r = sec(θ) − 2cos(θ), where -π/2 < θ < π/2
Convert this equation to rectangular coordinates.
Answers
Answer:
y = (x/(1-x))√(1-x²)
Step-by-step explanation:
The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
__
r = sec(θ) -2cos(θ)
r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)
r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²
(x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations
x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor
y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)
[tex]\boxed{y=\dfrac{x\sqrt{1-x^2}}{1-x}}[/tex]
__
The attached graph shows the equivalence of the polar and rectangular forms.
Related Questions
Emil is inviting 7 friends to a party. Each friend wants 5 cookies and each box has 12 cookies. How many boxes should Emil get?
Answers
Answer:
3 boxes.
Step-by-step explanation:
Solution,
Given,
The number of cookies : 7 × 5 = 35
Now,
The total number of cookies to cookies per box 35 ÷ 12 = 2.9 box
= 3 boxes.
The ratio of boys to girls in a class is 3:5. There are 40 students in the class. How many students are girls?
Answers
Answer:
25
Step-by-step explanation:
40/8 = 5
3:5 so u do 5x5 which is 25
brief explanation and hoped it helped xoxo
Answer:
25 girls
Step-by-step explanation:
boys: girls: total
3 5 8
Take the total number of students and divide by 8
40/8 = 5
Multiply each term by 5
boys: girls: total
3*5 5*5 8*5
15 25 40
There are 25 girls
What is the geometric mean of 9 and 18
Answers
[tex]\cfrac{9}{x}~~ = ~~\cfrac{x}{18}\implies 162=x^2\implies \sqrt{162}=x\implies \sqrt{9^2\cdot 2}=x\implies 9\sqrt{2}=x[/tex]
What is the volume of this right cone?
40π cm^3
300π cm^3
400π cm^3
480π cm^3
Answers
I Hope this Helps You?
What is the volume of this right cone? 40π cm³ 300π cm³ 400π cm³ 480π cm³
✓ The answer is 400pi because the area of a cone is A=1/3*pi*r^2*h1/3*pi*100*12 = 400pi
Write the ratio as a fraction in simplest form.
10 feet to 5 yards
Answers
Answer:
1:0.33
Step-by-step explanation:
This is because one foot= .333 yards
I hope this is what you were asking! :)
12a+3b
would it be 15ab?
I'm not understanding how to solve it
I'll give 20 points just please help me lol
Answers
They are unlike terms you can’t add them together
Please help me with this question on my homework (graded)
Answers
Answer:
could be plus ten and that gives u 49
Step-by-step explanation:
True or false: Outliers can cause data sets to be skewed.
Answers
Answer:
True
Step-by-step explanation:
Firstly, the definition of an outlier is a number farther away from the general populous of digits. For example, a number line can have a lot of numbers clustered at 2, 3, and 4 but might have one way over on 10. This would mean 10 is an outlier.Secondly, a skew is when a dot plot or a box and whisker plot is shaped a certain way. A negative skew would be a graph sloping to the right, and a positive skew is a graph sloping to the left. It looks a bit like a hill.Knowing that the shape is made up of the different numbers and their amount, we can conclude that an outlier, or a number that is stretched far from the others, would affect the data set.This means that the skew might change if there is a variable that is out of place.If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
If m∠16=57°, and m∠20=39°, calculate m∠11
Answers
Check the picture below.
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 52:29 There are two routes Lucas can take to walk to school. Route A is 2 and StartFraction 1 over 8 EndFraction miles and is StartFraction 3 over 8 EndFraction mile longer than route B. The equation b + StartFraction 3 over 8 EndFraction = 2 and StartFraction 1 over 8 EndFraction can be used to represent this situation, where b is the length of route B. How many miles will Lucas walk if he takes route B?
Answers
Answer:
Lucas will walk [tex]1\frac{3}{4}[/tex] miles if he takes route B
Step-by-step explanation:
Length of route A = [tex]2 \frac{1}{8} miles[/tex]
Length of route A [tex]=\frac{17}{8} miles[/tex]
We are given that route A is 3/8 mile longer than route B
Let b be the length of route B
So, [tex]b+\frac{3}{8} =2 \frac{1}{8} \\b+\frac{3}{8} =\frac{17}{8}\\b=\frac{17}{8}-\frac{3}{8}\\b=\frac{14}{8}\\b=\frac{7}{4}\\b=1\frac{3}{4}[/tex]
Hence Lucas will walk [tex]1\frac{3}{4}[/tex] miles if he takes route B
What is the smaller angle of (x+20) (5x+10)
Answers
Answer:
Step-by-step explanation:
Which of the following is the solution to |x|+5<1
Answers
Answer: No solutions
Step-by-step explanation:
|x|+5<1
Subtract 5 from both sides.
|x| < -4
No solutions is possible
The half-life of a radioactive kind of antimony is 4 days. How much will be left after 12 days,
if you start with 7,600 grams of it?
22
grams
Time
elapsed
Submit
01
16
Answers
The mass of the substance left after 12 days is 501.51g.
Data;
Half life = 4 daystime = 12 daysNo = 7600Half - LifeThis is defined as the time taken for the radioactive sample to decay to half it's initial size.
This is given as
[tex]T_\frac{1}{2} = \frac{\ln 2}{\lambda}[/tex]
where
λ = disintegration constantLet's substitute the values and find the disintegration constant
[tex]T_\frac{1}{2} = \frac{\ln 2}{\lambda} \\4 = \frac{0.693}{\lambda} \\\\\lambda = \frac{0.693}{4}\\ \lambda = 0.17325[/tex]
But the value of a radioactive substance present at a given time is
[tex]N_t = N_o e^-^\lambda ^t[/tex]
Let's substitute the values and solve.
[tex]N_t = 7600 e^-^0^.^1^7^3^2^*^1^2\\N_t = 7600 * 0.065988\\N_t = 501.509g[/tex]
The mass of the substance left after 12 days is 501.51g.
Learn more on radioactivity here;
https://brainly.com/question/2320811
Mileage Abilene Dallas El Paso Lubbock San Antonio Abilene 185 447 165 261 Dallas 185 633 351 277 El Paso 447 633 344 558 Lubbock 165 351 344 394 San Antonio 261 277 558 394 Find the distance from San Antonio to El Paso. 344 mi 633 mi 261 mi 558 mi
Answers
A type of cracker, rectangular in shape, is stored in a vertical column with all of the crackers stacked directly on top of each other. each cracker measures 2 inches in length by one and one-half inches in width. the volume of the column is 15 inches cubed. if there are 40 crackers in the column, what is the height of each individual cracker? startfraction 3 over 40 endfraction inch one-eighth inch one-fifth inch three-eighths inch
Answers
The height of each individual cracker is one-eighth inch. Then the correct option is B.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A type of cracker, rectangular in shape, is stored in a vertical column with all of the crackers stacked directly on top of each other.
Each cracker measures 2 inches in length by one and one-half inches in width.
The volume of the column is 15 inches cubed.
If there are 40 crackers in the column
The height of the cracker will be
[tex]\rm h = \dfrac{15}{1.5*2}\\\\h = 5[/tex]
The height of each individual cracker will be
[tex]\rm h_c = \dfrac{5}{40}\\\\\\h_c = \dfrac{1}{8}[/tex]
More about the geometry link is given below.
https://brainly.com/question/7558603
Answer:
BStep-by-step explanation:
is the answer
I rlly need help on this
Answers
Answer:
what the question
Step-by-step explanation:
7-40 = -5-8
Answer plz!
Answers
Answer:
Well if you are trying to say if they are the same then no
Step-by-step explanation:
-33≠-13
Hope this helps!
Each of the equal sides of an Isosceles Triangle is 4 times the third side. The perimeter of the triangle is 144 inches. Find the sides of the Triangle.
Answers
Answer:
16 + 64 + 64 are the 3 sides.
Step-by-step explanation:
There are two sides that are 4 times the third side.
Let the 3rd side = x
4x + 4x + x = 144 inchines
9x = 144 inches
x = 144/9
x = 16 inches.
So the base (which is the smallest side) = 16 inches.
One of the two sides remaining is 4x = 4*16 = 64
The other side = 64
Check
64 + 64 + 16 = 144 as it should.
Answer:
Step-by-step explanation:e
The ordered pairs in the table below represent a linear function.
х
6
9
y
2
8
What is the slope of the function?
1
1
O
O 2
O 4
Answers
E the anwser is c
Step-by-step explanation:Finding Slope from a Table Worksheet Step-by-Step Example. 1 Find the change in the y-values by subtracting from one row to the next. 2 Find the change in the x-values by subtracting from one row to the next. 3 Divide the difference in the y-values by the difference in the x-values.
PLEASE HELP!!!!! All my points Picture below
Answers
Answer:
19. 13
20. 6
21. 12
Step-by-step explanation:
what up................................................
Answers
Answer:
nothing wbuuuu
Step-by-step explanation:
Answer:
Hey
Step-by-step explanation:
How are you doing???
is 5/16 rational or
irrational
Answers
Answer:
Rational.
Step-by-step explanation:
It can be represented as a fraction
WILL MARK BRAINLIEST IF CORRECT PLEASE ANSWER!!!!
Square GHIJ circumscribes circle K. Find the area of the shaded region. Round your answer to the nearest tenth if necessary.
Answers
Answer:
13.7
Step-by-step explanation:
I just did the problem
Becka says that when she simplifies the expression below, the value is 6 less than her age. What is Becka’s age?
(7 + 11) − 8 ÷ 2
Answers
Answer:
20
Step-by-step explanation:
heart and brainliest pls
Answer:
18
Step-by-step explanation:
you have to do parentheses first, then division. Then you can subtract because of the order of operations, PEMDAS, which is parentheses, exponents, multiplication or division, and addition or subtraction. After you do the equation you get 12. That is 6 less than Becka's age, making Becka's age 6 more than that, which is 18
What is the volume of the rectangular prism?
3 inches
11 inches
6 inches
Answers
Answer:
198
Step-by-step explanation:
3x11x6=
PLEASE HELP ASAP!!!
1) what is the measure of <4? Explain
2) what is the sum of the measures of angles in a triangle?
3) <1 is in a triangle <4 and 53 angle. What is the sum of those two angles?
4) what is the measure of <1 explain
5) find the measure of <2 explain how you found it
6) what is the measure of <3 explaining
I will give Brainlist!!!
Answers
Answer:
1. 90 degrees because of supplementary angles
2. 180 degrees
3. 90 degrees
4. 37 degrees, since the sum of the interior angles add to 180, 180-90-53 = 37.
5. 127 degrees, supplementary angles 180-53
6 . 23 degrees, use the triangle sum theorem 180-30-127
Why are first time home buyers, on average, only able to pay around 5% for a down payment on a house?
Answers
Answer:
They don't have enough money to pay the full price so they have no option but to pay what they have in their saving account. Also as a first down payment its allowed to start from 3% and up. The much down payment the lower they will pay every month.
Step-by-step explanation:
A graph that represents 2x-3y=9
Answers
I attached to pictures, one of me solving the equation for you step by step and then what the graph should look like when i put it in my calculator!!
the slope is 2/3x and it translate down 3 units on the y-axis!!Toby has $65 to buy t-shirt for his bowling team each t-shirt costs $7
Answers
Answer:
$9.28 per t-shirt
Step-by-step explanation:
plz mark brainlest
Answer:
He has enough money to buy 9 t-shirts and he would have 2 dollars left over
Step-by-step explanation:
Divide 65 by 7. You would get 9 with a remainder of 2. So you have enough to buy 9 t-shirts.
The mean mass of a dairy cow is 634.5 kg with a standard deviation of 64.2 kg. A sample of 50 cows is obtained. Find the probability that the mean mass of the sample is at least 640 kg
Answers
Answer:
oh hun is 640kg stupid cow
Step-by-step explanation: