Identify the polar coordinates for each value in the table below, discuss the shape and behavior of the graphs, and use this to graph the equation of r=2 cos〖3θ.〗
Symmetry hint: see if the equation is true for the following:
the line θ = 90°: replace (r, θ) with (r, 180° – θ) or (-r, -θ)
the polar axis: replace (r, θ) with (-r, 180° – θ) or (r, -θ)
the pole: replace (r, θ) with (r, 180° + θ) or (-r, θ)
Answers
Answer:
we know that
the relationship between the 2-dimensional polar and Cartesian coordinates is
r = √(x² + y²)
Θ = tan⁻¹ (y/x)
so
Part a) (2, −2)---------> this point belong to the IV quadrant
r = √(x² + y²)------ r = √(2² + (-2)²)-----> r=√8
Θ = tan⁻¹ (y/x)---- Θ = tan⁻¹ (2/2)----> 45°
remember that the point belong to the IV quadrant
so
Θ=360-45-----> Θ=315°
the answer part A) is
(r,Θ)=(√8,315°)
Part b) (-1, 3)---------> this point belong to the II quadrant
r = √(x² + y²)------ r = √(-1² + (3)²)-----> r=√10
Θ = tan⁻¹ (y/x)---- Θ = tan⁻¹ (3/1)----> 71.57°
remember that the point belong to the II quadrant
so
Θ=180-71.57-----> Θ=108.43°
the answer part B) is
(r,Θ)=(√10,108.43°)
mark me branlest plz hope it helps
The answers are a) (r,θ) = (√8,315°) and b) (r, θ) = (√10,108.43°).
The relationship between the 2-dimensional polar and Cartesian coordinates is
r = √(x² + y²)
θ = tan⁻¹ (y/x)
so,
A) (2, −2 belongs to the IV quadrant,
r = √(x² + y²)
r = √(2² + (-2)²
r=√8
θ = tan⁻¹ (y/x)
θ = tan⁻¹ (2/2)
= 45°
The point belongs to the IV quadrant,
so,
θ = 360-45
θ = 315°
Therefore,
(r,θ) = (√8,315°)
B) (-1, 3) belong to the II quadrant,
r = √(x² + y²)
r = √(-1² + (3)²)
r = √10
θ = tan⁻¹ (y/x)
θ = tan⁻¹ (3/1)
= 71.57°
The point belongs to the II quadrant ;
so,
θ = 180-71.57
θ = 108.43°
Therefore,
(r, θ) = (√10,108.43°)
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Related Questions
Janet saved $3500 in 2007. If each year after
this she saves $750 more than the year before,
how much will she save in 2012?
(A) $5750
(B) $6500
(C) $7250
(D) $8000
(E) $8750
Answers
Answer:
7250
Step-by-step explanation:
The equation would be as follows
3500+750x=y
Between 2012 and 2007, there are 5 years, thus x=5
3500+750(5)=7250
What is the value of y
Answers
Answer:
42
Step-by-step explanation:
We know that in the triangle, there are 3 values. 2 of them are y and 1 of them is unknown.
So, in order to find the value of the unknown number, they gave us an angle supplementary to the unknown.
Supplementary angles are angles that add up to 180 degrees. So the equation for that would be x+88=180.
By subtracting from both sides, we get x=92. So, the unknown angle is 92.
To solve for y, we have to do the same thing, but since we have 2 y's the equation will be 2y+92=180. (92 is the interior angle, aka the unknown one)
Solve: -92 -92
2y=88
/2 /2
y=42
Hence, y is equal to 42.
(edit: sorry they don't line up correctly)
Which expression is equal to 20.92 ÷ 6.8?
A
209.2 ÷ 6.8
B
2.092 ÷ 68
C
2092 ÷ 68
D
209.2 ÷ 68
Answers
Answer:
D
Step-by-step explanation:
They both equal 3.08
The decimal is moved one to the right on both so the answer will be the same
Answer:
D. 209.2 ÷ 68
I hope this helps!
solve using substitution.
2x-3y
x+y=9
just so you know, I know the answer its (3,6). I just need the explanation on how to get that answer using substitution.
Answers
Answer:
(3,6)
Step-by-step explanation:
2x-3y = -12
x+y=9. Solve for either y or x
-x. -x
y = -x + 9. Substitute this for the y
2x-3(-x+9)= -12
2x +3x-27 = -12. Add like terms
5x -27 = -12
+27. +27. Inverse operations
5x = 15
÷5. ÷5
x = 3
x + y = 9
3 + y = 9. Substitute 3 for x
-3. -3. Inverse operations
y = 6
What is the volume of the cylinder below?
A. 256 units 3
B. 1024 units 3
C. 64x units 3
D. 128 units 3
Answers
Answer:
A 256 units 3
Step-by-step explanation:
The volume of the cylinder given below is 256π units .
Given,
Radius of cylinder = 8 units
Height of cylinder = 4 units
Now,
Volume of cylinder is given by
V = π×r²×h
r = radius of base
h = height of cylinder
So,
Substitute the values in the formula,
V = π × 8² ×4
V = π × 64 × 4
V = 256π units .
Thus the volume of the cylinder is 256π units .
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Solve for x rounded to the nearest tenth.
sin 52 =x/7
Answers
Answer:
6.9
Step-by-step explanation:
sin(52)=x
x=7sin(52)
Which statements are true?
Select each correct answer.
All parallelograms are quadrilaterals.
All rectangles are squares.
All rhombuses are rectangles.
All squares are rhombuses.
Answers
Answer:
All rectangles are squares, All parallelograms are quadrilaterals,
Answer:
all squares are rhombuses, all parallelograms are quadrilaterals
Step-by-step explanation:
this is what is true
Which polygons are similar?
Answers
What is the volume of a cylinder, in cubic meters, with a height of 5 meters and a base
diameter of 6 meters? Round to the nearest tenths place.
Answers
Answer:
the answer is 141.3 cubic meters ( if you use 3.14 for pi)
Step-by-step explanation:
the volume equation of a cylinder is
V= π[tex]r^{2} h[/tex]
we have to change the 6 meters to 3 meters because the equation for the volume of a cylinder wants the radius not the diameter
V= 3.14 × [tex]3^{2}[/tex] × 5
that equals 141.3
Answer:
141.4 meters3
Step-by-step explanation:
h\hspace{3px}=\hspace{3px}5\hspace{30px}d\hspace{3px}=\hspace{3px}6
h=5d=6
identify variables
r=
r=
\,\,3
3
radius is half of the diameter
V=
V=
\,\,\pi r^2h
πr
2
h
use volume of a cylinder formula
V=
V=
\,\,\pi(3)^2(5)
π(3)
2
(5)
substitute variables into formula
V=
V=
\,\,141.371669412
141.371669412
multiply
V=
V=
\,\,141.4\text{ meters}^3
141.4 meters
3
round to the nearest tenths place
Please give me the answer
Answers
Answer:
37°
Step-by-step explanation:
As we know the sum of angles of a triangle is 180 degrees.
Therefore,
angle A + angle B + angle C = 180°
In the given picture two angles are given and we have to find out the third angle.
x° + 45° + 98° = 180°
x° + 143° = 180°
x° = 180° - 143°
x° = 37°
The value of x in the triangle shown is 37°.
Tom likes to go over to his friend's house almost every night to play video games. They usually spend 3 hours a night playing the video game together. Last week, they spent a total of 15 hours playing the video game. If Tom went over every night, he would spend 21 hours playing the video game. Also, Tom's friend's mom gives Tom two cookies each time he is there. How many cookies does Tom get last week?
Answers
Answer:
it is 10
Step-by-step explanation:
Answer:
he got ten cookies because since they play for 3 hours a night you do 15/3 to get 5 nights. since his friends gets 2 cookies everyday he is there 5*2 is 10 cookies last week
Step-by-step explanation:
i was reading this i was like what do the video games have to do with it
3. Give two systems of equations that would be easier to solve by substitution
than by elimination. Then give two systems that would be easier to solve with
elimination. Finally, explain how you decide whether to use elimination or
substitution to solve a system.
Answers
Answer:These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
explanation Step-by-step explanation:ust to add a bit more information, "Elimination" Can have a variety of other interpretations. Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.' Do not worry if you have not heard of these terms. They are used in Linear Algebra when referring to "Elimination techniques"
Just to add a bit more information, "Elimination" Can have a variety of other interpretations. Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.' Do not worry if you have not heard of these terms. They are used in Linear Algebra when referring to "Elimination techniques"
Gaussian Elimination
Gauss-Jordan Elimination
LU-Decomposition
QR-Decomposition
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
Substitution is the preferred method for 2 equations in 2 unknowns. The constants are unimportant other than having a non-zero determinant. It is always easy to find multiplicative factors using LCMs of one variable or the other to allow substitution into the other equation:
Example:
4X + 5Y = 9
5X - 4Y = 1
Notice that 20 is a LCM of either the X or Y variable. So multiply the first by 4 and the second by 5 and then adding the two (Y's will drop out allowing for substitution)
4(4X + 5Y = 9)
5(5X - 4Y = 1)
Multiplying to produce the LCM factors:
16X + 20Y = 36
25X - 20Y = 5
Adding the equations
41X = 41
X = 1
Substitution into either equation yields
Y = 1
Simplify the expression.
4 (2m – 6) – 3p – 2m + 8
Answers
-------------------------------------------------------------------
4 (2m – 6) – 3p – 2m + 8
Expand 4 (2m – 6):
8m - 24– 3p – 2m + 8
Simplify 8m - 24– 3p – 2m + 8:
Group like terms:
8m - 2m - 3p - 24 + 8
Add similar elements:
6m - 3p - 24 + 8
Add subtract the numbers:
6m - 3p - 16
Your Answer Is 6m - 3p - 16
plz mark me as brainliest if this helped :)
PLEASE HELP I REALLY NEED IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Last year, the school library had a total of x books. Over the summer, the library acquired another 37 books and now has a total of 1,950 books. Which equation could be used to find x, the number of books the library had last year?
A.
1,950 + x = 37
B.
x + 37 = 1,950
C.
x - 37 = 1,950
D.
37x = 1,950
Answers
Answer: the answer is B
Step-by-step explanation:
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯¯ ? Round to the nearest hundredth. Enter your answer in the
Answers
Answer:
RT = 9.200 cm
Step-by-step explanation:
[tex]RT = \sqrt{ {11}^{2} - {6}^{2} } \\ RT = \sqrt{121 - 36} \\ RT = \sqrt{85} \\ RT = 9.219 \: cm \\ RT = 9.200 \: cm[/tex]
Help asap . thank youu
Answers
Answer:
yes
look at each one of the sides
the x row counts by 1
1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4
the y row counts by 2
3 + 2 = 5, 5 + 2 = 7, 7 + 2 = 9
( Hope this helps :D)
Please answer. Question in picture.
Answers
Ans
Step-by-step explanation:
i will mark brainliesttt!
Answers
Answer:
d = 52
Step-by-step explanation:
The two angles form a straight line so they are supplementary
Supplementary angles add to 180
d+128 = 180
Subtract 128 from each side
d+128-128 = 180-128
d = 52
Answer:
52
Step-by-step explanation:
so to solve this one, you have to get the value of d.
for this you need to first subtract the given angle from 180.
180-128=52
that is the value of d :) if u need any more help post a question, ill follow you!
In a relay race, Nancy ran her part in 15.25 seconds, John ran his part in 13.8 seconds, Sylas ran his part in 16.4 seconds. What wasthe total time for the three runners
Answers
Answer:45.45
Step-by-step explanation:
First add 15.25 and 13.8 together and with hat answer then you will go ahead and add the answer and 16.4 together and that will give you your total hope this helps
An artist can sell 20 copies of a painting at $100 each, but for each additional copy he makes, the value of each painting will go down by a dollar. Thus, if 22 copies are made, each will sell for $98. How many copies should he make to maximize his sales?
Answers
Answer:
40 more paintings in order to maximize sales making a total of 60 paintings
Step-by-step explanation:
Let x= no.of copies above 20
Total Sales(x) = (number of copies)(price per copy)
Sales (x)= (20 +x)(100 –x)
Open bracket
=1200-20x+100x-x^2
=1200+80x-x^2
Derivative of the sales
80-2x=0
80=2x
Divide both sides by 2
40=x
Because Sales(x)= –2, this is maximal by the second derivative test
The artist should make 40 more paintings in order to maximize sales making a total of 60 paintings.
The artist 60 copies should he make to maximize his sales
The artist can sell 20 copies at $100 each.
So, the total sales is:
Total =(20) * (100)
For each additional copy he makes, the value of each painting reduce by a dollar.
So, the total sales becomes
Total = (20 + x) * (100 - x)
Rewrite as:
[tex]y = (20 + x) * (100 - x)[/tex]
Expand
[tex]y = 2000 - 20x + 100x - x^2[/tex]
Evaluate the like terms
[tex]y = 2000 +80x - x^2[/tex]
Differentiate
[tex]y' = 80 - 2x[/tex]
Set to 0
[tex]80 - 2x = 0[/tex]
Collect like terms
[tex]- 2x = -80[/tex]
Divide both sides by -2
[tex]x = 40[/tex]
Recall that the initial copies is 20.
So, the new copies would be:
New = 20 + 40
New = 60
Hence, the artist 60 copies should he make to maximize his sales
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What is the shape of the cross section of the figure that is perpendicular to the rectangular base and passes through the top vertex of the figure? A rectangular pyramid. a parallelogram that is not a rectangle a rectangle a triangle that must have the same dimensions as one of the faces a triangle that does not have the same dimensions as one of the faces
Answers
Answer:
D
Step-by-step explanation:
The figure is a rectangular pyramid. The cross section is perpendicular to the rectangular base and passes through the top vertex of the figure. A triangle that does not have the same dimensions as one of the faces is formed. The sides of the new triangle are the heights of the triangles on the faces of the pyramid, and that is why their dimensions are different.
Answer:
d
Step-by-step explanation:
Chris collected $25.65 for a fundraiser. Remy collected $15.87 more than Chris. Sany collected 3 times as much as Remy. How much did Sandy collect for the fundraiser?
12 points please help it's for a quiz
Answers
Answer:
47.61$
Step-by-step explanation:
hope this helps please give me brainiest
25 points and brainly please help quick
Doug records how many miles and how long he rides his bike each day on a scatter plot.
Doug analyzes his data on the scatter plot and concludes that the more time he rides his bike, the slower his speed is. In two or more complete sentences, explain why or why not it is possible for Doug to make his conclusion based on his data.
Answers
Answer:
the plot shows he had a speed of 0.20 miles but the longer he travels the slower he gets, so his last speed is 0.17 miles a minute
Step-by-step explanation:
what is the value of z for the equation 1/2z = -3/4 + 1/4z?
-3
-1
1
3
Answers
Answer:
z= -3
Step-by-step explanation:
[tex]\frac{1}{2} z[/tex] = [tex]\frac{-3}{4} + \frac{1}{4} z[/tex]
[tex]\frac{1}{2} z - \frac{1}{4} z[/tex] = [tex]\frac{-3}{4}[/tex]
[tex]\frac{2z - z}{4} = \frac{-3}{4}[/tex]
[tex]\frac{z}{4} = \frac{-3}{4}[/tex]
4z = -3×4
4z = -12
[tex]\frac{4z}{4} = \frac{-12}{4}[/tex]
z = -3
Hope this helps!!!
The value of z in the equation (1/2)z = - 3/4 + (1/4)z is 3/2.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
given, (1/2)z = - 3/4 + (1/4)z and we have to find the value of z or solve for z.
∴ (1/2)z = - 3/4 + (1/4)z.
(1/2)z - (1/4)z = 3/4.
(1/2)z = 3/4.
z = (3/4)×(2/1).
z = 6/4.
z = 3/2.
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Please help image below with question
Answers
Answer:
1/3
Step-by-step explanation:
F = 36
G = 4
We know that The area is multiplied by the scale factor squared
F * (SF) ^2 = G
36 (SF) ^2 = 4
Divide each side by 36
36/36 (SF) ^2 = 4/36
(SF) ^2 = 1/9
Take the square root of each side
sqrt((SF)^2) = sqrt(1/9)
SF = 1/3
The scale factor is 1/3
explain how finding the volume of a cylinder is similar to finding the volume of a prism
Answers
Answer:
Finding the volume of a cylinder is similar to finding the volume of a prism because they share the same formula, that is:
V = base area x height
Hope this helps!
:)
Answer:
Volume of a prism is base area × height
Base of a cylinder is a circle,
Base area = pi× r²
Volume of cylinder = pi × r² × h
Which is the same as base area × height
Anna drives 15,500 miles a year for work. On average, how many miles does she drive a week?
Answers
Answer:
206 miles
Step-by-step explanation:
People generally work 5x a week so.. (15000 / 52)
52 indicates the amount of weeks in a year.
In total, that is 288.4 miles a week. Now, we're assuming she doesn't work on the weekend so we divide 288.4 by 7. That is 41.2 miles a day. Now, you times 41.2 by 5 and your answer should be 206 miles a week.
Approximate the real zeros of f(x)= x^4 -5x^3 +6x^2 -x -2 to the nearest tenth
Answers
Answer:
The zeros are approximately -0.433 and 3.352
Step-by-step explanation:
The easiest way to find the real zeros of a polynomial is to plot it and check where y = f(x) = 0. In the picture attached, the plot of f(x)= x^4 -5x^3 +6x^2 -x -2 is shown. Only two real zeros were found.
Answer:
it’s b
Step-by-step explanation:
you’re welcome
What is the distance from the right center field fence to third base? Show all of your work and round
your answer to the nearest tenth of a foot
Answers
Answer:
[tex]381.5\,\,\,ft[/tex]
Step-by-step explanation:
Given: Figure
To find: distance from the right center field fence to third base
Solution:
In a right angled triangle,
using Pythagoras theorem, square of hypotenuse is equal to sum of squares of base and perpendicular.
In ΔBAC,
[tex]BC^2=AB^2+AC^2\\(392)^2=x^2+(90)^2\\153664=x^2+8100\\153664-8100=x^2\\145564=x^2\\\sqrt{145564}=x\\381.5\,\,\,ft=x[/tex]
So,
distance from the right center field fence to third base is 381.5 foot.
The following equation f(x) = x³ + 0.5x² + 4.5 has only 1 real root. It lies between the interval [-1,0].
a. yes
b. no
c. cannot determine the answer
Please select the best answer from the choices provided
Answers
Answer:
I believe that a=the answer is C if It's not then probably A
Step-by-step explanation:
Answer:
the answer is
b.no
Step-by-step explanation: