x
where,
y = number of miles that Julian can drivex = gallons of gas used37.8 = constant = rate of changeIf x = 3 gallons
y = 37.8x
= 37.8 × 3
y = 113.4 miles
Learn more about rate of change:
https://brainly.com/question/8728504
The regular admission price to an amusement park is $28. You have a
coupon for 25% off the regular admission. Find the total cost of admission
to the park when the sales tax is 6% of the reduced price.
Answers
Answer:
$22.26
Step-by-step explanation:
To solve, all we need to do is 28(1-.25) to get 21, then we set up the equation 21(1+.03) and we get our total for the price.
we subtract in the first place, because it is a discount, and we add in the second one because it is a sales tax.
please rate and mark as brainlest.
(100 POINTS !!) Identify the vertex of the parabola.
Answers
Answer:
(-4,0)
Step-by-step explanation:
What is the slope of the line that is parallel to the line whose equation is 4x+y-2=0?
Answers
Answer:
4x+y-4=0
Step-by-step explanation: For an equation to be parallel to another all it needs is the same slope but a different y-intercept. So you can really other equations like 4x+y-3=0, 4x+y-5=0, 4x+y-6=0, etc. can be the answer to your problem.
x = y - 4
-2x + 3y= 6
Solve each system by equation
Answers
Answer:
Point form=(-6,-2)
Equation Form= x=-6, y=-2
Step-by-step explanation:
45 minutes before 10:35
Answers
Answer:
9:50
Step-by-step explanation:
Answer:
9:50
Step-by-step explanation:
Heres de answer
Henry is solving the problems 475 x 3. His first step is shown below (400 x ___) + ( 70 x ___ ) + ( 5 x ___ ) What number should Henry write in each of the blanks
Answers
Answer:
(400 × 3 ) + (70 × 3) + (5 × 3)
What is the measure of the
missing angle?
64°
97°
?
116°
O
o
78°
72°
80°
83°
Answers
Answer:
? = 83°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the angles and equate to 360°
? + 116° + 97° + 64° = 360° , that is
? + 277° = 360° ( subtract 277° from both sides )
? = 83°
Answer:
it is an obtuse angle so that should get rid of some of the answer choices
Step-by-step explanation:
Tony is flying from Los Angeles to Boston. His plane ticket costs $605 and the total flight distance is 3,052 miles. What is the cost per mile?
Answers
Answer:
AROUND $0.20 per mile
Step-by-step explanation:
605/3052 is around 0.198, which rounds to 0.20.
how much money is 1 quarter,1 dime and 1 nickle?
Answers
40 ¢
0Step-by-step explanation: 25 + 10 + 5 = 40
answer:40
Step-by-step explanation:
a quarter is 25
a dime is 10
a nickle is 5
25+10+5=40
Find the area. What type of triangle is triangle ABC?
Answers
Answer:
Isosceles right triangles are half squares, and if the length of one side is 6cm, that is the length of the other side since both segments are equal. Take the formula to find the area of a square (base times height), apply the side measurement of the triangle (6cm) and divide it in half to find the area of half of it (therefore, finding the area of the isosceles triangle.) (6x6) / 26x6 = 3636 / 2 = 18 The area of the isosceles triangle is 18 square centimeters.
Step-by-step explanation: