Answers
Answer:
A point in polar coordinates is written as (R, θ)
If we want to transform this point to rectangular coordinates, we get:
x = R*cos(θ)
y = R*sin(θ)
Now we can remember that the sine and cosine functions have a period of 2*pi, then:
cos(θ) = cos(θ + 2*pi)
or:
cos(θ) = cos(θ + 2*pi + 2*pi)
and so on.
Then the point (R, θ) is the same as (R, θ + 2*pi) and (R, θ + k*(2*pi))
where k can be any integer number.
Then if we have a point in polar coordinates:
(-4, -5*π/3)
Then another two polar representations of this point are:
(-4, -5*π/3 + 2*π) = (-4, -5*π/3 + 6*π/3) = (-4, π/3)
Now we can not add 2*π (nor subtract) because we would have an angle outside the range [-2*π, 2*π]
For example, if we have:
(-4, π/3 + 2*π) = (-4, 7*π/3)
And we can not change the value of the radius and get the coordinates for the same point.
So another representation could be something like:
(-8/2, π/3)
Where i just wrote -4 in another way.
Now, a really important point.
When working with polar coordinates, we always use R as a positive number (here you can see that R is negative) so this is not the standard notation for the polar representation of a point.
Related Questions
Please help me I am struggling I’m only 11
Answers
Answer:
-1/3(b+21)
Step-by-step explanation:
Answer:
Hope this helps, thank you !!
Does anyone know composite functions?
Answers
Mr. Patel bought lunch at a restaurant for $7.35. If he paid with a $10.00 bill, how much change did he get back?
A.
$2.55
B.
$2.65
C.
$3.35
D.
$3.65
Answers
Answer:
b. $2.65
Step-by-step explanation:
$10.00 - $7.35 = ?
$10.00 - $7.35 = $2.65
Answer:
your answer would be b. $2.65
secA-tanA/secA+tanA=cos^2A/(1+sin^2A) could somebody prove this pls......
Answers
9514 1404 393
Answer:
it cannot be proven
Explanation:
You cannot prove what isn't true.
We know you know how to use parentheses, so we take the left-side expression at face value. The left-side and right-side functions are different, so cannot be proved to be the same, except at specific angles.
A weight of 6 lb stretches a spring a distance of 12 in. Find the constant k for the spring.
Answers
Answer:
Let F = the force (6 lbs) and x be the distance that the spring is stretched (12 inches).
F = kx
6 lb = k*(12 in.)
6/12 = k = 0.5 lb/in.
A weight of 6 lb stretches a spring a distance of 12 in. The constant k for the spring will be 0.5 lb/in.
How to obtain acceleration from force applied on an object?If the object is of mass m kg and force applied on it is of F N in the direction of motion, then the acceleration of that object is evaluated as:
a= F/m
Given; A weight of 6 lb stretches a spring a distance of 12 in.
Also,
Let F = the force and x be the distance that the spring is stretched
F = kx
6 lb = k*(12 in.)
6/12 = k = 0.5 lb/in.
Therefore, the constant k for the spring will be 0.5 lb/in.
Learn more about spring here;
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The regular price of a camera is 180.00 the camera is on sale for 25% off the regular price. What is the sales price of the camera in dollars and cents
Answers
Answer:
$135
Step-by-step explanation:
180 decrease 25% =
180 × (1 - 25%) = 180 × (1 - 0.25) = 135
PLEASE HELP I'M SOO CONFUSED AND IT'S DUE TODAY!!!!!!!!!!!!!...I HAVE A LOT OF WORK TO DO TODAY AND I JUST NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
Answer:
2 Triangles with the bilateral of the sun to the 2nd power of pie
Step-by-step explanation:
I took the test ;)
PLEASEEEEE HELPPP ILL GIVE 30 POINTS PLSSS HELP
Answers
4multiplyed by 4 is 16
When the angle of elevation of the sun is 78 degrees, a tree casts a 13 foot shadow. How tall is the tree?
Answers
Answer: 61.16 ft
Step-by-step explanation:
We can think in this situation as a triangle rectangle.
where:
The height of the tree is one cathetus
The shadow of the tree is the other cathetus.
We know that the angle of elevation of the sun is 78°, an angle of elevation is measured from the ground, then the adjacent cathetus to this angle is the shadow of the tree. And the opposite cathetus will be the height of the tree.
Now we can remember the relationship:
Tg(A) = (opposite cathetus)/(adjacent cathetus)
Where:
A = 78°
Adjacent cathetus = 13ft
opposite cathetus = height of the tree = H
Then we have the equation:
Tg(78°) = H/13ft
Tg(78°)*13ft = H = 61.16 ft
What is the equation for a line that passes through the points (-4,-3) and (8,12)?
Answers
Answer:
y = 1.25x + 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
( -4 , -3 ) ( 8 , 12 )
12 + 3 15 = 5
8 + 4 12 = 4
↑ slope = 5/4
↓ point slope form: y - y₁ = m ( x - x₁ )
y + 3 = 5/4 ( x + 4 )
y + 3 = 5/4x + 5
-3
y = 5/4x + 2
y=3x+−7
Find the slope.
A. 7
B. -7
C. 3x
D. 3
Answers
Answer:
D.3
Step-by-step explanation:
In the equation for a line in the form y=mx+c, m represents the slope.
Therefore the slope is 3.
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + - 7 ← is in slope- intercept form
with slope m = 3
Which quotient is greater than 3?
Question 4 options:
42 ÷ 19
40 ÷ 18
38 ÷ 14
36 ÷ 11
Answers
Answer:
36/11
Step-by-step explanation:
Answer:
36/15
Step-by-step explanation:
Someone please help!
Answers
Answer:
10=1x+25
slope=1
y-int-25
Thats all i know so far i will keep working on it
Step-by-step explanation:
Find the midpoint of the interval [-3, 6] along the number line.
Answers
Answer:
1.5 or 3/2
Step-by-step explanation:
The midpoint of the interval [-3, 6] along the number line is 1.5.
The midpoint of an interval is the point that lies exactly in the middle of the two endpoints.
To find the midpoint of the interval [-3, 6], we use the midpoint formula:
Midpoint = (Endpoint1 + Endpoint2) / 2
In this case, Endpoint1 is -3, and Endpoint2 is 6:
Midpoint = (-3 + 6) / 2
Midpoint = 3 / 2
Midpoint = 1.5
The midpoint of the interval [-3, 6] is 3/2. This means that the point exactly halfway between -3 and 6 on the number line is 1.5 units to the right of -3 and 1.5 units to the left of 6.
Visually, if you plot -3 and 6 on a number line, the midpoint 3/2 (or 1.5) would be located at the center, equidistant from both endpoints.
To know more about number:
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which of the follow expressions are equivalent to (3^4)^-2 • (3^5)^3
Answers
Answer:
3^7
Step-by-step explanation:
Answer:
3^7
Step-by-step explanation:
(3^4)^-2 • (3^5)^3 = 2187
3^7 = 2187
Is the following g relation a function?
-yes
-No
Answers
Given:
The arrow diagram of a relation.
To find:
Whether the given relation is a function or not.
Solution:
A relation is a called a function it there exist a unique y-value or unique output value for each x-value or input value.
From the given arrow diagram it is clear that y=2 and y=-1 for x=-1.
Since we have more than one value of y at x=-1, therefore, the given relation is not a function.
Hence, the correct option is B.
question: which angles are vertical angles?
Answers
6 and 7 are vertical.
5 and 8 are vertical.
Answer:
<AOD, <BOC And <DOC ,<AOB
A cylinder has radius 3.8 meters. Its volume is 159 cubic meters. Find its
height to the nearest tenth of a meter.
Answers
Answer:
Step-by-step explanation:
If 1 large popcorn and 4 large drinks cost $21 how much does 1 large popcorn cost?
Answers
Answer:
6-7 dollars maybe?
Step-by-step explanation:
you didn't give a picture so Im just rounding
(sorry if I'm wrong)
Help me with this please!!!
Answers
this question answer is 4.25
Choose the two number sentences that are true.
