To find the radius of the circle with the polar equation r^2 - 8r(3cosθ + sinθ) + 15 = 0, we can use the following steps:
Complete the square for the terms involving r(3cosθ + sinθ).
We can do this by adding and subtracting the square of half the coefficient of r(3cosθ + sinθ) to the equation:
r^2 - 8r(3cosθ + sinθ) + 15 = 0
r^2 - 8r(3cosθ + sinθ) + 9(3^2 + 1^2) - 9(3^2 + 1^2) + 15 = 0
(r - 3cosθ - sinθ)^2 - 9(3^2 + 1^2) + 15 = 0
(r - 3cosθ - sinθ)^2 = 9(3^2 + 1^2) - 15
(r - 3cosθ - sinθ)^2 = 63
Take the square root of both sides to solve for r:
r - 3cosθ - sinθ = ±√63
r = 3cosθ + sinθ ±√63
Since the radius of a circle is always positive, we can discard the negative square root and obtain:
r = 3cosθ + sinθ + √63
Now we need to find the value of r when θ = π/4, since this will give us the radius of the circle at that point. Substituting θ = π/4 into the equation for r, we get:
r = 3cos(π/4) + sin(π/4) + √63
r = 3(√2/2) + (√2/2) + √63
r = (√2 + 1) + √63
r ≈ 8.765
Therefore, the radius of the circle with the given polar equation is approximately 8.765, which rounded to the nearest whole number is 9.
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Can someone please help me on this question? Question: What percent of a dollar is a quarter, a nickel, a dime, and two pennies?
Answer:
Its 42 percent
Step-by-step explanation:
0.25+0.5+0.10+0.2=0.42 or 42%
All the change added together is 42/100 because a dollar is just 100 cents.
m> 32
Which of the following could be a possible value for m?
32
33
100
n 31
find JQ if Q is the incenter of JLN
Answer:
Find each measure. 9. NP. ANSWER: 14. 10. PS.
Step-by-step explanation:
The length of JQ is 18.79 unit.
What is Pythagoras theorem?According to the Pythagoras theorem, a triangle's hypotenuse square equals the sum of its other two sides' squares.
Given:
Q is the incenter of JLN
QP= QK= QM= 9 units
Now, In Δ JPQ
JP= 16.5, QP =9 , QP⊥ JP
So, JQ = √JP² + QP²
JQ= √16.5²+ 9 ²
JQ= 18.79 units
Hence, the length of JQ is 18.79 unit.
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Divide 9 by t. Then, add 3.
Which of the following expressions matches the statement above?
OA. t + 9 + 3
OB. 9 + 3+ t
C. 9 + (t + 3)
OD. 9+t+3
A translation is shown on the grid below
Answer:
translation of ABC to A'B'C' is 5,3
14 Customers into the store over the course of seven minutes how many Internet store after one minute
Answer:
2
Step-by-step explanation:
14 divided by 7 is two customers in one minute
Answer:
After one minute there will be 2 people inside the store.
Step-by-step explanation:
First we put this into a proportion. Aka set up like a fraction.
14 (customers) x
------- ---> ------
7 (minute) 1 minute
In order to find x, we must divide by 7 because in order to make the bottom number one on the bottom, you must divide by 7 , so we do the same to the top.
14/7 is 2.
This means that per minute, there are 2 people inside the store.
After one minute, There will be 2 people inside the store.
Which of the following statements must be true about the diagram
Answer:
D ) x+y=w
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Will give brainliest!
Answer:
Step-by-step explanation:
Equation for line a:
x = - 4
Equation for line b:
x = 4
Equation for line c:
y = 4
Equation for line d:
y = - 2
Equation for line e:
y = − 0.75x + 1
Does anyone know how to solve this?
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.
Which of the following best describes the equation below?
y = -3x - 13
A.
both linear and nonlinear
B.
nonlinear
C.
neither linear nor nonlinear
D.
linear
Answer:
d. linear
Step-by-step explanation:
using the format y=mx+b
Help please
|2x + 5| = 11
Step-by-step explanation:
[tex]2x + 5 = 11 \\ 2x = 11 - 5 \\ 2x = 6 \\ x = 6 \div 2 \\ x = 3[/tex]
The midpoint of AB is M(-3,-3). If the coordinates of A are (-5, -1), what are
the coordinates of B?
Answer:
The coordinates of B are (-1, -5).
Step-by-step explanation:
Since the x-coodinate of M is 2 greater than that of B (note that -3 = -5 + 2), the x-coordinate of B is found by adding 2 to -3, obtaining -1. The y-coordinate of M is -3, which is 2 less than the y-coordinate of A; Thus, the y-coordinate of B is 2 less than -3, that is, -5.
The coordinates of B are (-1, -5).
Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the solution of the equation?
(its in the attachment)
Thank u lovely
Step-by-step explanation:
This is a edit. The answer is 30. Brainly won't save my work.
[tex]3 \sqrt[5]{ {(x + 2)}^{3} } + 3 =27 \\3 \sqrt[5]{ {(x + 2)}^{3} } =24 \\ \sqrt[5]{ {(x + 2)}^{3} } = 8 \\ {(x + 2)}^{3} = {8}^{5} \\( x + 2) = \sqrt[3]{ {8}^{5} } \\ ( x + 2) = 32 \\ x = 30[/tex]
help...........................
Answer:
Could you please repeat the question?
Answer:
Answer:
Step-by-step explanation:
What help!
Thanks for free points!
Have a nice day!
‘Basic exponent rules’ simplifying to a single power .
Answer:
64
Step-by-step explanation:
a dealer sells a camera to a man and makes 15% profit. The man sells the camera to another man for 414$ with 10% loss. Find the original cost of the camera.
Answer:
$386.75
Step-by-step explanation:
First we must find the price of the camera after the man sold it, with the 10% loss.
To do this we find 10% of 414, which is 41.4 . Meaning the camera was originally bought from the dealer for $455.40, as we have to add the 10% back onto the price.
Now we find 15% of 455 and subtract it, with 15% being 68.25, the original cost was $386.75. My guy was seriously ripped off :(.
Orignal price: $386.75Brandy has 8 pounds of candy. She wants to give each of her friends 1/3 pound. To how many friends can Brandy give candy?
Please help with this!?!?!?
Answer:
2$
Step-by-step explanation:
you can see that for every mile, the cost goes up 1.5 dollars, and if you tale the lowest amount, 2 miles, multiply by 1.5 = 3, and then subtract that from 5, you get 2
12-b=12.5. Solve each equation
what is the result of -4+5/3?
Answer:
-2⅓
Step-by-step explanation:
-4 + 5/3 Start out with this sum.
-4 + 1 ⅔ Make 5/3 into a mixed number.
-2 ⅓ Then add them together. The best way to do this is to first add -4 and 1 which makes -3. Then add ⅔ to -3 which is -2 ⅓
Solve for x: please help
Answer:
45 because an acute angle is 45 degrees
Answer:
22.5
Step-by-step explanation:
22.5 + 22.5 x 3 =
22.5 + 67.5 =
90
Hope that helps!
Fay has a lemonade stand.
She spends £42 on ingredients.
She sells each glass of lemonade for £1.20.
If she sells 50 glasses of lemonade, what is her total profit?
Answer:
she made a profit of 18$
50*1.2=60-42=18
Step-by-step explanation:
que es la radicasion
Answer:
La radicación es la operación inversa a la potenciación. Y consiste en que dados dos números, llamados radicando e índice, hallar un tercero, llamado raíz, tal que, elevado al índice, sea igual al radicando. En la raíz cuadrada el índice es 2, aunque en este caso se omite.
only 10-11 please, giving brainliest!
A ball falls from the top of a building. When it strikes the ground its velocity is 10 m/s. It took 5 seconds to fall. What is its acceleration? _____ m/s2
Answer:
a = 2 m/s²
Step-by-step explanation:
[tex]a = \frac{v-u}{t}[/tex]
where v is the final velocity, u is the initial velocity, and t is the time it takes. the intial velocity is always 0 m/s. given the equation, we subsitute:
[tex]a = \frac{10m/s - 0 m/s}{5s}[/tex]
a = 10m/s ÷ 5s
a = 2 m/s²
GIVING 10 POINTS
PLEASE HELP!
What does it mean when two expressions are equivalent?
Answer:
When two equations are equivalent it means that the two equations are equal to each other. Hope this helps, thank you !!
wouldnt x+x be 2x thanks
Answer:
Wym?
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I'll answer it on the comment or are u just playing?
2hours 24mins in fraction
Answer:
2 2/5
Step-by-step explanation:
2 24/60 = 2 2/5
there are 60 minutes in an hour so you can just put 24 over 60 and the two outside to write it as a mixed number fraction then reduce. If you want to write it as a improper fraction you can multiple 2 times 5= 10 then add 2 to get 12/5
Use the Distributive Property to rewrite the algebraic expression. 9(3p + 6)
wrong answers reported
Answer:
27p+54
Step-by-step explanation:
Multiply 9 to all the numbers inside the parenthesis!
Hope this helps! :)
You spent m minutes studying on Monday On Tuesday you studied 15 more minutes than you did on Monday. Wednesday, you studied 30 more minutes than you did Tuesday you studied twice as long on Thursday as you did on Monday on Friday you studied 20 minutes less than you did on thursday
Answer: 7m - 40
Step-by-step explanation:
Monday = m
Tuesday = m + 15
Wednesday = m + 15 + 30 = m + 45
Thursday = 2 × m = 2m
Friday = 2m - 20
The expression will now be:
= m + m + 15 + m + 45 + 2m + 2m - 20
= 7m- 40