write x=3 sin theta and y = 8cos theta in rectangular form
Answers
Answer:
x²/9 +y²/64 = 1
Step-by-step explanation:
You want the figure defined by x = 3sin(θ) and y = 8cos(θ) to be described by an equation in rectangular form.
Pythagorean identityThe trig identity sin(x)² +cos(x)² = 1 is helpful here.
x = 3sin(θ) ⇒ x/3 = sin(θ)
y = 8cos(θ) ⇒ y/8 = cos(θ)
Combining these using the above identity, we have ...
(x/3)² +(y/8)² = 1 . . . . . . the equation of an ellipse
We can simplify the denominators to ...
x²/9 +y²/64 = 1
__
Additional comment
The attached graph uses different colors and textures to show the two forms of expressing the graph result in the same figure.
Related Questions
What is the product for 20x4=
Answers
Answer:80
Step-by-step explanation:
Twenty, four times is 80, turn the problem into different segments like 20+20+20+20=80
A t-shirt printer can produce 40 tank tops with logos in 5 hours. At this rate, how many tank tops with logos can they printer produce in 7 hours?
Answers
Answer: It should be 56
Step-by-step explanation:
first we know for 40 tank-tops with logos can be finished in 5 hours, but we need to know how many shirts can be printed in 7 hours.
First we have x as 40 and y as 5. How many times can 5 go into 40?.. 8 times. So now we have 8. 8 x 7=56
X=56
Y=8
I hope this helps! Just to make sure it may not be correct, very sorry if it didn't work! Have a nice day/night!
-GreenteaStudys
help please xxxxxxxxxxxx
Answers
6(10)+12=72
If the growth factor of function f is k times the growth factor of function g, what is the value of k?
Answers
The value of k depends on the specific functions f and g and their growth rates. The growth factor is a measure of how quickly a function grows relative to another function. To determine the value of k, you would need to compare the growth rates of f and g.
Finding Value of kHere's how you can do to finding the value of k:
Define the functions f and g and specify their growth rates.Express the growth rate of f in terms of the growth rate of g.Solve for k.For example, if f(n) = n² and g(n) = n, then the growth rate of f is proportional to n² and the growth rate of g is proportional to n. To find the value of k, we can write:n² = k * n
Dividing both sides by n, we get:n = k
So in this case, the value of k is 1.This is just a simple example, and the specific value of k will depend on the growth rates of the specific functions you're comparing.
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william has a 26 2626-liter glass tank. first, he wants to put some marbles in it, all of the same volume. then, he wants to fill the tank with water until it's completely full. if he uses 85 8585 marbles, he will have to add 20.9 20.920, point, 9 liters of water. what is the volume of each marble?
Answers
The volume of each marble in a 26 liter glass tank is 12.
The tank's volume is listed as 26.
The tank requires 20.9 liters of water to fill when 85 marbles are placed inside.
So the volume of 85 marble
= 26-20.9 = 5.1
So, volume of each marble
= 5.1/85 = 0.06
Therefore, the volume that will be covered if William wishes to use 200 marbles is:
200*0.6 = 12
Therefore, the volume of marbles in a 26 litre tank is equal to 12
Water will therefore be needed to fill the tank.
= 26 - 12 = 14
Therefore, The volume of each marble in a 26 liter glass tank is 12.
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Complete question:
William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? How much water is necessary if William uses 200 marbles?
Two families attend a performance of the Circus Mage. The cost of a ticket for adult is
1.5 times higher than that of a child ticket. Clothilde buys a ticket for her, for her
husband and for her 2 children. She pays $90 in all, taxes included. Her friend Naomie
buys tickets for her 4 children and herself. Clothilde thinks that going to the circus
costs her less than Naomie. Is she right?
Answers
Clothilde thinks that going to the circus costs her less than Naomie and she is right
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let the cost of 1 child be "c"
Let the cost of 1 adult be "a"
Given a=1.5c
Clothilde buys a ticket for her, for her
husband and for her 2 children.
=> She buys for 2 adults and 2 children
price = 2a+2c
Substitute a=1.5c
price = 2(1.5c )+2c
= 3c+2c
= 5c
Naomie
buys tickets for her 4 children and herself.
=> She buys for 1 adult and 4 children
price = a+4c
Substitute a=1.5c
price = 1.5c +4c
= 5.5c
5c < 5.5c
So, Clothilde thinks that going to the circus costs her less than Naomie and she is right
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Cosec 2A + cot 4A = cot A - cosec 4A
Answers
The given trigonometric function Cosec 2A + cot 4A = cot A - cosec 4A can be proved using the properties of the trigonometric functions.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given that,
Cosec 2A + cot 4A = cot A - cosec 4A
Taking the LHS
= Cosec 2A + cot 4A
= 1 / sin 2A + cos 4A / sin 4A
To take the LCM we multiply and divide the first term by 2cos 2A:
= 2cos 2A / 2 sin 2A cos 2A + cos 4A/ sin4A
= 2cos 2A / sin 4A + cos 4A/ sin4A
= 2 cos 2A + 2 cos² A -1 / Sin 4A
= 2 cos 2A (1 + cos 2A) - 1 / sin 4A - 1/ sin 4A
= 2cos 2A 2cos² A / 2 sin 2A cos 2A - cosec 4A
= cos A / sin A - cosec 4A
= cot A - cosec 4A
Hence proved.
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What is Y=2x+1 I can’t find it
Answers
Y=2x+1 is an equation used in mathematics to calculate the relationship between two variables, X and Y.
What is equation?An equation is a physical and mathematical statement that describing physical phenomena are describe the relationship between different physical quantities it typically consists of two or more variable which are simple representing physical quantity and then equal sign the variable may be quantity such as force velocity or energy.
This equation is a linear equation, meaning it is a straight line when graphed. It is a very basic equation and one of the most commonly used equations.
To use this equation, you will need to know the value of X. Once you have determined the value of X, you can plug it into the equation to calculate the value of Y. For example, if X=3, then the equation would look like this: Y=2(3)+1, which equals 7. Therefore, when X=3, Y=7.
The equation Y=2x+1 is often used in a variety of math problems, such as determining the slope of a line, calculating the area of a triangle, and finding the equation of a circle. It is also used in physics to calculate velocity or acceleration. As you can see, this equation is quite versatile and can be used in a variety of situations.
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A small tree was planted at a height of 5 feet. The tree has been planted for 15 months, and is now 42.5 feet tall. Which equation could be used to find x, the average number of feet the tree grew each month?
A.
15x + 5 = 42.5
B.
5x + 15 = 42.5
C.
15x + 42.5 = 5
D.
42.5x + 5 = 15
Answers
The equation that shows the height of the tree is 42.5 = 15x + 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The slope intercept form of the linear equation is:
y = mx + b
where m is the slope and b is the initial value.
Let y represent the height of the small tree and x represent the average number of feet the tree grew each month. Hence:
A small tree was planted at a height of 5 feet. Hence, b = 5.
The tree has been planted for 15 months, and is now 42.5 feet tall. This makes:
42.5 = 15x + 5
The equation is 42.5 = 15x + 5
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Pls po i really need this help. I'll mark brainliest who answered po.
Answers
The table is filled as follows
x P(x) x P(x) (x - μ)²
3 3 9 961
4 7 28 900
5 22 110 841
6 60 360 784
7 85 595 729
8 32 256 676
9 8 72 625
mean, μ = 34.05
variance = 919.33
standard deviation = 30.32
How to solve for the meanThe mean is calculated using the information provided as follows
= summation of (x P(x) ) / summation of x
= 1430 / 42
=34
The variance is solved by the formula
= summation of (x - μ)² / (n - 1), where n = 7
= 5516 / (7 - 1)
= 5516 / 6
= 919.33
the standard deviation is solved using the formula
= √variance
= √919.33
= 30.32
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Susan Marciano invested part of her $32,000 bonus in a fund that paid a 9% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each
investment if her overall net profit was $2,040.
The amount invested at 9% is $.
The amount invested in stock is $
Answers
Let x be the amount of money invested in the 9% fund. Then the amount invested in the stock is $32,000 - x. The profit from the 9% investment is 0.09x and the loss from the stock investment is -0.03(32000 - x).
What exactly does compounding mean?
Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
The overall net profit was $2,040, so we can set up the following equation to solve for x:
0.09x - 0.03(32000 - x) = 2040
Expanding the second term,
0.09x - 9600 + 0.03x = 2040
Combining like terms,
0.12x - 9600 = 2040
Adding 9600 to both sides,
0.12x = 1640 + 9600
Simplifying,
0.12x = 11240
Dividing both sides by 0.12,
x = 93, 666.67
So, the amount invested in the 9% fund is $93,666.67 and the amount invested in the stock is $32,000 - $93,666.67 = $-61,666.67.
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Find the slope of the line that passes through (-3,-7) and (7,9)
Answers
Answer:
Step-by-step explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
Slope = (y2 - y1) / (x2 - x1)
Plugging in the given points, we get:
Slope = (9 - (-7)) / (7 - (-3))
= 16 / 10
= 1.6
So the slope of the line passing through (-3, -7) and (7, 9) is 1.6.
Answer:
m = 8/5
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
(-3,-7) and (7,9)
We see the y increase by 16 and the x increase by 10, so the slope is
m = 16/10 = 8/5
So, the slope is 8/5
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation c -3/7x+3=y; A(...; 6), B(9; ...)
Answers
To find the missing coordinates of the points A and B [1], you can use the equation c -3/7x + 3 = y. Plugging in the given x-coordinates for A and B, you can solve for their y-coordinates.
A: x = -2, y = -3 B: x = 9, y = 6
To find the slope of the line, you can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates for A and B, you can calculate the slope as m = (6 - (-3))/(9 - (-2)) = 9/11.
To further explore the topic, you can look into how to graph equations in slope-intercept form, as well as how to find equations of parallel and perpendicular lines. You can also learn how to use the equation of a line to calculate distances between points, and how to calculate the midpoint of a line segment.
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When my wife and I drove to Boston from Chicago (a trip of about 1170 miles), the trip took a total of 20 hours. The first part of the trip, I drove at an average speed of 55 mph. The second part of the trip was driven by my wife, who drove at an average speed of 65 mph. For how many hours did each of us drive?
Answers
Let's call the time you drove "x" and the time your wife drove "y". We know that the sum of the two times is 20 hours:
x + y = 20
We also know the distance traveled during each part of the trip. The first part of the trip was 55x miles, and the second part of the trip was 65y miles. The total distance of the trip was 1170 miles:
55x + 65y = 1170
We can use the first equation to solve for x in terms of y:
x = 20 - y
We can then substitute this expression for x in the second equation:
55(20 - y) + 65y = 1170
Simplifying and solving for y:
1100 - 55y + 65y = 1170
10y = 70
y = 7
So your wife drove for 7 hours. We can use the first equation to find your driving time:
x + 7 = 20
x = 13
So you drove for 13 hours.
Answer:
13 hours
Step-by-step explanation:
Part A
BOXES The diagram shows the dimensions of a box used by a manufacturing company to
ship products.
s+2
s+3
What is the volume of the box? Write the expression in standard form.
Answers
the difference of their volumes of the boxes is 2lh+2bh+2lb+4b+4l+4h+8.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Let the 1st box have length l, width b and height h.
So the 2nd box will have l+2, b+2 and h+2.
volume of 1st box is l*b*h.
volume of 2nd box is (l+2)*(b+2)*(h+2)= (lb+2l+2b+4)(h+2)
=lbh+2lh + 2bh+4h+2lb+4l+4b+8
The difference of their volumes = 2lh+2bh+2lb+4b+4l+4h+8
Hence the difference of their volumes of the boxes is 2lh+2bh+2lb+4b+4l+4h+8.
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A family wants to rent a car to go on vacation. Company A charges $35.50 and 9¢ per mile. Company B charges $55.50 and 13¢ per mile. How much more does Company B charge for x miles than Company A?
Answers
The amount of money company B charges more for x miles than company A is 4¢
How much more does Company B charge for x miles than Company A?let
Number of miles= x
Company A:
35.50 + 9x
This means company A charges 9¢ per mile
Company B:
55.50 + 13x
This means company B charges 13¢ per mile
The amount of money company B charges more for x miles than Company A = 13¢ - 9¢
= 4¢
Therefore, company B charges 4¢ more than company A for x miles.
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I need help with getting an answer for these
Answers
Answer:
Step-by-step explanation:
(-1, 6/5) = logbase4(5x^2) etc
only 5 = ln(x+5) = ln (x-1) + ln(x+1)
only 3 = log(x-1) etc.
(-1, 5) = e^x^2 = e^4x+5
At a small high school, 5 students took Mrs. Jones's AP Statistics class last year. The student's names are Ashley, Brayden, Carmen, Dale, and Eve. Ashley, Brayden, and Carmen each got a 5 on the AP Statistics exam. Mrs. Jones would like to use the results of these 5 students to demonstrate how to create a sampling distribution of the sample proportion for simple random samples of size n = 2 for her current students. a) What is the value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam? Explain. b) Using the table provided, list all 10 possible simple random samples of size n = 2, and for each sample calculate the sample proportion of students who got a 5 on the AP Statistics exam. The first one is completed for you. SRS n = 2 А, В P 1 c) Using the number line provided, create a dotplot to display the sampling distribution of p. d) is the sample proportion an unbiased estimator of the population proportion? Explain.
Answers
Answer:
Step-by-step explanation:
a) The value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam, is 3/5. This is because out of the 5 students, 3 (Ashley, Brayden, and Carmen) got a 5 on the AP Statistics exam.
b) The 10 possible simple random samples of size n = 2 are:
Ashley, Brayden; P = 2/2 = 1
Ashley, Carmen; P = 2/2 = 1
Ashley, Dale; P = 1/2 = 0.5
Ashley, Eve; P = 1/2 = 0.5
Brayden, Carmen; P = 2/2 = 1
Brayden, Dale; P = 1/2 = 0.5
Brayden, Eve; P = 1/2 = 0.5
Carmen, Dale; P = 1/2 = 0.5
Carmen, Eve; P = 1/2 = 0.5
Dale, Eve; P = 0/2 = 0
c) To create the dotplot for the sampling distribution of p:
Label the number line with 0, 0.5, 1
For each sample proportion calculated, place a dot above the corresponding value on the number line
Repeat this process for all sample proportions
d) Yes, the sample proportion is an unbiased estimator of the population proportion. This means that on average, the sample proportion will equal the population proportion. In other words, the mean of the sampling distribution of the sample proportion will equal the population proportion.
17 Problem-solving Orla drove 155 km in 2 hours. Then she drove 48 km at a speed of 60 km/h. 48 Work out Orla's average speed for the whole journey.
Answers
The average speed for the whole journey is 72.5 km/h. The result is obtained by using the formula for the average speed.
What is average speed?Average speed is the overall speed of a moving object during a given amount of time. It can be expressed as
Avg speed = Total distance covered / Total time taken
The speed itself is
v = s/t
Where
v = speeds = distancet = time takenOrla drove 155 km in 2 hours. Then, she drove 48 km at a speed of 60 km/h. Find the average speed for the whole journey!
We have
s₁ = 155 kmt₁ = 2 hourss₂ = 48 kmv₂ = 60 km/hThe time taken in the second journey is
v₂ = s₂/t₂
60 = 48/t₂
t₂ = 48/60
t₂ = 0.8 h
The average speed will be
= total distance covered / total time taken
= (s₁ + s₂)/(t₁ + t₂)
= (155 + 48)/(2 + 0.8)
= (203)/(2.8)
= 72.5 km/h
Hence, the whole journey will have the average speed of 72.5 km/h.
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How is (8÷ 2) + (4 x 7) written as a verbal description?
Answers
The expression "8 divided by 2 plus 4 multiplied by 7" is written as (8 ÷ 2) + (4 x 7) in mathematical notation.
the length of a rectangle is 4 times the width. if the length is decreased by 5cm and the width is increased by 2cm, the perimeter will be 74. Find the dimensions of the original rectangle.
Answers
Answer:
w=6, L=24
Step-by-step explanation:
let the width be x,
then, L=4x
Perimeter=2(l+w)
=2(4x+x)
the new dimensions,
perimeter=2(l+w)
74 =2(4x+5+x+2)
=2(5x+7)
=10x+14
10x=74-14
10x=60
x=60/10
x=6
Therefore, The width is 6 cm
L=4x
=4(6)
=24
Therefore the length is 24 cm
if you draw five cards at random from a standard deck of 52 cards, what is the probability that there are at least 4 distinct characters (letters or numbers)?
Answers
If you draw five cards at random from a standard deck of 52 cards, the probability that there are at least 4 distinct characters (letters or numbers) is 0.8406.
This probability is calculated using the combination formula. The formula states that the number of possible outcomes when selecting r items from a set of n is equal to n!/(r! (n-r)!). consider a deck of 52 cards, each with a unique letter or number. When selecting 5 cards at random, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters.
This is because if there are 4 distinct characters, there must be a fifth card with a character that has already been drawn. Therefore, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters. Since there are 52 possible characters and we are selecting 5 cards, the probability can be calculated using the combination formula and is equal to 0.8406.
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what is the domain and range
Answers
Write the slope-intercept form of the equation of the line satisfying the given conditions.
Through (-2,4); slope: -3/4
Write the equation in slope-intercept form.
(Simplify your answer. Type your answer in slope-intercept form.)
Answers
I’m pretty sure it’s y = 0x+4
How many solutions does the system of equations have?
A. No solution
B. Four solutions
C. Exactly one solution
D. Infinitely many solutions
Answers
Answer:
C. Exactly one solution
Step-by-step explanation:
You want to know the number of solutions of the system of equations shown in the graph.
Point(s) of intersectionA solution to a system of equations is the set of points on a graph where all of the equations are satisfied simultaneously. For a system of two linear equations, it will be the point(s) where the lines intersect.
Here, the lines intersect at one point, so there is exactly one solution.
Equations with variable on both sides
Answers
Answer:
n = -3
Step-by-step explanation:
3n - 15 = 7n + n
3n - 15 = 8n
3n - 8n = 15
-5n = 15
n = -3
Help me please I really need this
Answers
Answer:
x = 56°
Step-by-step explanation:
x and 124° are a linear pair and sum to 180° , that is
x + 124° = 180° ( subtract 124° from both sides )
x = 56°
Answer:
56°
Step-by-step explanation:
angle on a straight line = 180°
124° + x =180°
x = 180° - 124
x = 56°
8 − 1 − (18 − 2) ÷ 8
Answers
Answer: 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
First do 18-2 which is 16
Then do 16 divided by 8 which is 2
Right now the equation is 8 - 1 - 2
Then we minus 8 by 1 which is 7
and then 7 - 2 which is 5
So then our final answer is 5
(2a^2 - 5a + 10) - (a^2 - 9)
How do you answer this?
Answers
Answer:
a^2 -5a + 19
Step-by-step explanation:
(2a^2 - 5a + 10) - (a^2 - 9)
= (2a^2 - 5a + 10) - a^2 + 9 [Distribution]
= a^2 -5a + 19
John had 72 flyers supposed around town last week he posted 1/3of them this week he posted 5/6 of the remaining flyers how many flyers has he still not posted
Answers
Answer:
8 posters
Explanation:
first you need to find how many he posted the first week. You do this by multiplying 72 by 1/3, or 72/3. That is 24. Then, you need to subtract that amount, 72-24 is 48. Then, you need to figure out how many he posted the second week. To do that, you need to figure out what 1/6 of 48 is first. So you would need to divide 48 by 6, which equals 8. So if John posted 5/6 of 48, you then need to multiply 8 by 5, equaling 40. If john posted 40 of his 48, then 48-40 is 8, meaning he has 8 posters to post.