Answers
Answer:
13. [tex]x^2+y^2+2x-3\sqrt{x^2+y^2}=0[/tex]
14. [tex]r=3\cos(\theta)-2\sin(\theta)[/tex]
Step-by-step explanation:
Question 13
Conversion from Polar equation to rectangular equation:
[tex]x=r \cos(\theta) \implies \cos(\theta)=\dfrac{x}{r}[/tex]
[tex]y=r \sin(\theta) \implies \sin(\theta)=\dfrac{y}{r}[/tex]
[tex]x^2+y^2=r^2 \implies r=\sqrt{x^2+y^2}[/tex]
Given:
[tex]r=3-2\cos(\theta)[/tex]
[tex]\textsf{Substitute }\cos(\theta)=\dfrac{x}{r}:[/tex]
[tex]\implies r=3-\dfrac{2x}{r}[/tex]
Multiply both sides by r:
[tex]\implies r^2=3r-2x[/tex]
[tex]\implies r^2+2x-3r=0[/tex]
[tex]\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }r=\sqrt{x^2+y^2}:[/tex]
[tex]\implies x^2+y^2+2x-3\sqrt{x^2+y^2}=0[/tex]
---------------------------------------------------------------------------------------------
Question 14
Conversion from Rectangular equation to polar equation:
[tex]x=r \cos(\theta)[/tex]
[tex]y=r \sin(\theta)[/tex]
[tex]x^2+y^2=r^2 \implies r^2\cos^2(\theta)+r^2\sin^2(\theta)=r^2[/tex]
Given:
[tex]x^2+y^2-3x+2y=0[/tex]
[tex]\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }x=r \cos(\theta)\:\textsf{and }y=r \sin(\theta):[/tex]
[tex]\implies r^2-3r\cos(\theta)+2r\sin(\theta)=0[/tex]
Factor out common term r:
[tex]\implies r(r-3\cos(\theta)+2\sin(\theta))=0[/tex]
Divide both sides by r:
[tex]\implies r-3\cos(\theta)+2\sin(\theta)=0[/tex]
Rewrite to make r the subject:
[tex]\implies r=3\cos(\theta)-2\sin(\theta)[/tex]Related Questions
What is the value of X
Using sines
Answers
sin alpha= a/c
sin 23° = x/13
x= sin 23° ×13
x≈ 5.08
Which equation could john solve to find w, the greatest width in centimeters he can use for the mosaic? w(w – 2) = 48 w(w 2) = 48 2w(w – 2) = 48 2w(w 2) = 48
Answers
The equation solved by the John to find w, the greatest width in centimeters he can use for the mosaic, is w(w + 2) = 48.
How to find the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
The area of the tile is 48 square cm. John wants to make the mosaic with this tile having the length 2 cm longer than the width.
Let the width of the rectangle mosaic is w cm. Thus, the length of it is,
[tex]l=w+2[/tex]
As the area of a rectangle is the product of its length and width and Tte area of the tile is 48 square cm. Thus,
[tex]A=l\times w\\48=(w + 2)\times w \\48=w(w+2)\\w(w+2)=48[/tex]
The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic is
[tex]w(w+2)=48[/tex]
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Answer:
B. w(w + 2) = 48
Step-by-step explanation:
I just took the quiz.
Have the day you deserve :)
What is 25 time 39 divided by 2150?
Answers
Answer:
Approx 0.453488372
Step-by-step explanation:
You can get this with a calculator.
25 × 39 = 975
975÷2150≈ 0.453488372
I'm not sure if I'm supposed to round this or not, so I won't. If you need it rounded, comment, and I will!
I would love brainliest!!!!
Help!!!!!!!!!!!!!!!!!!!!!!! Pleaseeeeee
Answers
Answer:
C) 43.96
Step-by-step explanation:
1. Use the formula to find the circumference of a circle whic is C= πR
2. First multiply the radius (7 in) by 2
3. 7 x 2 = 14
4. Then multiply 14 by 3.14
5. 14 x 3.14 = 43.96
5. There's your answer :)
Hope this helps :)
NEED ANSWERS QUICK! CORRECT ANSWER GETS BRAINLIEST
Find the quotient of 4 5/8 and 2 1/2. Express your answer in the simplest form.
Answers
Answer:
1 5/32
Step-by-step explanation:
this is the answer
Answer:
The correct answer is 1 5/32
Step-by-step explanation:
First,convert both of the mixed numbers into improper fractions.Next,do the KCF method.Keep,change,and flip.First,like up 4 5/8 and 2 1/2 next to eachother with a multiplication sign in the middle.(Must be in this order!!)Next,turn the multiplication sign into a division sign.After this,change the second mixed number,and flip the denominator and the numerator.Then simply multiply the top numerators and the denominators.That is where you get you answer, Simplifying may be needed. :)
The ratio of acrobats to dancers was 13 to 15. If there were 247 acrobats, how many dancers were there?
Answers
Answer:
im terreb.le at math
Step-by-step explanation:
Answer:
285 dancers
Step-by-step explanation:
[tex]\frac{acrobats}{dancers}[/tex] = [tex]\frac{13}{15}[/tex] = [tex]\frac{247}{x}[/tex]
After cross-multiplication:
13x = ( 15 )( 247 )
13x = 3705
x = 285 dancers
Which expressions represent rational numbers? select all the apply. startroot 100 endroot startroot 100 endroot 13.5 startroot 81 endroot startroot 9 endroot startroot 729 endroot startroot 64 endroot startroot 353 endroot one-third startroot 216 endroot three-fifths 2.5
Answers
The expressions are irrational 1/3 + √216 and √64+ √353 and the expressions √100 × √100, 13.5 + √81, √9 + √729, and 1/5 + 2.5 are rational number.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
1. √100 × √100
→ √100 × √100
→ 10 × 10 = 100
This is a rational number.
2. 13.5 + √81
→ 13.5 + √81
→ 13.5 + 9 = 22.5
This is a rational number.
3. √9 + √729
→ √9 + √729
→ 3 + 27 = 30
This is a rational number.
4. √64+ √353
→ √64 + √353
→ 8 + √353
This is an irrational number.
5. 1/3 + √216
→ 1/3 + √216
→ 1/3 + √216
This is an irrational number.
6. 1/5 + 2.5
→ 1/5 + 2.5
→ 0.2 + 2.5 = 2.7
This is a rational number.
More about the rational number link is given below.
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Answer:
A, B, C, F
Step-by-step explanation:
edge
Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. the table below shows the information about the two credit cards brandon currently uses. card a card b amount $1,463.82 $1,157.98 apr 13% 17% monthly payment $24.60 $22.14 after 8 years, how much will brandon have saved in interest by consolidating the two balances? a. $581.76 b. $194.40 c. $256.32 d. $325.44 please select the best answer from the choices provided. a b c d
Answers
The amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.
What is monthly payment?Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.
It can be calculated with the following formula.
[tex]M=P\left (\dfrac{r}{1-(1+r)^{-nt}}\right)[/tex]
Here, (P) is the principal amount, (r) is the interest rate and (t) is time.
Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate.
The table below shows the information about the two credit cards Brandon currently uses.
Cards Amount APR Monthly PaymentCard a $1,463.82 13% $24.60Card b $1,157.98 17% $22.14
Interest rate for the card a is,
[tex]r=\dfrac{13}{12\times100}=0.01083[/tex]
The time period is 8 years and there are 12 months in one year. Thus, the monthly payment of card A will be,
[tex]M=1157.98\left (\dfrac{0.01083}{1-(1+0.01083)^{-12(8)}}\right)\\M=19.47[/tex]
In the 8 years, there is total 96 monthly payments. Thus, the total payment by card A is,
[tex]P_a=19.47\times96=1869.12[/tex]
For the card B the monthly payment is $22.14. Thus the total payment by card B is,
[tex]P_b=22.14\times96=2125.44[/tex]
The difference in the payment is,
[tex]d=2125.44-1869.12\\d=256.12[/tex]
Hence, the amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.
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Answer:
C. 256.32
Step-by-step explanation:
Which product has 4 zeros after the digit 3?
0.03 x 104
0.3 x 104
0.3 x 10
0.03 X 109
Answers
Answer:
0.03×104=3.12
0.3×104=31.2
0.3×10=3
0.03×109=3.27
these are the products
hope it helps!
at the clothing store 1/8 of the plots arch shirts of the shirt .1/4 are green what fraction of the clothing and the store are green shirts
Answers
Answer:
Diana works at a clothing store. She sold 1/5 of the total number of green shirts on Monday and 3/12 of the total number of green shirts on Tuesday.
someone help me please
Answers
Answer:
x ≈ 5.8 degrees
Step-by-step explanation:
the sum of all exterior of any polygon is 180 degrees
so: 7x+4 + 5x+4 + 4x+9 + 9x-6 + 4x+1 = 180
combine 'like terms':
29x + 12 = 180
29x = 168
x ≈ 5.8
A pound of clementines costs $2.49 and ms. wild buys 1.8 pounds. how much did she spend?
Answers
Answer:
i believe she spent $4.482 on clementines
I’ll give you brainiest who ever answer this right
Answers
Answer:
y=x+1
Step-by-step explanation:
at each x you move up by 1
Solve the equation and enter the value of x below.
6x + 3 = 27
X=
Answers
Answer:
x=4
Step-by-step explanation:
6x+3 = 27
Subtract 3 from each side
6x+3-3=27-3
6x = 24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
x=4
Step-by-step explanation:
6x+3=27
6x=24
x=4
please help fast!!! a shirt is regularly priced at $35.50 if it is discounted by 45% what is the sales price
Answers
A triangle has an angle that measures 90°. The other two angles are in a ratio of 2:7. What are the measures of those two angles?
Answers
Answer:
70° and 20°
let the other 2 angles be 7x and 2x
90+7x+2x=180
9x=180-90
x=90/9
x=10
7x=7x10
70
2x=2×10
2p
Which set of ordered pairs does not represent a function?
O {(8,-4), (-5,6), (-5,7), (-3,-5)}
O{(-1,0), (1,0), (3,-2), (2, -9)}
O {(3,-7), (-2, -9), (9,3), (7, - 7)}
O {(8, –9), (-3,9), (-9,2), (-2,0)}
Answers
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.
Reflect the shape A in the line x=-1
What are the coordinates of the vertices of the image?
please answer random who answered my last question
Answers
Answer:
(-5,3) (-7,3) (-5,6)
Step-by-step explanation:
So the line x= -1 is also a vertical line but this time it passes through the point (-1,0).
I hope this helps!!
Steve claims tan(x) - 3
What value of cos(x) supports Steve's claim?
9
41
0
9
40
40
41
41
40
Answers
The value of cos(x) that supports Steve's claim is 1/√10
SOH CAH TOA identityGiven the following trigonometry identity
tan(x) = 3
According to the theorem;
tan x = opposite/adjacent = 3/1
Opposite = 3
Adjacent = 1
Determine the hypotenuse
hyp = √3² + 1²
hyp = √10
Since cos(x) = adj/hyp
cos(x) = 1/√10
Hence the value of cos(x) that supports Steve's claim is 1/√10
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A plane contains 9
distinct horizontal lines and
9
distinct vertical lines. These lines divide the
plane into separate regions. How many of these
separate regions have a finite, nonzero area?
Answers
A finite, nonzero area formed by the lines would have a fixed measurement
The number of separate region that have a finite, nonzero area is 64
How to determine the number of separate regions?The given parameters are:
Horizontal lines, h = 9Vertical lines, v = 9The number (n) of separate region that have a finite, nonzero area is calculated as:
n = (h - 1) * (v - 1)
This gives
n = (9 - 1) * (9 - 1)
Evaluate the product
n = 64
Hence, the number of separate region that have a finite, nonzero area is 64
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what are two numbers that multiply to 64 and add to - 20
Answers
Answer:
-4 and -16
Step-by-step explanation:
Let x = first number
Let y = second number
Given:
The two numbers multiply to 64⇒ xy = 64
Given:
The two numbers add to -20⇒ x + y = -20
Rewrite x + y = -20 to make x the subject:
⇒ x = -20 - y
Substitute into xy = 64 and solve for y:
⇒ (-20 - y)y = 64
⇒ -20y - y² = 64
⇒ y² + 20y + 64 = 0
⇒ (y + 4)(y + 16) = 0
⇒ y = -4, y = -16
As x + y = -20
If y = -4 then x = -16
If y = -16 then x = -4
Therefore, the two numbers are -4 and -16
Let they be a and b
a+b=-20--(1)ab=64So
[tex]\\ \rm\rightarrowtail (a-b)^2=(a+b)^2-4ab[/tex]
[tex]\\ \rm\rightarrowtail (a-b)^2=(-20)^2-4(64)=400-256=144[/tex]
[tex]\\ \rm\rightarrowtail a-b=12\dots(2)[/tex]
From both equations
2a=-8=>a=-4-4+b=-20b=-16a) What is the size of angle ABC?
b) Use your answer to part a) to work out the size of reflex angle CBD.
Give your answers to the nearest degree.
