Given the polar coordinates (4,-pi/3) which of the following rectangular coordinate pairs represents the same point?
a) (-2,2sqrt3)
b) (2,-2sqrt3)
c) (2sqrt3,-2)
d) (2sqrt3, 2)
Answers
The rectangular point that represents (4, - pi/3) is the one in option b: (2, -2√3).
How to change the coordinates?
For a point (x, y), the polar coordinates are:
R = √(x^2 + y^2)θ = atan(y/x).Then we must have:
R = 4 = √(x^2 + y^2)
Notice that for all the given points we have the radius equal to 4, so the only part that we care is the angle one:
-pi/3 = Atan(y/x)
tan(-pi/3) = y/x = -1.73
So, y and x must have different signs, and because the angle is negative, we will say that the y-component must be negative.
So the correct option will be b: (2, -2√3)
y/x = -2*√3/2 = √3 = -1.73
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Answer: Quiz answer Unit 4 lesson 6
all answers are right
Step-by-step explanation:
1.) Given the polar coordinates (4,-pi3)which of the following rectangular coordinate pairs represents the same point?
Answer is B: (2,-2sqrt3)
2.) Given the rectangular coordinates (-5 5) which of the following polar coordinate pairs in, radians, represent the same points?
the correct option is D. (5√2,3π4)
3.)Rewrite in rectangular form: r=8 sin theta -2 cos theta.
Answer:
The equation in rectangular form is:
4.)Rewrite in polar form: x^2+y^2-6y-8=0
the Answer is B. r^2=6r sin 0+8
5.)The graph of r=-9 cos theta has which of the following characteristics?
Answer:
"circle; diameter of 9; center at (-4.5,0)"
6.)Which conic section is represented by the polar equation r=1/4-6 cos theta?
Answer:
Option 2 - Hyperbola
7.)Identify the horizontal and vertical intercepts of the limaçon represented by the equation r=7+3 cos theta ?
Answer:
vertical intercepts: (7, pi/2) and (-7, pi/2)
horizontal intercepts: (10,0) and (-4,0)
8.) Classify the limaçon represented by the equation r=1/2-1/2 sin theta.
A. Cardioid
9.)Write the equation for the graph of the rose curve.
answer C: r=9 sin 4 theta
10.) Write the equation for the graph of the lemniscate.
answer D: r^2=-49 sin 2theta
(pls don't report for me not explain it took a lot of time typing this and im just trying to help people have less stress on their shoulders :p )
Related Questions
If B (x,y)=(x-3,y+5), what is B(4,7)?
Can anyone help me please
Answers
Answer:
(B (4, 7 ) = (1, 12 )
Step-by-step explanation:
given
B (x, y ) = (x - 3, y + 5 ) , then
B (4, 7 ) = (4 - 3, 7 + 5 ) = (1, 12 )
Math, help, please!
Find the value of x
Answers
Answer:
x = 130
Step-by-step explanation:
A triangle always adds up to 180 de grees. If we do this we can find the value of x!!
33 + 97 + y = 180
130 + y = 180
180 - 130 = 50
Since the line x is on is a flat line and a flat line also equals 180, we will subtract the 50 from 180 to get x's value
180 - 50 = 130
Your answer is 130 :)
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Answer:
x = 50°
Step-by-step explanation:
if you know the measure of two angles in a triangle then the third angle measure will be 180 minus the sum of the other two
in this case the two interior angles add to 130
180-130 = 50
check: 33 + 97 + 50 should equal 180, and it does
A box of sunflower seeds contains p packets. Each packet of sunflower seeds contains s seeds. Which equation can be used to find the number of sunflower seeds in a box, b? *
5 points
p = sb
s = pb
b = sp
b + s = p
Answers
Answer:
b = sp
Step-by-step explanation:
box = seeds per packet
The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.
What are equations?Equations are relations shown between two equal algebraic expressions.
How do we solve the given question?We are given a box of sunflower seeds, containing p packets of seeds, each of which contains s number of seeds.
We are asked to write an equation that can be used to find the total number of seeds in the box, b.
We know that the box contains p packets of seeds.
In 1 packet we have s number of seeds.
∴ In p packets, we will have an s*p number of seeds or sp seeds.
Since the box contains p packets and the total number of seeds in the box is b, then we can say that
b = the number of seeds in p packets
or, b = sp, which is the required equation.
∴ The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.
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What is the value of x
Answers
Answer: 37
Step-by-step explanation:
74=2x
37=x
You are trying to get X by itself. Since it's 2x usually you would multiply it but in this case, divide it by itself into both sides so 74 divide 2 equals 37. If you know the order of operations then reverse it.
I'm just confused about how the answer choices are only 108 and 18.
Answer:
[tex]\huge\boxed{\sf x = 37}[/tex]
Step-by-step explanation:
Since, vertically opposite angles are equal:
74 = 2x
Divide 2 to both sides
74 / 2 = x
37 = x
OR
x = 37
[tex]\rule[225]{225}{2}[/tex]
What is the mean of the following data set?
3.245, 3.678, 3.3, 2.499, 2.9, 3.206, 2.081
Answers
Answer:
2.987
Step-by-step explanation:
The mean is calculated by dividing the sum of the terms by the # of terms.
For this problem, add all of the terms together:
3.245 + 3.678 + 3.3 + 2.499 + 2.9 + 3.206 + 2.081 = 20.909
Now, divide the product by the number of terms there are. There are 7 terms.
20.909 ÷ 7 = 2.987
Two marathon runners start a race at different times. Runner A stars her race first. and then Runner B starts his race 30 minutes later. Runner A runs 4 miles per hour. Runner B runs 6 miles per hour. Which equation can be used to determine the time in hours, t, that the runners will be side by side, the same distance from the starting line?
Answers
Answer:
4t = 6(t - 1/2)
Step-by-step explanation:
For Runner A, the expression is 4t since this runner's rate is 4 mph. For Runner B, the expression is 6(t - 1/2) since Runner B starts 1/2 hour after Runner A, and this runner's rate is 6 mph. Set these two expressions equal to each other.
What is the area of the patio if the yard is 12 feet on each side?
How do I do this?
Answers
144 feet squared
Step-by-step explanation:Squares are 4 sided shapes that have an equal length on each side.
Area Formula
The area of a square (or rectangle) is [tex]l*w[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width. Due to the fact that squares have four equal sides, the formula can be rewritten as [tex]l^2[/tex].
Solving For Area
Plug the length value into the formula.
[tex]12^2=144[/tex]Then, add the units to the answer. Because the length is multiplied by itself and the original unit is feet, the units are feet squared.
An integer number is chosen randomly between 1 and 1000. What is the probability that the number picked is divisible by 3 or 5 (i. E. , either 3 or 5 or both)?
Answers
Answer:
Umm..... sorry but.....my answer came.......
The probability that the number picked is divisible by 3 or 5 is 0.555.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
An integer number is chosen randomly between 1 and 1000.
The number of numbers divisible by 3, which is;
[tex]\rm \dfrac{1000}{3}=3333.3 = 333[/tex]
The number of numbers divisible by 5, which is;
[tex]\rm \dfrac{1000}{5}=200[/tex]
The probability that the number picked is divisible by 3 or 5 is;
[tex]\rm Probability=\dfrac{Number \ divisble \ by \ 3+ Number \ divisble \ by \ 5}{1000}\\\\ Probability =\dfrac{333+200}{1000}\\\\Probability=\dfrac{533}{1000}\\\\Probability=0.533[/tex]
Hence, the probability that the number picked is divisible by 3 or 5 is 0.555.
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Find the volume of a cone with a height of 3.25 centimeters and
a diameter of 2.2 centimeters.
Answers
Answer:
As per Provided Information
Height of cone h is 3.25 cm
Diameter of cone is 2.2 cm
Radius = Diameter/2Radius = 2.2/2
Radius = 1.1 cm
We have been asked to determine the volume of the cone .
Using Formulae
[tex] \boxed{\bf \:Volume_{(Cone)} = \cfrac{1}{3} \pi {r}^{2}h}[/tex]
Substituting the given value and let's solve it
[tex]\sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 3.14 \times {1.1}^{2} \times 3.25 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 3.14 \times 1.21 \times 3.25 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 3.14 \times 3.9325 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 12.34805 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{12.34805}{3} \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = 4.11 {cm}^{3} [/tex]
Therefore,
Volume of the cone is 4.11 cm³ .If I have 1 and 10 dollar bill and 4 quarters, that makes 15$.
Answers
Hey there!
$10.00 + 0.25¢ + 0.25¢ + 0.25¢ + 0.25¢
= $10.25 + 0.25¢ + 0.25¢ + 0.25¢
= $10.50 + 0.25¢ + 0.25¢
= $10.75 + 0.25¢
= $11.00
OR YOU COULD READ THE EQUATION LIKE:
$10.00 + $1.00
= $11.00
Thus, your answer is: FALSE because $10 + 4 quarters gives you $11 NOT $15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
False
Step-by-step explanation:
$10+$1=$11 and .25+.25+.25+.25=$1
which would equal $12 so your answer would be falses if thats what your asking
is x-1 taking away an x or adding an x?? im trying to find the perimeter of area tiles, and the perimeter is x + x + x + (x-1) + 1 + 1 + 1 so would it be 2x+3 or 4x + 3??
Answers
Answer:
4x + 2
Step-by-step explanation:
x - 1 is adding an x and subtracting a 1 ,so
x + x + x + (x - 1) + 1 + 1 + 1
= x + x + x + x - 1 + 1 + 1 + 1 ← collect like terms
= 4x + 2
Find the area of the triangle b= 12.4 cm and h= 18 cm
Answers
Answer:
111.6 cm
Step-by-step explanation:
The area of a triangle can be calculated using the following formula:
Area = (base x height) / 2
Using this formula we can solve this problem in the following way:
We know base = 12.4, and height = 18(12.4 x 18) / 2 = 111.6Hope this helps!!
Answer:
answer 111.6 cm^2.......
Why is the Area for my shape not correct and can you explain why?
Answers
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here, We have given
2 squares , In which 1 square is enclosed within the another square and it arranged in a form that it forms 4 right angled triangle The height and base of the given right angled triangles are 6 and 3 each.We know that,
Area of triangle
[tex]{\sf{=}}{\sf{\dfrac{1}{2}}}{\sf{ {\times} base {\times} height }}[/tex]
Subsitute the required values,
[tex]{\sf{=}}{\sf{\dfrac{1}{2}}}{\sf{ {\times} 3 {\times} 6}}[/tex]
[tex]\sf{ = 3 {\times} 3 }[/tex]
[tex]\bold{ = 9 }[/tex]
Therefore,
Area covered by 4 right angled triangles
[tex]\sf{ = 4 {\times} 9 }[/tex]
[tex]\bold{ = 36}[/tex]
Now,
We have to find the area of the big square
The length of the side of the big square[tex]\sf{ = 6 + 3 = 9 }[/tex]We know that,
Area of square
[tex]\sf{ = Side {\times} Side }[/tex]
Subsitute the required values,
[tex]\sf{ = 9 {\times} 9 }[/tex]
[tex]\bold{ = 81 }[/tex]
Therefore,
The total area of shaded region
= Area of big square - Area covered by 4 right angled triangle
[tex]\sf{ = 81 - 36 }[/tex]
[tex]\bold{ = 45 }[/tex]
Hence, The total area of shaded region is 45 .
Part 2 :-Here,
We have to find the area of non shaded region
According to the question
Hypotenuse = The length of squareLet the hypotenuse of the given right angled triangle be x
Therefore,
By using Pythagoras theorem,
This theorem states that the sum of the squares of the base and perpendicular height is equal to the square of hypotenuse.That is,
[tex]\sf{ (Perpendicular)^{2} + (Base)^{2} = (Hypotenuse)^{2} }[/tex]
Subsitute the required values
[tex]\sf{ (6)^{2} + (3)^{2} = (x)^{2} }[/tex]
[tex]\sf{ 36 + 9 = (x)^{2} }[/tex]
[tex]\sf{ x = \sqrt{45}}[/tex]
[tex]\bold{ x = 6.7 }[/tex]
That means,
The length of the small square = 6.7We know that ,
Area of square
[tex]\sf{ = Side {\times} Side }[/tex]
Subsitute the required values,
[tex]\sf{ = 6.7 {\times} 6.7 }[/tex]
[tex]\bold{ = 44.89 \:\: or \:\: 44.9 }[/tex]
Therefore ,
Area of non shaded region
= Area of big square - Area of small square
[tex]\sf{ = 81 - 44.9 }[/tex]
[tex]\bold{ = 36.1 }[/tex]
Hence, The total area of non shaded region is 36.1 or 36 (approx) .
Part 3 :-Here, we have to
find the total area of the figure Therefore,The total area of the figure
= Non shaded region + Shaded region
[tex]\sf{= 36 + 45 }[/tex]
[tex]\bold{= 81}[/tex]
Hence, The total area of the given figure is 81 .
What is zero raised to the power zero?
Answers
Answer:
1
Step-by-step explanation:
this is because anything to the power of zero is 1
Please Help! Will Give Brainlest!
Answers
Answer:
height of tress is 20 feet
Step-by-step explanation:
because tan = perpendicular/ height
we see option only 20 feet satisfy it
Answer:
Option D :- 20 feet
Step-by-step explanation:
[tex] \sf \tan ( \theta) = \frac{height}{distance} [/tex]
[tex] \rightarrow \sf \: \tan (\theta) = \frac{20}{50} [/tex]
[tex] \sf \: height \: = 20 \: ft[/tex]
what is the algabric way to find the area of a triangle
Answers
The parameters for computing the area of triangle is first listed out and the expression for the area of triangle was used to find the algebraic method
Area of TriangleParameters for find the area of triangle are
BaseHeightLet the base be x, and let the height be y
We know that the expression for the area of triangle is given as
Area = 1/2 (Bass* Height)
Substituting our parameters we have
Area = 1/2*x*y
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What is the volume of a rectangular prism with a length of 7 centimeters, a width of 3 centimeters, and a height of 2 centimeters?
Enter your answer in the box.
V = cm³
Answers
Answer:
42cm³
Step-by-step explanation:
7*2*3=42
7*2=14
14*3=42
42
please help i am confused.
Answers
This is because C and F do not join on the shape
cual es el máximo común divisor de 72, 90 y 36?
Answers
Answer:
6
Step-by-step explanation:
6 x 6 = 36
6 x 12 = 72
6 x 15 = 90
Select the two values of x that are roots of this equation.
Answers
Answer:
C and D :)
Step-by-step explanation:
Answer:
c and d
Step-by-step explanation:
please help this question is hard (25 POINTS!!)
An experiment involves rolling two dice simultaneously. The following table shows the possible outcomes using the format of (die 1,die 2).
1 2 3 4 5 6
1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
What is the probability of rolling 2 even numbers?
Enter your answer as a reduced fraction, like this: 3/14
Answers
Answer:
1/9
Step-by-step explanation:
Sum = 4: (1,3) (2,2) (3,1)
Sum = 12: (6,6)
4/36 = 1/9 or 0.111
hope that helps
i dont understand this question im very bad at maths
Answers
so it’s 2400
2400cm³
Step-by-step explanation:[tex]Volume=15\times 20\times 8[/tex][tex]=300\times 8\\ =2400cm^3[/tex]
[tex](Analyze\ the\ information\ carefully)[/tex]
I hope this helps you
:)
-2 (3x -5) -2= 22 - 68
Answers
Answer:
9
Step-by-step explanation:
Answer:
i belive the awnser is 9
Step-by-step explanation:
The perimeter of a notebook is 28
inches. The area is 48 square inches.
What are the dimensions of the
notebook?
Answers
Area = length x width
Half the perimeter = length + width
half the perimeter = 14 inches.
Find 2 numbers when added together = 14 and when multiplied together = 48
6 + 8 = 14
6 x 8 = 48
the dimensions are 6 inches by 8 inches
van brought a 16 pound bag of dog food .hos dog ate 2/3 of the food. how many pounds of dog food did the dog eat
Answers
Answer:
10.66
Step-by-step explanation:
16/3 = 5.3
5.3 x 2 = 10.66
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Gertrude takes out a $5,500 subsidized stafford loan, which must be paid back in ten years. gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and gertrude makes monthly payments, how much interest will she pay by the time the loan is repaid? round all dollar values to the nearest cent. a. $4,462.40 b. $1,213.28 c. $1,713.69 d. $2,094.80
Answers
The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.
What is compound interest?Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.
Gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments.
Put the values in the above formula as,
[tex]5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29[/tex]
In the 10 years, the refund she gets,
[tex]A_r=63.29\times12\times100\\A_r=7594.8[/tex]
Interest paid by her is,
[tex]I=7594.8-5500\\I=2094.8[/tex]
Thus, the total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.
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Answer: D
Step-by-step explanation:
You put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly. how much will you have after 23 years? round to the nearest cent. a. $46,683.28 b. $4,564,471.88 c. $2,949.39 d. $3,832.84
Answers
After 23 years $125.32 will be matured to $46,683.28.
What is the formula for recurring investment?The formula for Recurring maturity is given by:
[tex]A=P_n\dfrac{p\times n \times(n+1)}{24}\times \dfrac{r}{100}[/tex]
Where A=matured amount
P =Principal value
n=Number of months
r=Interest rate(annual)
We have P= $125.32
n=23*12 = 276 months
r=2.5*12 =30%
Put these values in the above formula
we get A= $46,683.28
Therefore, After 23 years $125.32 will be matured to $46,683.28.
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The diameter of a circle is 10 3/4 inches What is the radius, r, of the circle?
Answers
Answer:
10
Step-by-step explanation:
Using the formula
d=2r
Solving for r
r=d
2=10
2=5
Please Help! What is the measure of the reference angle that corresponds to an angle of measure 278°
Answers
Answer:
82 degrees
Step-by-step explanation:
Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive.
82 DEGREES
On a map with a scale of 1 : 50000 , he shortest distance from the railway line to the river is 2.1km. What distance on the map would represent this?
Answers
Answer:
105,000
Step-by-step explanation:
I'd the scale is 1 : 50,000, you would first take the 2.1km and multiply it by your 50,000. This will put your answer to scale coming in at 105,000 km on the map