A. 5+7= 11+2
B. 3 + 3 = 20 - 9
C. 5+9 = 19 - 4
D. 12 +7 = 5 + 14
E18 - 6 = 15 - 1
Answers
Answer:
D
because 12+7=19
5+14=19
There are (2^6)^3• 2^0bacteria in a sample. What is the total number of bacteria in the sample?
Answers
Answer:
262,144
Step-by-step explanation:
2^0 = 1
(2^6)^3 = 2^18 = 262,144
Answer: 262,144.
Step-by-step explanation: (26)3(20)
=(643)(20)
=262144(20)
=(262144)(1)
=262144
In triangle ABC, A is a right angle, and mB = 45°. Find BC. If your answer is not an integer, leave it in simplest radical form.
Answers
This triangle is called a 45-45-90 triangle, and the side ratio for the sides opposite to the 45-45-90 degree angles respectively are 1-1-sqrt2
Now we know one side is 6 and its opposing the 45 degrees angle and BC is opposing the 90 degrees angle the ratio between the sides are 1:sqrt2
Therefore BC=6*sqrt2=6sqrt2
Thus B is the correct answer!
Hope this helped any questions just leave them in the comments of this answer.
50 POINTS!
In the diagram, d = 4. What is the value of x? Express your solution in simplest radical form, if necessary.
Answers
Answer:
146
Step-by-step explanation:
180=4+30+x
180=34+x
180-34=x
146=x
explanation:
Who ever get it right I will give Brainly thx u
Answers
It be 12 cause from the smaller one 2*4 would = to 8 and 5*4 also = to 20 so 3*4 = to 12.
A random sample of 1000 people who signed a card saying they intend to quit smoking were contacted 9 months later. Turned out that 210 (21%) of the sampled individuals had not smoked in the past 6 months. What is the population, parameter, sample and statistic?
Answers
Answer:
Population is the total number of people that fall into the description of those that the research concerns.
In this case, Population is: Everyone who signed a card saying that they intend to quit smoking.
Sample. This is a subset of the population that the research is based on.
Sample = 1,000 people surveyed.
Parameter and Statistic are both descriptive measures but parameter is for the population and statistic is for the sample.
Parameter = Percentage of total population who have not smoked in 6 months.
Statistic = 21% of sample who have not smoked in 3 months.
use the table to solve the equation -6x>18
Answers
The answer is,
[tex]x < - 3[/tex]
A car travels at an average speed of 68 miles per hour. How many miles does it travel in 5 hours and 45 minutes?
Answers
Answer:
391.
Step-by-step explanation:
There is 60 minutes every hour, so you divide by 60. 68 / 60 = 1.1333333333.
Now, we have to find out how many minutes there are in 5 hours and 45 minutes. Since there is 60 minutes every hour, 6 x 5 + 45 = 300 + 45 = 345. 1.1333333333 x 345 = 390.9999999885, rounded = 391.
There are 120 counters in a bag.
40% of the counters are red.
3/8 of the counters are yellow.
The rest of the counters are green.
Find what fraction of the counters are green.
Answers
Answer:
9/40
Step-by-step explanation:
120 × ⅖ = 48
120 × ⅜ = 45
120 - 93 = 27
27/120 = 9/40
Based on the proportions and the counters in the bag, the fraction that is green is 9 / 40.
Number of Green countersYou can find the number of green counters by:
= Number of counters - Red counters - Yellow counters
= 120 - (120 x 40%) - (120 x 3/8)
= 120 - 48 - 45
= 27 green counters
Fraction of green counters= Number of green counters / Total number of counters
= 27 / 120
To take it to the lowest term, divide both numbers by 3:
= 9 / 40
In conclusion, the fraction is 9 / 40.
Find out more about fractions at https://brainly.com/question/17743912.
which sentence demonstrates the multiplicative identity?
1. 1/2•1=1/2
2. 1/2•2=1
3. 1/2+0=1/2•
Answers
Answer:
It’s 1/2•2 equals 1 because it showed correctly in the calculator. 0.5x2=1
Step-by-step explanation: