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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please show work 3[x+4]+4x= -2
Answer:
x = -2
Step-by-step explanation:
First, you eliminate parentheses using the distributive property.
3(x +4) +4x = -2
3x +12 +4x = -2
Then you collect terms.
7x +12 = -2
You can subtract 12 (from both sides).
7x = -14
Finally, divide by the coefficient of the variable.
x = -14/7 = -2
The solution is x = -2.
____
Comment on the work
When you add, subtract, multiply, divide, or perform any other operation on one side of the equation, you must do the same thing on the other side. That is how the equal sign stays valid. That is why we subtracted 12 from both sides of the equation. It is also why we divided both sides of the equation by 7.
Those steps, subtract 12, divide by 7, are chosen for the purpose of getting the x-term by itself, then getting by itself. In general, when there's an added term you don't want, add its opposite to both sides of the equation. When there's a factor you don't want, divide both sides of the equation by that.
x is less than nine
Answer:
x < 9
Step-by-step explanation:
x is less than nine
x < 9
Answer:
x<9
Step-by-step explanation:
less than symbol is this <
The question is x is less than 9
so
x<9
Hope this helps!
Rewrite 118 as a fraction in lowest terms.
Help me I will give extra points
Answer: g(x) = -4x + 5
Please mark me brainliest instead of points
please help me quick ill give brainliest
Answer:
23/99
Step-by-step explanation:
nearly any number /9 or /99 or /999 etc is a repeating decimal.
Answer:
23/99
Step-by-step explanation:
9/8=1.125
23/99≈0.232
9/20=0.45
3/40=0.075
hope this helps
Help me please not good at math
Answer: I think option A
Step-by-step explanation:
say you have (-4,-4) and (8,4)
which ones are the y2, y1, x2, and x1
how would you factor a quadratic expression like 9x^2-4
Hello, we need to see it as a difference of two squares as we know that for all a and b real numbers
[tex]a^2-b^2=(a-b)(a+b)[/tex]
So, here
[tex]9x^2-4=(3x)^2-2^2=(3x-2)(3x+2)[/tex]
Voila !
Thank you
manuel works at cheese cake king. He earns $15 per hour as a busboy. the waiters he helps give him 25% of their tips.
a) if manuel worked 6 hours today, how much did he earn, without tips?
b) the waiters mauel assited waited on 16 tabels, and the total bill from all the these tabels was $1,188. the waitress earned 15% in tips, and 25% of these earnings to manuel. How much money did manuel make in tips?
c)what was manuel's total salary for the day?
d) what was manuel's average ernings per hour, including tips? round to the nearest cent
Answer:
a. 90
b. 44.55
C. 134.55
D. 22.42
Step-by-step explanation:
A. 6*15 = 90
B. 15 % of 1188 is 178.2, and 178.2 divided by 4 (0.25%) is 44.55
C 90 + 44.55 = 134.55
d. 134.55 divided by 6 hours worked is 22.42
a. The earning should be 90.
b. The money that should be made is 44.55.
c. The total salary for the day is 134.55
d. The Manuel average earnings per hour, including tips is 22.42
Calculation of the earning, money, total salry, and average earnings per hour:a.
The earnings should be
= 6(15)
= 90
b. The money made should be
The 15% of 1188 should be 178.2
Now we have to divide the 178.3 from 4 so it comes 44.55.
c. The total salary should be
= 90 + 44.55
= 134.55
d. The average earnings per hour should be
Here 134.55 divided by 6 hours = 22.42
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Find f (7) when f (x) = -5x + 2.
Step-by-step explanation:
f(x) = -5x + 2
f(7) = (-5)(7) + 2
= -35 + 2
= -33
Answer:
f (x) = -5x + 2.
= -5*7+2
= -13
Step-by-step explanation:
I guess I was help full for u
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Combine like terms
3x + 2x + 11y - 7y
Help
Answer:
5x + 4y
Step-by-step explanation:
3x + 2x = 5x
11y - 7y = 4y
HELP
Simplify.
5 + (-5
-5 + 1)
1-2 - 31
Answer:
answer is
Step-by-step explanation:
-37
have a good day
i need points
Salvador runs 24.5 miles per week. How many miles does he run each day?
Answer:
3.5 miles per day
Step-by-step explanation:
There are 7 days in a week
24.5 miles in a week
24.5 / 7 days
3.5 miles per day
Answer:
3.4 miles
Step-by-step explanation:
You would divide 24.5 by 7 since there are 7 days in a week giving you a quotient of 3.5
Point S is on line segment RT. Given ST = 2x – 10, RS = 2x - 5, and
RT = 3x + 1, determine the numerical length of RT.
Answer: 49
Step-by-step explanation:
The numerical length of RT is 49 units if point S is on the line segment RT. Given ST = 2x – 10, RS = 2x - 5, and RT = 3x + 1.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Point S is on line segment RT.
ST = 2x – 10,
RS = 2x - 5, and
RT = 3x + 1,
RT = RS + ST
3x + 1 = 2x - 5 + 2x - 10
The above equation is representing a linear equation in one variable.
After simplifying:
3x + 1 = 4x - 15
4x - 3x = 15 + 1
x = 16
RT = 3x + 1
Plug x = -14
RT = 3(16) + 1
RT = 48 + 1
RT = 49
The numerical value of RT = 49
Thus, the numerical length of RT is 49 units if point S is on line segment RT. Given ST = 2x – 10, RS = 2x - 5, and RT = 3x + 1.
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please solve this question..
Answer:
vertex = (- 1, - 4.5 )
Step-by-step explanation:
Given
f(x) = [tex]\frac{1}{2}[/tex] (x - 2)(x + 4)
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To find the zeros let f(x) = 0, that is
[tex]\frac{1}{2}[/tex] (x - 2)(x + 4) = 0
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x + 4 = 0 ⇒ x = - 4
The x- coordinate of the vertex is therefore
x = [tex]\frac{-4+2}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
Substitute x = - 1 into f(x) for corresponding y- coordinate
f(- 1) = [tex]\frac{1}{2}[/tex] (- 1 - 2)(- 1 + 4) = [tex]\frac{1}{2}[/tex] × - 3 × 3 = 0.5 × - 9 = - 4.5
Coordinates of vertex = (- 1, - 4.5 )
Write 18/27 in simplest form
Answer:
Step-by-step explanation:
2/3
which of the numbers doesnot belong in the number series
1 – 2 – 5 – 10 – 13 – 26 – 29 – 48
is it
a. 1
b. 5
c.26
D.27
E. 48
Answer:
the sequence first numbe * 2, +3, *2
so 48 doesnot belong it should be 58
Step-by-step explanation:
1/4 of the total bird population in your town is 200 birds. How many birds are there in your town?
Answer:
800
Step-by-step explanation:
234 + 300 and scram. ok bio now go do homework no ples
Answer:
534
Step-by-step explanation:
Express the first number as a percentage of the second number. 29 pounds of recyclable trash in a barrel of 53 pounds of trash. The 29 pounds of recyclable trash is what % of the barrel of 53 pounds of trash.
Divide first number by second number:
29 /53 = 0.54716981
Multiply by 100 to get percent:
0.54716981 x 100 = 54.716981%
Round the answer as needed.
1. Set A represents rational numbers. Set B represents integers. Which diagram shows
the numbers placed in the correct
sets?
Set A
Set A
1.5
1
10
3
3.1
С
Set B
Set B
-12
Set A
Set A
7.1
10
2
win
mi
B
D
Set B
Set B
-3.4
-6.8
Answer: Choice C) Upper right corner (aka northeast corner)
====================================================
Explanation:
Rational numbers are ones where we can write as a fraction of two integers. Any rational number is in the form a/b where a,b are integers and b is nonzero.
Terminating decimals can be written as a rational number. Something like 3.1 is equivalent to 31/10.
Of the four answer choices, only choice C is correct.
Choice A has the value '3' as a rational number, but it doesn't have it in the set of integers as well. So that's why choice A is incorrect.
Choice B has -3.4 in the set of integers, which is not correct. Integers do not have any decimal portion. The same applies to choice D also. We can rule choices B and D out.
The graph of y = |x-1|+7 is reflected across the y-axis and then translated up 1 unit. What is an equation of the transformed graph?
The original equation: y = |x - 1| + 7
The new equation: y = |-x - 1| + 8
eric ran 3 miles in 20 minutes. what is eric’s speed?
Answer:
Step-by-step explanation:
speed=distance/time
20 minutes=1/3 hours
=3*3/1
=1miles/hour
catering company uses a linear function to determine the total cost of parties. The following table shows the costs for dinner parties with varied numbers of guests. What is the cost to cater a dinner party with 90 guests?
Answer:
Your answer is B. #795. Hope this helps!
Answer:
B. $795
Step-by-step explanation:
James has 1,836 marbles. He decides to divide them equally among 23 boxes. How many marbles will James have left over?
he has less marbles
Step-by-step explanation:
cuz he doesAnswer:
79.83
I rounded to the nearest hundredth
Gabriella makes a profit of $.80 for every cup of coffee that she sells at her coffee shop she wanted to make a profit of at least $75 today on coffee if she’s sold 90 cups today which statement is correct
Answer:
Gabriela needs to sell 4 more cups of coffee to make a profit of $75.
She sells 90 cups and makes $0.80 profit on each cup. That equals $72 profit.
90 x $0.80= $72
She wants to make $75 profit.
$75 - $72 = $3 profit short for the day
$3/$0.80 = 3.75 cups of coffee short so to make her profit she must sell a total of 94 cups of coffee for the day or an additional 4 cups.
Step-by-step explanation:
jimmy has a pool sixteen feet wide and twelve feet long how much material does he need to cover the pool
Answer:
192 square feet of material
Step-by-step explanation:
You find the area of the pool, which is length x width, and that is 12 x 16, which is equal to 192
I hope this helps!
Answer:
16 x 12=192
Step-by-step explanation:
Write the equation of the line in point-slope form that passes through the given point with the given slope (1,5); m = -3
Answer:
y - 5 = -3(x-1)
Step-by-step explanation:
We have the slope and a point
Point slope form is
y-y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line
y - 5 = -3(x-1)
Predict how many times Max will choose a rectangular cracker if he carries out this process 200 times
Answer:
70 times.
Step-by-step explanation:
The following data were obtained from the question:
SHAPE >>>>>>>>>>>>> FREQUENCY
Oval >>>>>>>>>>>>>>> 18
Rectangle >>>>>>>>>> 14
Star >>>>>>>>>>>>>>> 8
TOTAL >>>>>>>>>>>>> 40
next, we shall determine the probability of chosing a rectangular cracker. This is illustrated below:
Event of Rectangle (nR) = 14
Sample space (S) = 40
Probability of chosing rectangle, P(R) =?
P(R) = nR/nS
P(R) = 14/40
P(R) = 7/20
Therefore, the probability of chosing a rectangular cracker is 7/20.
Thus, if the process were carried out 200 times, the probability of chosing a rectangular cracker will be:
= P(R) × 200
P(R) = 7/20
= 7/20 × 200
= 70
Therefore, max will chose a rectangular cracker 70 times.
a company's budget increase from 29 million to 133 million over a period of 10 years. growing by the same percent each year. What was the annual percent increase? Express your answer as a common fraction