Answers
Answer:
a. 120 Degrees
b. 180-120=60 60 Degrees
Step-by-step explanation:
A straight line has a maximum of 180 degrees.
ABC is 120, so CBD is 60
a) The size of angle ABC is 120 degrees.
b) The size of reflex angle CBD is 240 degrees.
a) The size of angle ABC is 120 degrees by inspecting at the protractor and counting from 0° 1o 120°
Reflex angles are formed by extending one of the sides of an angle beyond the straight line, creating an angle greater than 180 degrees. They can be visualized as the "extra" portion of a rotation around a point, beyond the 180-degree mark
b) To determine the size of reflex angle CBD, consider that a reflex angle measures more than 180 degrees but less than 360 degrees. Since angle ABC is 120 degrees, subtract this angle from 360 to find the remaining measure of the reflex angle CBD.
Reflex angle CBD = 360 degrees - 120 degrees
= 240 degrees.
Therefore, the size of reflex angle CBD is 240 degrees.
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Davion wants to buy 4 tickets to a basketball game. He sees that there is a discount for $25 o his
entire purchase at checkout, so the tickets would cost him $215 before tax,What was the original
price of each ticket?
Answers
Answer:
$60 per ticket
Step-by-step explanation:
$215 is what it costs after the discount, so add the amount taken off, back on.
215+25
240
Then, divide by 4 to find the cost of each individual ticket.
240/4
60
I need help with this one plis quickly !!!
Answers
Answer:
3
Step-by-step explanation:
Hard to see but pretty sure thats it
center and the radius please!
Answers
The leading brand of cosmetics in the US had about 20% of the total sales in the industry. The total sales were $ 200,000. What was the leading brands sales? Show your work.
Answers
Answer: $40000
Step-by-step explanation:
200000(0.2) = $40000
Do u guys have apps for solving geometry/ triangle problems????
Answers
This is the best I could find
Some recommended apps for solving geometry and triangle problems are "Ge oGebra," "De smos Geometry," and "Ma thway."
Ge oGebra: Ge oGebra is a versatile mathematics app that covers various topics, including geometry and triangles. It provides interactive tools for constructing and analyzing geometric shapes, making it a valuable resource for visualizing and understanding different properties and theorems related to triangles.
De smos Geometry: While De smos is primarily known for its graphing capabilities, the De smos Geometry app also offers tools for creating and manipulating geometric shapes, including triangles. It can help users explore and solve various triangle-related problems.
M athway: M athway is a comprehensive math problem-solving app that covers a wide range of topics, including geometry and triangles. Users can input specific problems, and the app provides step-by-step solutions, making it a helpful tool for both learning and verifying answers to geometry and triangle problems.
To know more about geometry, click here.
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------------The given question is incomplete, the complete question is:
"What are some recommended apps for solving geometry and triangle problems?"-------------
A square pyramid has
a base edge of 8 inches
and a surface area of 304
square inches. Find the
Slant height of the
pyramid.
Answers
The slant height of the square pyramid that has a surface area of 304 sq. in. is: 16 inches.
What is the Surface Area of a Square Pyramid?Surface area (SA) = a² + 2al
Given the following parameters:
Surface area = 304 sq. in.a = 8 in.l = ? (slant height)Plug in the values into (SA) = a² + 2al:
304 = 8² + 2(8)l
304 = 64 + 16l
304 - 64 = 16l
240 = 16l
240/16 = l
15 = l
l = 16
Therefore, the slant height of the square pyramid that has a surface area of 304 sq. in. is: 16 inches.
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Pleassee helpp, find X.
Answers
x=37.5
if you need an explanation i can type it in the comments
Consider the enlargement of the triangle and use the measurements to calculate the scale factor. 2 triangles have corresponding side lengths of 8 centimeters and 64 centimeters. scale factor =
Answers
The scale factor when a triangle of 8cm side is enlarged to a triangle of 64cm side is 8.
Side of the first triangle = 8cm
Side of the second triangle = 64cm
What is a scale factor?A scale factor is a number by which the size or dimension of an object is enlarged or diminished.
For example, if an equilateral triangle with a side x is dilated by a scale factor of 2, the enlarged size of the side will be 2a.
So, scale factor = side of the second triangle/ corresponding side of the first triangle.
Scale factor = 64/8
Scale factor = 8
Therefore, The scale factor when a triangle of 8cm side is enlarged to a triangle of 64cm side is 8.
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Answer:
8 I did the assignment
Step-by-step explanation: