Answer:
the region of the circle in polar coordinate can be expressed as:
[tex]\mathbf{- \dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2} , 0 \leq r \leq 11 cos \theta}[/tex]
Step-by-step explanation:
Given that:
[tex]x^2 +y^2 = 11x[/tex]
This implies that :
[tex](x-5.5)^2 + y^2 = 5.5^2[/tex]
center (5.5, 0) and radius = 5.5
The relation between the cartesian coordinates (x,y) and the polar coordinates (r, θ) is as follows:
x = rcosθ
y = rsinθ
Thus, [tex]x^2 + y^2 = r^2[/tex]
[tex]x^2 + y^2 = 11x[/tex]
[tex](rcos \theta)^2 + (r sin \theta)^2 = 11(rcos \theta)[/tex]
[tex]r^2 = 11r cos \theta[/tex]
Thus, the angle θ runs between [tex]- \dfrac{\pi}{2}[/tex] to [tex]\dfrac{\pi}{2}[/tex]
Therefore, the region of the circle in polar coordinate can be expressed as:
[tex]\mathbf{- \dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2} , 0 \leq r \leq 11 cos \theta}[/tex]
The required region is,
[tex]x=\frac{11}{2}+\frac{11}{2}cos\theta , 0\leq \theta\leq2\pi \\y=\frac{11}{2}sin\theta ,0\leq r \leq \frac{11}{2}[/tex]
Given circle is,
[tex]x^2 +y^2 = 11x[/tex]
Computation:
Solving the given circle,
[tex]x^2-11x+y^2=0\\x^2-2(\frac{11x}{2})+y^2=0[/tex]
Adding [tex]\frac{11}{2}[/tex] both sides we get,
[tex]x^2-2(\frac{11x}{2})+\frac{121}{4}+y^2=\frac{121}{4}\\(x-\frac{11}{2})^2+y^2=(\frac{11}{2})^2[/tex]
It represents a circle having the radius [tex]\frac{11}{2}[/tex] and centred at [tex](\frac{11}{2},0)[/tex]
So, in polar coordinate,
[tex]x=\frac{11}{2}+\frac{11}{2}cos\theta , 0\leq \theta\leq2\pi \\y=\frac{11}{2}sin\theta ,0\leq r \leq \frac{11}{2}[/tex]
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Which statement about proportional relationships is false? A proportional relationship must graph as a line. A graph of a proportional relationship must pass through (0, 0). Each point (or pair) in a proportional relationship must share the same ratio. Each point (or pair) in a proportional relationship must share the same difference.
Answer:
D: Each point (or pair) in a proportional relationship must share the same difference.
Answer: It's D
Step-by-step explanation:
| x | >= 4 draw the graph
Answer:
Solve for x
x ≤ −4 or x ≥ 4
The spray from a sprinkler reaches 21 feet from the sprinkler and creates a circle as it spins. What is the circumference of the circle sprayed by the sprinkler? Use 22/7 for π.
C=πd
r=21
d=42
C=132 ft, and D is your final answer. Hope it help!
Answer:
132
Step-by-step explanation:
D
5(5z - 7), when z = -1
Answer:
5(5(-1)-7)
-25-35
-60
Step-by-step explanation:
Answer: -60
Step-by-step explanation:
Image!!
I just need the Inequality plz
You want to adopt a new puppy. The adoption fee is $250, and you have $105.50 saved up so far. If your after school job pays $7.50 per hour.
Answer:
Hi there!
An inequality to demonstrate this is:
105.5 + 7.5x >= 250
Hope this helps
Consider the expression 2 3 (14x − 3) − 3x( 4 5 + 5). Which statements are true about simplifying this expression? Check all that apply. Using the distributive property, the Two-thirds would be multiplied to 14x and to –3. Combining Four-fifths + 5 can be done before multiplying it by 3x. Using the distributive property, 3x times Four-fifths is subtracted, but the 3x times 5 is added. Combining 14x – 3 can be done before multiplying by Two-thirds. Subtracting 3x is the same as adding –3x.
Answer:
1. using the distributive property, the two-thirds would be multiplied to 14x and to –3. 2. combining four-fifths + 5 can be done before multiplying it by 3x. 3. subtracting 3x is the same as adding –3x. (A, B, & E)
Step-by-step explanation:
just finished this lesson lol
Using the distributive property, the Two-thirds would be multiplied to 14x and to –3.
Combining Four-fifths + 5 can be done before multiplying it by 3x. The correct option is A and B.
What is an Expression?An expression is a mathematical statement consisting of variables, constants, and mathematical operators.
The expression is
[tex]\rm \dfrac{2}{3} (14x -3) - 3x( \dfrac{4}{5} +5)[/tex]
Applying Distributive Property
[tex]\rm \dfrac{2}{3} * 14x - \dfrac{2}{3} *3 - 3x * ( \dfrac {4 + 25}{5})[/tex]
Therefore, Using the distributive property, the Two-thirds would be multiplied to 14x and to –3.
Combining Four-fifths + 5 can be done before multiplying it by 3x. The correct option is A and B.
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4/3y = 16 solve for y
Answer:
y=12
Step-by-step explanation:
First we should rewrite the left side to look like
4y/3=16
Then multiply 3 to both sides
4y=48
Now divide by 4
y=12
The equivalent value of the expression is y = 12
Given data ,
Let the equation be represented as A
Now , the value of A is
( 4/3 )y = 16
On simplifying the equation , we get
( 4/3 )y = 16
So , the left hand side of the equation is equated to the right hand side by the value of ( 16 )
Divide by 4 on both sides , we get
( 1/3 )y = 16/4
( 1/3 )y = 4
Multiply by 3 on both sides , we get
y = 4 x 3
On simplifying , we get
y = 12
Therefore , the value of y = 12
Hence , the expression is y = 12
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This year omar watched 80 movies. He thought that 54 of them were very good. of the movies he watched, what percentage did he rate as very good
Answer:
percentage flim rated very good = 54/80*100%
= 67.5%
Step-by-step explanation:
!!!!25 POINTS HELP NOW PLEASE!!!! Emily and Hunter tracked the average temperature in their city for the past 8 days. They recorded their temperature findings in this list. 66°F, 57°F, 61°F, 65°F, 54°F, 62°F, 59°F, 56°F What is the mean absolute deviation of this data set? Enter your answer in the box.
( 5 - 2i)2 Write answer in standard form a +bi. Remember you can not have i2 in your answer it is a number.
(5 - 2i)^2
Simplify.
25 - 20i + 4i^2
Remember that i^2 = -1.
25 - 20i - 4
Combine like terms
21 - 20i
5445,568
Step-by-step explanation:
Help ASAP
Find the Distance between (5,2) and (-3,-4)
Answer:
[tex]d = 10[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in your 2 coordinates into the formula to find distance d:
[tex]d=\sqrt{(-3-5)^2+(-4-2)^2}[/tex]
[tex]d=\sqrt{(-8)^2+(-6)^2}[/tex]
[tex]d=\sqrt{64+36}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]d = 10[/tex]
100 POINTS!! ASAP - Pls Show all WORK
Answer:
x ≈ 28.7 ft
Step-by-step explanation:
Step 1: Define variables
Height (vertical leg of triangle) = 2 ft
∅ = 4°
We are trying to find the length of the hypotenuse x
Step 2: Use trig
sin∅ = opposite over hypotenuse
sin4° = 2/x
Step 3: Solve for x
xsin4° = 2
x = 2/sin4°
x = 28.6712
x ≈ 28.7 ft
Answer:
the Length of ramp is 28.7 feet.
Step-by-step explanation:
see attached image for clarity
give:
height (h) of clinic = 2 feet
angle of ramp = 4°
find:
Length (L) of ramp
using the formula : sin(Ф) = height (h)
Length of ramp (hypothenuse)
plugin values into the formula:
sin (4) = 2
L
L = 2
sin(4)
L = 28.7 feet
therefore,
the Length of ramp is 28.7 feet.
simplify (4x+1)(3+9x)
Answer:
36 x 2 + 21 x + 3
Step-by-step explanation:
Simplify the expression.
Add and subtract the second term to the expression and factor by grouping. You get 3 ( 4 x + 1 ) ( 3 x + 1 )
what is the opposite of the opposite of 8
Answer:
8
Step-by-step explanation:
The opposite of the opposite of 8 is just 8
Answer:
-8
Step-by-step explanation:
the opposite of 8 is -8 because of positive and negative numbers
PLS HELP I DONT UNDERSTAND :( WILL GIVE BRAINLIEST !!!
the answer is c
i already done it
Answer:
1/3 would be your answer
Step-by-step explanation:
anyway have a great day
4 1/2 x 2 3/5 what is the answer simplified into fraction
Answer:I tnink its 21 sorry if wrong
Step-by-step explanation:
Solve for j.
-12 + 6j = 7j
Answer:
[tex]\large\boxed{j = -12}[/tex]
Step-by-step explanation:
-12 + 6j = 7j
Subtract 6j from both sides of the equation
[tex]\large\boxed{j = -12}[/tex]
This kind of equation can usually be solved by moving the numbers to the opposite side of the equation as the variables.
Hope this helps :)
A teacher earns 32500 per year if 33% of her income is withheld for taxes, how much money is withheld for taxes
Answer:
$11,357 is withheld for taxes
How do you draw the probabilities for this tree diagram?
Step-by-step explanation:
The prize is equally likely to have been placed behind doors 1, 2, and 3, so the probabilities of D₁, D₂, and D₃ are equal.
P(D₁) = P(D₂) = P(D₃) = 1/3
The contestant initially chooses door 1, so the host will not open it.
P(H₁|D₁) = P(H₁|D₂) = P(H₁|D₃) = 0
The host will not open the door with the prize.
P(H₂|D₂) = P(H₃|D₃) = 0
The remaining probabilities for each door are equal.
P(H₂|D₁) = P(H₃|D₁) = 1/2
P(H₃|D₂) = 1
P(H₂|D₃) = 1
If 40% of a number is 32, find 10% of that number.
Answer:
8
Step-by-step explanation:
your cell phone plans costs$34.99 per month plus $0.11 for each text message you send or receive you have at most $40 to spend on your cell phone bill what is the maximum number of text messages that you can send or receive next month ?
The maximum number of text messages that you can send or receive next month Next month, you can send or receive up to 45.54 text messages in total.
What is maximum in mathematics?In mathematics, a point at which a function's value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. If it is merely greater than any nearby point, it is a relative, or local, maximum
Considering the information provided;
Given that the monthly expense is $34.99
and $0.11 for each text as well (sent or received)
Suppose y is the whole cost.
Set x as the quantity of text.
The test messages make up the difference between the cost of the plan and the $40 you must spend, which is represented by the equation
4034.99=5.01
in the model for the overall cost,
y=34.99+0.11x.
Count the number of messages you can send, you must divide.
5.01÷0.11
=45.54
The maximum number of messages is 45
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Help me please not good at math
Answer: I think option A
Step-by-step explanation:
Una piscina rectangular de 15 metros de largo por 9 metros de ancho està rodeada por un
camino de cemento de ancho uniforme. Si el área del camino es 112 metros cuadrados, ¿cuánto
mide su ancho?
Answer: 2 meters.
Step-by-step explanation:
Let w = width of the cement path.
Dimensions of pool : Length = 15 meters , width = 9 meters
Area of pool = length x width = 15 x 9 = 135 square meters
Along width cement path, the length of region = [tex]2w+15[/tex]
width = [tex]2w+9[/tex]
Area of road with pool = [tex](2w+15) (2w+9)[/tex]
[tex]= 4w^2+30w+18w+135\\\\=4w^2+48w+135[/tex]
Area of road = (Area of road with pool ) -(area of pool)
[tex]\Rightarrow\ 112 =4w^2+48w+135- 135\\\\\Rightarrow\ 112= 4w^2+48w\\\\\Rightarrow\ 4 w^2+48w-112=0\\\\\Rightarrow\ w^2+12w-28=0\ \ \ [\text{Divide both sides by 4}]\\\\\Rightarrow\ w^2+14w-2w-28=0\\\\\Rightarrow\ w(w+14)-2(w+14)=0\\\\\Rightarrow\ (w+14)(w-2)=0\\\\\Rightarrow\ w=-14\ or \ w=2[/tex]
width cannot be negative, so w=2 meters
Hence, the width of the road = 2 meters.
What is the solution of the equation 8x^3 = -64?
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
[tex]8x^3=-64[/tex]
Divide both sides by 8:
[tex]\frac{8x^3}{8}=\frac{-64}{8}[/tex]
[tex]x^3=-8[/tex]
Cube root both sides:
[tex]\sqrt[3]{x^3} =\sqrt[3]{-8}[/tex]
[tex]x=-2[/tex]
How many liters each of a 30% acid solution and a 50 % acid solution must be used to produce 70 liters of a 40 % acid solution? (Round to two decimal places if
necessary.)
Answer:
30%: 35 liters
50%: 35 liters
Step-by-step explanation:
The desired concentration is halfway between the concentrations of available solutions, so the mixture will be equal amounts of each.
35 liters of 30% acid and 35 liters of 50% acid must be used
_____
If you want to write an equation, it usually works well to let the variable represent the amount of the most concentrated constituent: 50% acid. Then the amount of acid in the final mix is ...
0.50x +0.30(70 -x) = 0.40(70)
0.20x +21 = 28 . . . . simplify
0.20x = 7 . . . . . . . . . subtract 21; next, divide by 0.20
x = 35 . . . . . . amount of 50% solution (liters)
70-x = 35 . . . amount of 30% solution (liters)
SOMEONE PLEASE HELP ME WITH THIS QUESTION 2.5x - 3 = 2x - 2
I don't get what x is equal to
Answer:
2
Step-by-step explanation:
Use the property of equality :)
every square root is a rational number true or false
Answer:
False
Step-by-step explanation:
The principal square root of most numbers is an irrational number with an infinite decimal expansion.
Not every square root is irrational but the statement says EVERY so false.
Hope I helped!
Please label mine as brainliest!
Answer:
False
There can be irrational numbers too. Complex, even. Also, Imaginary.
PLEASE ANSWER FAST
Find the square root of 16.
O a
-4
Ob
4
Ос
+4
Od
-8
Answer:
the square root of 16 is 4
twice the difference if a number A and 7
Answer:
-Twice means muliply by 2
-The difference of a number and 7 means subtract a number/variable and 7.
-Is equal to 9 means =9
2(X - 7) = 9
Write each expression in simplest form.
3d + 6d
2 + 55-4
2z+3-92-8
Answer:
9d
53
2z-97
Step-by-step explanation:
Its basically just simplification btw.
pingu!