Answers
The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Here are two key characteristics of the polar coordinate system:
1. Radial Distance (Radius): In the polar coordinate system, the location of a point is determined first by its distance from a fixed point, called the pole, analogous to the origin in the Cartesian coordinate system. This distance is often denoted as \( r \), and it can be thought of as the radius of a circle centered at the pole, with the point lying on the circumference of this circle.
2. Angular Coordinate (Angle): The second characteristic of a point's location in the polar coordinate system is the angle [tex]\( \theta \)[/tex] (theta), which is measured from a fixed direction, typically the positive x-axis of the corresponding Cartesian coordinate system. This angle, usually measured in degrees or radians, determines the direction of the line from the pole to the point.
These two values, [tex]\( r \)[/tex] and [tex]\( \theta \)[/tex], are called polar coordinates, and they provide an alternative to the Cartesian (rectangular) coordinate system for representing points on a plane, particularly useful in scenarios where the geometry or the nature of the problem is radially symmetric, such as in the cases of circular motion or fields (gravitational, electric, etc.).
Related Questions
Plzzzzz help! Will mark brainliest
Answers
Answer:
i am not 100% sure but i believ the answer is C i hope im not too late
Step-by-step explanation:
There are 10 millimeters in 1 centimeter.Convert 27 centimeters to millimeters.
A. 2.7
B. 27
C. 270
D. 2700
Answers
Answer:
C. 270
Step-by-step explanation:
If there are 10 millimeters in 1 centimeter, that means there is 10 times the number of millimeters in a centimeter. So, we would multiply 27 centimeters by 10 to find the number of millimeters.
What is the area of this composite figure, in square centimeters? A triangle with base of 11 centimeters and height of 6 centimeters is on top of a rectangle with length 16 centimeters and width 11 centimeters. Whats the area? A.176 B.209 C.242 or D.264 ??? IS it B?
Answers
Answer:
209
Step-by-step explanation:
i hoped this helped saying no one else wanted to answer have a nice day
The solution is , 209 is the area of this composite figure, in square centimeters.
What is the area of triangle?Area of triangle is defined as the total region that is enclosed by the three sides of any particular triangle.
Formula: area= 1/2× base × height
here, we have,
given that,
A triangle with base of 11 centimeters and height of 6 centimeters is on top of a rectangle with length 16 centimeters and width 11 centimeters.
now, we know,
area of triangle:
area= 1/2× base × height
A = 1/2 * 11 * 6
=33
again,
we have,
Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
so, A = 16* 11
=176
finally, the area of this composite figure, in square centimeters is,
33+176 = 209
Hence, The solution is , 209 is the area of this composite figure, in square centimeters.
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i need help pls asap !!
Answers
Answer:
143
Step-by-step explanation:
Because triangles JKL and JUV are similar, the ratio of JV:LJ also applies to the ratio of UJ:JK. JV:LJ=130:60=13:6, so 17x+7=13\6*(66).
KJ=17x+7=11*13=143
Hope this helps!
Ariel has made a circular flower garden in her yard and she would like to put a plastic border around it. The garden has a radius of 6 feet. Which expression could be used to find the length (in feet) of the plastic border she will need to put around her garden?
Answers
Answer: C = 2 x π x 6
Step-by-step explanation:
Hi, to answer this question we have to calculate the circumference of the circular flower garden.
Since it’s a circle we have to apply the next formula:
Circumference: 2 x π x radius
Replacing with the value given, the expression that represents this situation is:
C = 2 x π x 6
If we solve it:
C= 37.69 feet
Answer:
C = 2 × π × 6
Step-by-step explanation:
Please refer to the attached image for explanations
A fraction has a denominator of 20. The numerator has a value of "x less than the denominator." If the fraction is equivalent to , what is the value of x?
Answers
Answer:
x = 4
Step-by-step explanation:
Extracting the key information from the question:
*** A fraction has 20 as its denominator.
*** The value of the denominator = 20 - x
*** If the fraction is equivalent to or the same as 4/5.
*** We are basically required to calculate the value of x.
Since we are not told what the fraction is equivalent to, we can fix any random fraction in order to help us to understand what we are basically required to do in to get through this sort of question. Now, let us assume that the fraction that this unknown fraction is equivalent to is 4/5.
We have also been informed that this fraction has a denominator of 20 and a numerator that is x less than the denominator. This means/ signifies that the denominator = 20 and the numerator = 20 - x.
i.e the fraction in question = (20 - x)/20.
Since this very fraction is equivalent to 4/5, then:
20-x/20 = 4/5
We will then cross multiply and make "x" the subject of the formula.
(20-x)×5 = 20×4
100 - 5x = 80
5x = 100 - 80
5x = 20
x = 20/5
x = 4
According to the Bureau of Labor Statistics, students who have an after-school job spend an average of 42 fewer minutes per day on schoolwork than students who don't work. If the school year is 180 days, how many more hours per year would the average non-working student spend on schoolwork than the average student with an after-school job?
Answers
Answer:
126 hrs
Step-by-step explanation:
-Given the school year has 180 days and the non-working student spends 42 minutes more than the working student.
-The total time during the school year is calculated as;
[tex]Total Time=Time/day \times No \ of \ Days\\\\=42\ minutes \times 180\\\\=7560\ minutes[/tex]
We convert our calculated time in hour(1hr=60 minutes):
[tex]=\frac{7560\ mins}{60\ mins}\\\\=126\ hrs[/tex]
Hence, the average non-working spends an average of 126 hrs that the working student.
Answer:
weekday,Weekday
Step-by-step explanation:
HAVE A GREAT DAY!!!!!! :)) wrong question lol
40 POINTS PLEASE HELP
Explain how solve 4^(x + 3) = 7 using the change of base formula log^ b y= log y/ log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answers
Answer:
-1.596
Step-by-step explanation:
4^(x + 3) = 7
log4 both sides
log4[4^(x + 3)] = log4(7)
(x + 3) × log4(4) = lg7/lg4
x + 3 = 1.403677461
x = -1.596322539
Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y EndFraction? StartFraction X Y Over T S EndFraction StartFraction S Y Over R Y EndFraction StartFraction R X Over X T EndFraction StartFraction S T Over Y X EndFraction
Answers
Answer:
△RST ~ △RYX by the SSS similarity theorem. Which ratio is also equal to RT/RX and RS/RY ?
A.XY/TS
B.SY/RY
C.RX/XT
D.ST/YX
Step-by-step explanation:
Check attachment for solution
Answer:
D
Step-by-step explanation:
Hello so I need help with my math since that's not my best subject and I'm also squarely brained so can I get some help
Answers
Answer:
212
Step-by-step explanation:
47 goes into 99 2 times
Bring down the 5
47 goes into 56 1 time
Bring the 9
47 goes into 94 2 times
Dayle and his two brothers each eat 5/12 (five-twelfths) of a chocolate bar. How much chocolate bar did they eat altogether? Solve, show your work, and record your answer on a piece of scratch paper. *
Answers
Answer:
N = 5/4 = 1.25
Altogether they eat 1.25 chocolate bar
Step-by-step explanation:
Dayle and his two brothers each eat 5/12 (five-twelfths) of a chocolate bar;
Three of them ate = 5/12 chocolate bar each
Total for the 3 of them N;
N = 3 × 5/12 = 15/12
N = 5/4 = 1.25
Altogether they eat 1.25 chocolate bar
Write an expression to show how many meters are equivalent to x centimeters.
Answers
Answer:
1 metre = 100 centimetres
Step-by-step explanation:
Donna paints ornaments for a school play.Each ornament is made up of two identical cones,as shown. How many bottles of paint does she need to paint 70 ornaments?
Answers
12 bottles of paint does she need to paint 70 ornaments. Hence 12 is correct answer.
1. Calculate the surface area of one cone:
The surface area of a cone is the sum of the area of the base (a circle) and the lateral surface area. Since the cone is cut in half vertically, we only need to consider half of the base and lateral surface area.
Base area: The base is a circle with radius r. The area of a circle is πr². Since the cone is cut in half, the base area is πr² / 2.
Lateral surface area: The lateral surface area is a sector of a circle with radius r and arc length equal to the circumference of the base. The circumference of the base is 2πr. The area of a sector is (arc length × radius) / 2. In this case, area of sector is (2πr×r) / 2 = πr^2.
Therefore, total surface area of one cone is (πr²/ 2) + πr² = 3πr² / 2.
2. Calculate the surface area of one ornament:
Since each ornament is made up of two identical cones, the surface area of one ornament is twice the surface area of one cone. Therefore, the surface area of one ornament is 2×(3πr² / 2) = 3πr^2.
3. Calculate the total surface area of all ornaments:
If Donna needs to paint 70 ornaments, the total surface area she needs to cover is 70×3πr² = 210πr².
4. Convert the surface area to square meters:
However, if you provide the radius in meters, you can multiply the surface area you calculated in 3 by 1 to convert it to square meters.
5. Estimate the number of bottles of paint needed:
The total surface area in square meters, you can estimate the number of bottles of paint Donna needs by dividing the surface area by the coverage area of one bottle of paint. This information is typically available on the paint bottle itself. For example, if one bottle of paint covers 10 square meters, and the total surface area of the ornaments is 210 square meters, Donna would need approximately 210 square meters / 10 square meters/bottle = 21 bottles of paint.
The total cost of attending a state university is $19,700 for the first year. • A student's grandparents will pay half of this cost. • An athletic scholarship will pay another $5,000. Which amount is closest to the minimum that the student will need to save every month in order to pay off the remaining cost at the end of 12 months?
Answers
Answer:
The student will have to save $404.2 minimum monthly
Step-by-step explanation:
Given that the total cost for the first year= $19,700
The grandparents paid half the amount = 1/2(19700)= $9850
The remaining balance to be paid is
19,700 - 9850=$9850
If an athlete paid $5000
The the remaining balance to be paid = 9850-5000=$4850
For the student to clear this amount in 12 months he must save
monthly 4850/12= $404.166
Hence the minimum amount to be saved per month is $404.2
Answer:
The student will have to save a minimum of $404.17 every month.
Step-by-step explanation:
The total cost of attending the sate university is $19, 700 for the first year alone.
Total cost for a year = $19700
A student's grandparent will pay half of the cost . This means the grand parents will pay
1/2 of the total cost for a year
1/2 × 19700 = $9850
The grand parent will pay $9850
An athletic scholarship will pay $5000 . It will be 9850 - 5000 = 4850 . The remaining amount to pay is $4850 .
At the end of 12 months the minimum amount the student will save every month to be able to pay the remaining amount will be the amount payable divided by 12 month.
minimum amount to save every month = 4850/12
minimum amount to save every month = 404.16666667
minimum amount to save every month ≈ 404.17
Point A is at (-5, –4) and point B is at (5,-3).
What is the midpoint of line segment AB?
Answers
The midpoint of the line segment AB with points A at (-5, -4) and B at (5, -3) can be found by averaging the x and y coordinates of the two points. The x-coordinate of the midpoint is 0 and the y-coordinate is -3.5, hence the midpoint is (0, -3.5).
Explanation:The subject of this question is Mathematics, specifically discussing the concept of finding the midpoint of a line segment in a 2D coordinate system. The midpoint of a line segment can be calculated using the coordinates of the two ends of the line segment. To find it, you add the coordinates (x, y) of the two points and divide each sum by 2. In this case, the coordinates of points A and B are (-5, -4) and (5, -3) respectively. Thus, the x-coordinate of the midpoint is (-5 + 5)/2 = 0 and the y-coordinate of the midpoint is (-3 - 4)/2 = -3.5. Therefore, the midpoint of line segment AB is at (0, -3.5).
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The dot plot below represents the number of dollars in allowance that students receive each week in mrs.jimenez’s class.what is the median amount of allowance?
Answers
Answer:
6
Step-by-step explanation:
search up on quizizz
Miss turner drove 900 miles in March. She drove 3 times as many miles in March as she did in January. She drove 4 times as many miles in February than January. How many miles did Ms turner drive in February?
Answers
Answer:
1200 miles
Step-by-step explanation:
Miss Turner drove 900 miles in March.
We are told that she drove 3 times as many miles in March as she did in January. This means that to get the number of miles she drove in January, we divide the number of miles she drove in March by 3:
900 / 3 = 300 miles
We are also told that she drove 4 times as many miles in February than January. This means that to get the number of miles she drove in February, we multiply the number of miles she drove in January by 4:
300 * 4 = 1200 miles.
Hence, she drove 1200 miles in February.
Three streets intersect to form a right triangle as shown below. The parts of streets that make up the legs of this triangle are 42 yd. Long and 56 yd. Long. How long is the third side of the triangle formed by the three streets?
Answers
Answer:
70 yd.
Step-by-step explanation:
The three streets at the intersection form a right triangle.
For a right triangle, the length of the longest side (called hypothenuse) is given by Pythagorean's theorem:
[tex]h=\sqrt{x^2+y^2}[/tex]
where
x is the length of the 1st side
y is the length of the 2nd side
h is the length of the hypothenuse
Here we want to find the hypothenuse.
We have:
x = 42 yd (length of the 1st side)
y = 56 yd (length of the 2nd side)
Substituting, we find h:
[tex]h=\sqrt{42^2+56^2}=70 yd[/tex]
Answer:
70
Step-by-step explanation: i don't why it only says one answer i thing brainly messed up cause it says i have no brainliest ether to.
find the diameter of a circle with an area of 90.25 pi square meters
Answers
Answer:
19 meters
Step-by-step explanation:
The area of a circle is given as [tex]90.25\pi[/tex]
-A circle's area is calculated using the formula:
[tex]A=\pi r^2, r=0.5D, D=Diameter[/tex]
#We substitute for area in the equation and solve for D;
[tex]A=\pi (0.5D)^2\\\\90.25\pi=\pi (0.5D)^2\\\\\sqrt{90.25}=0.5D\\\\D=19[/tex]
Hence, the circle's diameter is 19 meters
Diameter of a circle = 19 meters
Circle :
Circle is a rounded figure that consists of points that are equidistance from the center
Area of a circle :Area of a circle is the area enclosed by the circle . The distance between the center to the circumference of circle is the radius.
Diameter is a straight line from one end of circle to the other end and it passes through the center of the circle
Given that area of the circle is 90.25 pi square meters
Area of the circle formula is
[tex]Area = \pi r^2\\90.25\pi =\pi r^2\\divide \; both \; sides \; by \; pi\\90.25=r^2\\take \; square \; root \; on \; both \; sides\\r=\sqrt{90.25}\\ r=9.5[/tex]
diameter of the circle = 2 times of the radius
Diameter = 2 times 9.5=19 meters
Diameter of a circle = 19 meters
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The Captain has probability \dfrac{1}{2} 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{1}{6} 6 1 start fraction, 1, divided by, 6, end fraction. If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?
Answers
Answer:
0.083 is the required probability.
Step-by-step explanation:
We are given the following in the question:
Probability of captain hitting pirate's ship =
[tex]P(A) = \dfrac{1}{2}[/tex]
Probability of pirate hitting the captain's ship =
[tex]P(B) = \dfrac{1}{6}[/tex]
Probability that both the pirate and the Captain hit each other's ships:
[tex]P(A\cap B) = P(A)\times P(B)[/tex]
Putting values, we get,
[tex]P(A\cap B) =\dfrac{1}{2}\times \dfrac{1}{6} = \dfrac{1}{12} \\\\P(A\cap B) = 0 .083[/tex]
0.083 is the probability that both the pirate and the Captain hit each other's ships.
For what value of X is expression
2x-1/x
[tex]2x - 1 \div x[/tex]
Answers
Steps to simplify:
2x - 1 / x
~Convert to fraction
2xx/x - 1/x
~Combine the fractions
2xx-1/x
~Simplify
2x²-1/x
Best of Luck!
There are k players, with player i having value vi > 0, i= 1, ..., K. In every period, two of the players play a game, while the other k -2 wait in an ordered line. The loser of a game joins the end of the line, and the winner then plays a new game against the player who is first in line. Whenever i and j play, i wins with probability
Answers
A geometric random variable represents the number of games played until a player loses. The probability can be calculated using the formula P(X = k) = (1-p)^(k-1) * p, where p is the probability of losing a game and k is the number of games.
Explanation:A geometric random variable, denoted as X, represents the number of games played until a player loses. It is a type of random variable in probability theory. We can calculate the probability that it takes a certain number of games until the player loses by using the formula P(X = k) = (1-p)^(k-1) * p, where p is the probability of losing a game and k is the number of games. For example, if p = 0.57 and we want to find the probability that it takes five games until the player loses, we can calculate P(X = 5) = (1-0.57)^(5-1) * 0.57.
Zachary is making a scale model of the sydney oprera house fir a report on sydney.Tge sydney opera house is 213 feet tall measuring from the ground to thr tip of thevjighest roof shell.If thevmodel is 1/100 the actual size of the sydney operahouse,how tall is the model?
Answers
Answer:
The height of Sydney opera house in the model is 2.13 feet.
Step-by-step explanation:
We are given the following in the question:
Height of Sydney opera house = 213 feet
Height in model =
[tex]\dfrac{1}{100}\text{ of the actual height}[/tex]
We have to evaluate the height of Sydney opera house in model.
Height in model =
[tex]=\dfrac{1}{100}\times 213\\\\=2.13\text{ feet}[/tex]
Thus, the height of Sydney opera house in the model is 2.13 feet.
PLEASE HELP WILL MARK BRAINLIEST!
What is measure of angle P?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
Answer:
60 degrees
Step-by-step explanation:
it is a special 30-60-90 triangle
Answer:67.4
Step-by-step explanation:
This is a basic triangle you have to memorize these angles
Let x1, x2, and x3 represent the times necessary to perform three successive repair tasks at a certain service facility. suppose they are independent, normal rv's with expected values m1, m2, and m3 and variances s21, s2, and s23, respec- tively.
Answers
Answer:
P(T₀ < 200) = 0.99856
P(150 < T₀ < 200) = 0.99856
Step-by-step explanation:
The expected values for each of the tasks is μ₁ = 60, μ₂ = 60, μ₃ = 60
The variances for each of the 3 tasks
σ₁² = 15, σ₂² = 15, σ₃² = 15
calculate P(T₀ < 200) and P(150 < T₀ < 200)
When independent distributions are combined, the combined mean and combined variance are given through the relation
Combined mean = Σ λᵢμᵢ
(summing all of the distributions in the manner that they are combined)
Combined variance = Σ λᵢ²σᵢ²
(summing all of the distributions in the manner that they are combined)
Distribution of total time taken for the 3 successive tasks
= X₁ + X₂ + X₃
Expected value = Combined Mean = μ₁ + μ₂ + μ₃ = 60 + 60 + 60 = 180
Combined Variance = 1²σ₁² + 1²σ₂² + 1²σ₃²
= (1² × 15) + (1² × 15) + (1² × 15)
= 45
standard deviation of the combined distribution = √(variance) = √45 = 6.708
Since each of the distributions are said to be normal, the combined distribution too, is normal.
P(T₀ < 200)
We first standardize 200
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (200 - 180)/6.708 = 2.98
The required probability
= P(T₀ < 200) = P(z < 2.98)
We'll use data from the normal probability table for these probabilities
P(T₀ < 200) = P(z < 2.98) = 0.99856
b) P(150 < T₀ < 200)
We first standardize 150 and 200
For 150
z = (x - μ)/σ = (150 - 180)/6.708 = -4.47
For 200
z = (x - μ)/σ = (200 - 180)/6.708 = 2.98
The required probability
= P(150 < T₀ < 200) = P(-4.47 < T₀ < 2.98)
We'll use data from the normal probability table for these probabilities
P(150 < T₀ < 200) = P(-4.47 < T₀ < 2.98)
= P(z < 2.98) - P(z < -4.47)
= 0.99856 - 0.0000 = 0.99856
Hope this Helps!!!
This question relates to the times needed for repair tasks at a service facility and involves concepts such as expected values, variances, and probability distributions. It also mentions sample standard deviations, estimates of population standard deviations, and sample means.
Explanation:The question is about the times necessary to perform three successive repair tasks at a service facility. Let x1, x2, and x3 represent the times for each task. Assuming they are independent, normal random variables, we can calculate the expected values and variances using the given information. For example, the expected value of x1 is m1, and the variance is s21.
The question also refers to different figures that represent probability distributions for the repair times. In Figure 5.19, the shaded area represents the probability that the repair time is less than three. In Figure 5.18, the shaded area represents the probability that the repair time is greater than two. These figures provide visual representations of the probabilities associated with the repair times.
Finally, the question mentions the concepts of sample standard deviations, estimates of population standard deviations, sample means, and population means. These concepts are relevant for analyzing the repair times and understanding the characteristics of the data.
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Given f(x) = 3x – 2, find f(-5).
Answers
Answer:
f(-5)= -17
Step-by-step explanation:
We want to find at what value of f(x), or y, does x=-5
So, to find when x=-5, or f(-5), substitute -5 in for x
f(x)=3x-2
f(-5)=3(-5)-2
Multiply first (PEMDAS)
f(-5)=-15-2
Subtract
f(-5)= -17
Hope this helps! :)
Answer:
f(-5) = -17
Step-by-step explanation:
f(x) = 3x – 2 Substitute -5 for x
f(-5) = 3(-5) - 2 Multiply
f(-5) = -15 - 2 Subtract
f(-5) = -17
16.85 - 3.9 what is the answer
A 16.46
B 12.95
C 20.75
D 16.811
Answers
3t^6 x 8t^-6
^ this is an exponent signal^
x is multipulcation
Answers
Answer:
24
Step-by-step explanation:
3t⁶ × 8(t^-6)
3 × 8 × t⁶ × t^-6
24 × t^(6-6)
24 × t⁰
24 × 1
24
Judy currently has one credit card. She owes $500 and the credit card has a rate of 15%
per month. How much does Judy owe 8 months from now?
Answers
$ 1,100
Step-by-step explanation:
Well use the simple interest equation;
A = P(1 + rt)
Where:
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
A = 500 (1 + 0.15*8)
A = 500 (2.2)
= 1100
Ivan wants to ship a box that is 6 in. Tall, 4 in. Wide, and 5 in. Long to his cousin, and used the calculation below. What was his error, and what is the correct volume? V = lwh V = 5 x 4 x 6 = 20 x 6 = 26 in.3
Answers
Answer:
the correct volume is 120in.3
Step-by-step explanation:
he did his math wrong, 20 x 6 is not 26.
V = 5 x 4 x 6 = 20 x 6 = 120
Answer:
He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.
Step-by-step explanation:
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