The limaçon has a characteristic loop is evident in the Cartesian equation. e.
The given equation is in polar form and it represents a limaçon.
We can convert this equation into Cartesian form using the following equations:
x = r cosΘ()
y = r sin(Θ)
Substituting r = 3 cos(Θ) get:
x = 3 cos(Θ) cos(Θ)
= 3 cos²(Θ)
y = 3 cos(Θ) sin(Θ)
= 3 sin(Θ) cos(Θ)
= (3/2) sin(2Θ)
The Cartesian equation of the curve is:
x²/9 + y²/27 = cos²(Θ) + (1/4)sin²(2Θ)
This equation represents a limaçon is a type of curve formed by a point moving around a fixed point while a second point moves around the first.
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Anits takes 8 hours to build 5 birdhouses. How many birdhouses could she Build in 24 hours?
Write an recursive formula for an, the nth term of the sequence 7, 10, 13,
Answer:
What's the nth term for 7,10,13,16? The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.
Step-by-step explanation:
HELLLPPPPP WITHHHH MATHHHH
Answer:
54 inches
Step-by-step explanation:
6/18=7/x
6x=7(18)
6x=126
x=21
21+15=18=54
What percent of 56 is 42?
I need an answer ASAP
a
23%
b
42%
c
75%
d
90%
Answer:
nicki monaj is the queen of rap
Step-by-step explanation:
periodt purr
in a standard deck of cards, what is the probability that you would draw an ace
Answer:
Step-by-step explanation:
Since there are four aces and 52 total cards.
P(A)=4/52=1/13
Answer:
The probability that you would draw an ace in a deck of cards would be 8%
eddie who earns $5 per hour worked two hours longer zach who earns $12 per hour. together they earn $30
Can someone help me with number 3 please there is 3 answers!!
Answer:
m<J = 83
m<L = 97
m<M = 97
Step-by-step explanation:
The corners across (left to right/right to left) from each other of a trapezoid are always equal.
So, it would be like this:
Angle J is equal to angle K
Angle M is equal to angle L
See how they are across from each other?
Therefore, Angle J will be 83 degrees.
To find the other 2 angles subtract 83 from 180
180 - 83 = 97
So, Angle L and M are 97 degrees.
To check your answer you can add up all the corners and they should equal 360 degrees:
83 + 83 + 97 + 97 = 360
360 = 360
Hope this helps!!
- Kay :)
If 3x−y=12, what is the value of
8x
2y
Answer:
[tex]8x=32\\2y=-24[/tex]
Step-by-step explanation:
When solving for 1 variable, set the other to 0 and solve.
[tex]3x-y(0)=12\\3x=12\\x=4\\4*8=32\\8x=32\\\\3(0)-y=12\\-y=12\\y=-12\\-12*2=-24\\2y=-24[/tex]
someone plz help!!!!
Answer:
7/8 > 3/4
Step-by-step explanation:
Find a common denominator first and here it is 8. To get 3/4 to 8ths, you multiply the numerator and denominator by 2 to get 6/8 and 7/8 is greater
12.) Joe sold 56 tickets to the school play and collected $215. Tickets
for adults cost $4.50 and student tickets cost $3.50 each. How many
of each did he sell?
Answer:
I DONT KNOW!!
Step-by-step explanation:
Find the coordinates of the turning point when y=5x^3 - 6x^2 - 4X + 8
Given:
The equation is
[tex]y=5x^3-6x^2-4x+8[/tex]
To find:
The coordinates of the turning point.
Solution:
We have,
[tex]y=5x^3-6x^2-4x+8[/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=5(3x^2)-6(2x)-4(1)+(0)[/tex]
[tex]\dfrac{dy}{dx}=15x^2-12x-4[/tex]
For the turning points [tex]\dfrac{dy}{dx}=0[/tex].
[tex]15x^2-12x-4=0[/tex]
Using quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(15)(-4)}}{2(15)}[/tex]
[tex]x=\dfrac{12\pm \sqrt{144+240}}{30}[/tex]
[tex]x=\dfrac{12\pm \sqrt{384}}{30}[/tex]
Now,
[tex]x=\dfrac{12+\sqrt{384}}{30}\text{ and }x=\dfrac{12-\sqrt{384}}{30}[/tex]
[tex]x\approx 1.053\text{ and }x\approx-0.253[/tex]
Putting x=1.053 in the given equation, we get
[tex]y=5(1.053)^3-6(1.053)^2-4(1.053)+8[/tex]
[tex]y\approx 2.973[/tex]
Putting x=−0.253 in the given equation, we get
[tex]y=5(-0.253)^3-6(-0.253)^2-4(-0.253)+8[/tex]
[tex]y\approx 8.547[/tex]
Therefore, the turning points are (1.053,2.973) and (-0.253, 8.547).
pleaseee help me asap
1.What is the unit rate of the graph?
2.What is the slope of the graph?
Compare your answers to #1 and #2
Answer:
The unit rate[tex]\frac{4}{1}[/tex] of the graph is 4, the slope of the graph is 4, and the comparison between answers is that they are equal.
Step-by-step explanation:
For every increase of 1 in the X value of the graph, the Y value increases by 4, so the slope would be [tex]\frac{4}{1}[/tex] or 4.
An icecream factory makes 140 quarts in 10 hours . How much can be made in 12 ?
Find quarts per hour:
140 quarts / 10 hours = 14 quarts per hour.
Now multiply quarts per hour by hours:
14 quarts per hour x 12 hours = 168 quarts
a cyclist travels for 5 days and covers 375km in total.
He covers 67km 78km 46km and 89km on the fist 4 days .How far does he travel on day 5
Answer:
95km
Step-by-step explanation:
5 days = 375km
4 days = 67km + 78km + 46km + 89km= 280km
5 days - 4days = the 5th day
375km - 280km = 95km
Sofia is making a batch of slime using a recipe that includes glue, water, and salt solution. She uses 7.5 fl. oz of glue. The amount of glue is 12.5 times the amount of salt solution. There are 4.2 less fluid oz of salt solution in the water. How many fluid ounces of water does Sofia use to make a batch of slime?
Answer:
its 4.8
Step-by-step explanation:
i divided 7.5 by 12.5 and got 0.6 and added 4.2 and got 4.8
Equation is formed of two expressions. The amount of water that is used by Sofia to make the slime is 4.8 fl oz.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount of salt solution used by Sofia be x, and the amount of water used by Sofia be y.
As it is given that the amount of glue used is 12.5 times the amount of salt solution used, and the amount of glue used is 7.5 fl oz. Therefore, the equation can be written as,
Amount of glue = 12.5 x Amount of salt solution
[tex]7.5 = 12.5 \times x\\\\x = \dfrac{7.5}{12.5}\\\\x = 0.6[/tex]
Also, it is given that the amount of water used is 4.2 fl oz. less than the amount of salt solution used, since we know the amount of salt solution used, therefore, the equation can be written as,
Amount of salt solution = Amount of water - 4.2 oz
[tex]x = y -4.2\\\\(0.6)=y-4.2\\\\y = 4.8[/tex]
Hence, the amount of water that is used by Sofia to make the slime is 4.8 fl oz.
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Do the following dogs appear to be SIMILAR? Please answer Yes or No and explain using math terminology!
Answer:
yes but no
Step-by-step explanation:
one is bigger than the other by prolly 1 foot
Answer:
1 is bigger by abt a foot or so
Step-by-step explanation:
The question is 3(2x +4) = 6x + 10
Answer:
no solution
Step-by-step explanation:
when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.
Answer:
The answer is False meaning it's no solution
Step-by-step explanation:
1. Distribute 3 through the parentheses which will be 6x+12=6x+10
2.Cancel equal terms on both sides of the equation and you will get 12=10 which isn't a true statement.
rs10,000 for 1 year at 8% per annum compounded half yearly.
Step-by-step explanation:
Answered 1 year, 9 months ago
Given,
Principal, P =Rs.10000, Rate, R = 8% per annum compounded half yearly for 1 year.
Now, There are two half years in a year. Therefore compounding has to be 2 times.
And rate = half of 10% = 5% half yearly.
Therefore, the required amount = = Rs. 10816
And Compound Interest, C.I. = Amount - Principal = Rs. (10816 - 10000) = Rs. 816.
hope it helps you
Plz help due tomorrow
Answer:
It's C) -6y
Step-by-step explanation:
I know someone already answered but I figured I could explain since it looks like you are getting a little confused. The reason it's not A is because its
-5 + 5 which is zero. So it gets rid of x so your just left with -6y. If it was
5x+5x then it would 10x but the negative makes it 0
John worked "x" hours this week and Shanique worked eight hours less than John. Write an algebraic expression for the number of
hours that Shanique worked this week.
A) 8x
B) X-8
C)8-X
D)X - 8
Answer:
B or D, I can't tell from these answer choices. X-8
Step-by-step explanation:
Shanique has 8 less questions than John (X).
Convert equation from slope intercept form to standard form y=-7/3x+1
Answer:
7x + 3y = 3
7x + 3y = 3
7x + 3y = 3
what are the answers to the variables? and how do i find them?
Answer:
Step-by-step explanation:
Please help am stuck thanks
Answer:
12.4 did this before
Step-by-step explanation:
Answer:
sɪʀ ʏᴏᴜʀ ᴀɴsᴡᴇʀ ɪs 12.4
ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴍɪᴅ ᴘᴏɪɴᴛ ᴛʜᴇʀᴏᴇᴍ
A man shares a $1,200,00 inheritance between his 3 sons in ratio 1: 3: 6. Calculate the difference between the largest share and the smallest share
Answer:
60000
Step-by-step explanation:
You should treat the first son with the 1 ratio as x. Because of this, the second son would be 3x and the third would be 6x. All of them need to equal 120000 so 10x=120000. Next you isolate the and x= 12000. Fill in 1200 for x and the first son gets 12000, the second gets 36000, and the third gets 72000. Lastly you subtract and you get 60000.
Mr. Velasquez built a playground. It has one section with a slide and another section with a swing set. A pathway connects the two areas. The slide is 2 meters high. The ares and the pathway are covered in asphalt. Mr velasquez want to know how much of the playground is covered in asphalt
Answer:
[tex]A_1 = 24m^2[/tex] -- Swing set
[tex]A_2 = 16m^2[/tex] -- Slide
[tex]A_3 = 5m^2[/tex] --- Pathway
Step-by-step explanation:
Missing part of the question:
Fill in the table above to show the area of each section (see attachment for table)
The area of each section is calculated as:
[tex]Area = Length * Width[/tex]
For the Swing set
[tex]A_1 = 8m * 3m[/tex]
[tex]A_1 = 24m^2[/tex]
For the Slide
[tex]A_2 = 8m * 2m[/tex]
[tex]A_2 = 16m^2[/tex]
For the Pathway
[tex]A_3 = 5m * 1m[/tex]
[tex]A_3 = 5m^2[/tex]
The total area is:
[tex]Area=A_1 + A_2 + A_3[/tex]
[tex]Area = 24m^2 + 16m^2 + 5m^2[/tex]
[tex]Area = 45m^2[/tex]
solve for x or find x
Answer:
63+ 2x- 17 = 180 degree
or, 2x+46=180degree
or, 2x=180-46=134degree
or, x = 134÷2=67 degree ans.
Can anyone help me with this problem # 9
Answer:
72 apples will be used and 4 will not
Answer:
She will use 72 apples and 4 apples will not be used.
Step-by-step explanation:
If she requires 9 apples for one pie... the she can make only 8 pies out of 76 apples.
hence she uses 72 apples...
Find the unknown side length x. Write your answer in simplest radical form
Answer:
B
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 30² = 50²
x² + 900 = 2500 ( subtract 900 from both sides )
x² = 1600 ( take the square root of both sides )
x = [tex]\sqrt{1600}[/tex] = 40 → B
How many terms are in this expression?
s+3u+10=
What is the area, in square inches, of the trapezoid below? 15.7 in 8 in 6.6 in
Answer:
What is the area, in square inches, of the trapezoid below? 15.7 in 8 in 6.6 in-by-step explanation:
The area, in square inches, of the trapezoid, is 89.2 in².
We have given that,
A = 89.2 in²
The area (A) of a trapezoid is calculated as,
What is the area trapezoid?A = 1/2 h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 8, b₁ = 6.6, b₂ = 15.7 , then
A = 1/2 × 8 × (6.6 + 15.7)
A= 4 × 22.3
A= 89.2 in²
The area, in square inches, of the trapezoid, is 89.2 in².
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