find the x- and y-intercepts of the generic ellipse described by x 2 m2 y 2 n2 = 1. find a parametric description of this ellipse
Answers
The x-intercepts of the ellipse are (-m, 0) and (m, 0), while the y-intercepts are (0, -n) and (0, n).
A parametric description of this ellipse can be given as x = m cos(t), y = n sin(t), where t is a parameter that varies from 0 to 2π.
The equation of the ellipse is x^2/m^2 + y^2/n^2 = 1, where m and n are the lengths of the semi-major and semi-minor axes, respectively. To find the x-intercepts, we set y = 0 and solve for x, which gives x = ±m. Similarly, to find the y-intercepts, we set x = 0 and solve for y, which gives y = ±n.
A parametric description of an ellipse can be given in terms of its semi-major and semi-minor axes as x = a cos(t), y = b sin(t), where t is a parameter that varies from 0 to 2π. In this case, the semi-major and semi-minor axes are m and n, respectively, so the parametric description of the ellipse is x = m cos(t), y = n sin(t).
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Related Questions
divide (3x^2-14x-5) by (x-5)
Answers
Answer:
3x+1
Step-by-step explanation:
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
x
-
5
3
x
2
-
14
x
-
5
Divide the highest order term in the dividend
3
x
2
by the highest order term in divisor
x
.
3
x
x
-
5
3
x
2
-
14
x
-
5
Multiply the new quotient term by the divisor.
3
x
x
-
5
3
x
2
-
14
x
-
5
+
3
x
2
-
15
x
The expression needs to be subtracted from the dividend, so change all the signs in
3
x
2
−
15
x
3
x
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
Pull the next terms from the original dividend down into the current dividend.
3
x
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
Divide the highest order term in the dividend
x
by the highest order term in divisor
x
.
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
Multiply the new quotient term by the divisor.
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
+
x
-
5
The expression needs to be subtracted from the dividend, so change all the signs in
x
−
5
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
-
x
+
5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
-
x
+
5
0
Since the remander is
0
, the final answer is the quotient.
3
x
+
1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
x
-
5
3
x
2
-
14
x
-
5
Divide the highest order term in the dividend
3
x
2
by the highest order term in divisor
x
.
3
x
x
-
5
3
x
2
-
14
x
-
5
Multiply the new quotient term by the divisor.
3
x
x
-
5
3
x
2
-
14
x
-
5
+
3
x
2
-
15
x
The expression needs to be subtracted from the dividend, so change all the signs in
3
x
2
−
15
x
3
x
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
Pull the next terms from the original dividend down into the current dividend.
3
x
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
Divide the highest order term in the dividend
x
by the highest order term in divisor
x
.
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
Multiply the new quotient term by the divisor.
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
+
x
-
5
The expression needs to be subtracted from the dividend, so change all the signs in
x
−
5
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
-
x
+
5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
+
1
x
-
5
3
x
2
-
14
x
-
5
-
3
x
2
+
15
x
+
x
-
5
-
x
+
5
0
Since the remander is
0
, the final answer is the quotient.
3
x
+
1
The solution after divide (3x² - 14x - 5) by (x - 5) will be (3x + 1).
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ Divide (3x² - 14x - 5) by (x - 5)
Now,
Divide (3x² - 14x - 5) by (x - 5) as;
x - 5 ) 3x² - 14x - 5 ( 3x + 1
3x² - 15x
- +
------------------
x - 5
x - 5
- +
--------------------
0
Thus, The solution after divide (3x² - 14x - 5) by (x - 5) will be (3x + 1).
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What is the area of the trapezoid? The diagram is not drawn to scale.
A. 36 cm2
B. 9 cm2
C. 21 cm2
D. 16.5 cm2
Answers
Answer:
Area of trapezoid = 21 cm²
Step-by-step explanation:
Given:
Length of rectangular shape = 4 cm
Width of rectangular shape = 3 cm
Base of triangle = 3 cm
Number of triangle = 3 cm
Find:
Area of trapezoid
Computation:
Area of trapezoid = Area of middle rectangle + Number of triangle[Area of triangle]
Area of trapezoid = [l x b] + 2[(1/2)(b)(h)]
Area of trapezoid = [4 x 3] + 2[(1/2)(3)(3)]
Area of trapezoid = 12 + 9
Area of trapezoid = 21 cm²
For a population with a proportion equal to 0.39, calculate the standard error of the proportion for the following sample sizes.A. 30B. 60C. 90
Answers
The standard error of the proportion decreases as the sample size increases. This means that larger sample sizes provide more accurate estimates of the population proportion.
To calculate the standard error of the proportion, we can use the formula:
SE = √(p(1-p)/n)
Where:
SE = standard error
p = proportion of the population
n = sample size
For each sample size, we can plug in the values and calculate the standard error:
A. For a sample size of 30:
SE = √(0.39(1-0.39)/30) = 0.088
B. For a sample size of 60:
SE = √(0.39(1-0.39)/60) = 0.062
C. For a sample size of 90:
SE = √(0.39(1-0.39)/90) = 0.051
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Irracionais menores que √5
Answers
Answer:
2.23 this the answer use the calculator
Find the interest on the following loan. $6000 at 8% for 6 months Find the future value of the loan. Assume 365 days in a year. $9275 at 7.57% annual simple interest for 13 months
Answers
The future value of the loan is approximately $10,070.29.
To find the interest on the loan, we can use the formula:Interest = Principal × Rate × Time
Given:
Principal (P) = $6000
Rate (R) = 8% per year (0.08 as a decimal)
Time (T) = 6 months (0.5 years)
Plugging in the values into the formula:
Interest = $6000 × 0.08 × 0.5 = $240
Therefore, the interest on the loan is $240.
To find the future value of the loan, we can use the formula for simple interest:
Future Value = Principal + Interest
Given:
Principal (P) = $6000
Interest = $240
Plugging in the values into the formula:
Future Value = $6000 + $240 = $6240
Therefore, the future value of the loan is $6240.
For the second scenario:
Given:
Principal (P) = $9275
Rate (R) = 7.57% per year (0.0757 as a decimal)
Time (T) = 13 months (13/12 years)
To find the interest, we can use the same formula:
Interest = Principal × Rate × Time
Plugging in the values into the formula:
Interest = $9275 × 0.0757 × (13/12) = $795.29
Therefore, the interest on the loan is approximately $795.29.
To find the future value of the loan, we can use the same formula as before:
Future Value = Principal + Interest
Plugging in the values into the formula:
Future Value = $9275 + $795.29 = $10,070.29
Therefore, the future value of the loan is approximately $10,070.29.
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HELP
i’ll mark brainlist if correct
Answers
Answer:
41.90
Step-by-step explanation:
FORMULA 1/3×πr×r×h
what's the area of a trapezium with a height of 6cm and a length of 9cm and 15cm?
Answers
Answer:
72cm²
Step-by-step explanation:
Hello!
The formula for area of a trapezoid: \(A = \frac12(b_1 + b_2)h\)
We find the average of the bases, and multiply it by the height.
Plug in the values and solve\(A = \frac12(b_1 + b_2)h\)\(A = \frac12(9 + 15)6\)\(A = \frac1224(6)\)\(A = 12(6)\)\(A = 72\)The area of the trapezoid is 72cm²
What additional information is obtained from an ordinal scale compared to a nominal scale?
Answers
An ordinal scale provides more information than a nominal scale since values linked with an ordinal variable will be in natural order, whereas values connected with the nominal variable won't.
Types of Variables:Ordinal variables as well as nominal variables are the two categories of variables listed here. This sort of variable cannot be submitted to the same forms of statistical tests as interval and ratio variables, hence it is crucial to be able to recognize them accurately. Both of these variables fall within the qualitative category. This contrasts with interval as well as rate variables, both of which are categorized as quantitative.
An illustration of an ordinal variable is a Likert scale with words for mood (such as joyful, neutral, or sad). An illustration of a nominal variable is the names of cities in the Canadian province of Alberta.
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Use context to determine the meaning of the word unabated as it is used in Narrative of the Life of Frederick Douglass, An American Slave. Write your definition of unabated here and tell how you found it.
Answers
The wοrd "unabated" is used in Narrative οf the Life οf Frederick Dοuglass, An American Slave.
The wοrd "unabated" in this cοntext can be interpreted tο mean "cοntinuing withοut any reductiοn in intensity οr strength." "That cheerful eye, under the influence οf slavery, swοre red with rage; that vice, made all οf sweet accοutrement, changed tο a οne οf harsh and hοrrid discοrd; and that angelic face gave way tο that οf a demοn."
The authοr is describing hοw the slavehοlder's pοwer οver the slaves cοrrupts the wοman's character, turning her previοusly kind demeanοur intο οne οf rage and discοntent. The wοrd "unabated" emphasises hοw persistent and unyielding this transfοrmatiοn is and hοw unlikely it is that it will diminish.
By examining the surrοunding text and cοmmοn usage, I was able tο determine the definitiοn οf the wοrd "unabated." In this sentence, the authοr's descriptiοn οf the slavehοlder's transfοrmatiοn is well-suited tο the wοrd "unabated," which is generally used tο describe sοmething that cοntinues withοut any lοss οf intensity οr strength.
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Claire walked her dog 2 1/5 miles. Carson walked her dog 1 3/4 times as far as Claire did. How many more miles did Carson walk her dog than Claire?
Answers
The word "times" means you have to multiply.
2 1/5 times 1 3/4 is 3 17/20.
The phrase "how many more" means you have to subtract.
3 17/20 minus 2 1/5 is 1 13/20.
Carson walked her dog 1 13/20 more miles than Claire did.
Sorry for the lazy explanations Imao
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? explain. Write an equation to represent this relationship.
Answers
Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
Given:
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.
y varies directly as x :
y = kx
k = constant of proportionality
y = 2.56 and x = 32
y = kx
k = y/x
= 2.56/32
k = 0.08
substitute k we get
y = 0.08x.
so x and y are directly proportional.
Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
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……………………………
3x + 7 = 2(x+1)+x
Answers
its 0=-5
ur mom lolololololoOLOOLOLLLLO
in order to determine an interval for the mean of a population with unknown standard deviation, a sample of 59 items is selected. the mean of the sample is determined to be 32. what is the associated number of degrees of freedom for reading the t value?
Answers
The associated number of degrees of freedom for reading the t-value is 58.
The aim is to determine an interval for the mean of a population.
The standard deviation is unknown to us. The sample consists of 59 items. The mean of the sample is determined to be 32. We need to calculate the associated number of degrees of freedom for reading the t value.
We know that the degree of freedom is one less than the number of items in the sample space.
The associated number of degrees of freedom for reading the t-value is 59-1.
The associated number of degrees of freedom for reading the t-value is 58.
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I really need help ASAP ILL GIVE BRAINLY
Answers
Answer: D.
Step-by-step explanation:
You can start out with the form AX = B and solve for matrix X that would yield the answer
Then X = (A^-1)(B)
A = [1 -1]
[1 1]
A^-1 = (1/(1 - (1)(-1)))*[1 1]
[-1 1]
which can be written as (1/2) * [1 1]
[-1 1]
B = [26]
[6]
(A^-1)(B) = (1/2)*[1 1] [6]
[-1 1] [26]
= (1/2)*[32]
[20]
= [16]
[10]
Can you help me pls this was very hard for me
Answers
Given:
The equation is,
\(\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}\)Explanation:
Simplify the right hand side of equation.
\(\begin{gathered} -8x-3-\frac{53}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2} \\ =\frac{-8ax^2-3ax+16x+6-53}{ax-2} \\ =\frac{-8ax^2+(-3a+16)x-47}{ax-2} \end{gathered}\)From left side and right side of equationn it can be observed that,
\(-8ax^2=24x^2\text{ and (-3a+16)x=}25x\)Simplify the equation for a.
\(\begin{gathered} -8a=24 \\ a=\frac{24}{-8} \\ =-3 \end{gathered}\)OR,
\(\begin{gathered} -3a+16=25 \\ -3a=25-16 \\ a=\frac{9}{-3} \\ =-3 \end{gathered}\)So value of a is -3.
Option B is correct.
Which choice is equivalent to the fraction below? Hint: Rationalize thedenominator and simplify.10/√2
Answers
The given fraction is:
\(\frac{10}{\sqrt[]{2}}\)To rationalize the denominator, multiply numerator and denominator by square root(2) and simplify:
\(\frac{10\cdot\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}}=\frac{10\sqrt[]{2}}{(\sqrt[]{2})^2}=\frac{10\sqrt[]{2}}{2}=5\sqrt[]{2}\)The answer is D.
you want to obtain a sample to estimate a population mean age of the incoming fall term transfer students. based on previous evidence, you believe the population standard deviation is approximately . you would like to be 99% confident that your estimate is within 2.5 of the true population mean. how large of a sample size is required? round your critical value to 2 decimal places.
Answers
To estimate the population mean age of incoming fall term transfer students with 99% confidence and a margin of error of 2.5, a sample size of 166 is required, assuming a population standard deviation of .
Explanation: To determine the required sample size, we need to use the formula:
n = ((z*σ) / E)^2
Where:
n = sample size
z = critical value
σ = population standard deviation
E = margin of error
Since we want to be 99% confident and the population standard deviation is given as , we can use the z-value for a 99% confidence level, which is 2.58 (rounded to two decimal places). The margin of error is given as 2.5. Substituting these values in the formula, we get:
n = ((2.58 * ) / 2.5)^2 = 166 (rounded to the nearest whole number)
Therefore, a sample size of 166 is required to estimate the population mean age of incoming fall term transfer students with 99% confidence and a margin of error of 2.5. It's important to note that the sample should be selected randomly to ensure that the estimates are representative of the population, and the assumptions of normality and independence should be met for the sample to be valid.
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What is the quotient startfraction 2 m superscript 9 baseline n superscript 4 baseline over negative 4 m superscript negative 3 baseline n superscript negative 2 baseline endfractionin simplest form? assume m not-equals 0, n not-equals 0.
Answers
The given expression's quotient is \(-\frac{m^{12}n^6}{2}\).
Exponential expressions are simply a shorthand way of writing powers. The exponent indicates how many times that base has been used as a factor to multiply. So, in the case of 32, it is 2x2x2x2x2x2 = \(2^5\), where 2 is the "base" and 5 is the "exponent." This expression is translated as "two to the fifth power." In general, an=axaxax...xa(n times), where 'a' is the base and 'n' is the exponent, will be read as "a to the nth power."
Given that the exponential expression is \(\frac{2m^9n^4}{-4m^{-3}n^{-2}}\)
The given expression's quotient is
\(=\frac{2m^9n^4}{-4m^{-3}n^{-2}}\\\\\frac{1}{a^x}=a^{-x}\\\\=\frac{m^9n^4m^{3}n^{2}}{-2}\\\\=\frac{m^{9+3}n^{4+2}}{-2}\\\\=\frac{m^{12}n^6}{-2}\\\\=-\frac{m^{12}n^6}{2}\)
As a result, the given expression's quotient is\(-\frac{m^{12}n^6}{2}\).
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Emma brought $23. 75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4. 50 left over after buying these items
Answers
The cost of the brush is $ 1.75 , The cost of the paint set is $ 10.5 and
The cost of the sketchbook is $ 7
The total amount Emma has is $23.75
Let the cost of paint set = x
Cost of sketchbook = 2x/3
Cost of brush = (1/6)x
23.75 = x + 2x/3 + x/6 + 4.50
23.75 - 4.50 = (6x + 4x +x)/6
19.25 × 6 = 11x
x = 10.5
Cost of sketchbook = 2x/3
Cost of sketchbook = (2 × 10.5)/3
Cost of sketchbook = 7
Cost of brush = (1/6)x
Cost of brush = (1/6)10.5
Cost of brush = 1.75
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The larget taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. The total weight of thee two ingredient wa 617. 3 kg. How many kilogram of each ingredient were ued?
Answers
The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg
What is a unit amount in math?
When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio
1 k + 6.6 k = 617.3
Where “k” is a constant value, a multiplier.
Solving for k:
7.8 k = 617.3
k = 617.3 /7.8
k= 79.17
So:
Amount of onion used:
1 (79.17) = 79.17 kg
Amount of grilled steak used:
6.6 (79.17) = 538.356 kg
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bath towels sell for $13.25 each and hand towels sell for $4.50 each. julie buys some of each type of towel for a total of $62.25. if she spends $17.25 more on bath towels than she spends on hand towels, how many of each type does she buy?
Answers
On solving the provided question, we cans ay that thee equation is x+y=62.50 and she buys 5 hand towels and 3 bath towels
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
let x=bath towels
y=hand towels
x+y=62.50
she spends 17.25 more on bath towels
\(x =y+17.25\\y+(y+17.25)=62.25\\ 2y+17.25=62.25\\ y=22.50\)
she spends 22.50 on hand towel
22.50+17.25 on bath towels
she buys 5 hand towels and 3 bath towels
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Sarah is going to the grocery store to buy milk. She buys 0.75 gallons of milk for $1.80. How much money, in dollars, would it cost Sarah to buy an entire gallon of milk?
Answers
Answer: $2.40
Step-by-step explanation:
With simple multiplication, 18/3 is 6.
Since 0.75 is equivalent to 3/4, you can assume that 1.80 divided by 3 equals 60cents. 60x4 equals 240.
Answer:2.40
Step-by-step explanation:
A Local restaurant offers burgers with a choice of the following toppings: cheese, lettuce, tomato, pickle, onion, jalapeños, avocado, relish, ketchup, mustard and mayonnaise. How many different 3 topping burgers can be made with these toppings?
Answers
GD DAY AND NIGHT EMMANUEL MUDIAY
A square tile mesures 20 cm by 20cm a rectangular tile is 3 cm longer and 2 cm narrower. What is the different in area between the two tiles?
Answers
Answer:
Rectangular tile has 14 cm² larger area-----------------
Find each area and then find their difference.
A(square) = 20² = 400 cm²A(rectangle) = (20 + 3)(20 - 2) = 23*18 = 414 cm²The difference is:
414 - 400 = 14 cm²Graph a line that contains the point (-3, 5) and has a slope of -2/5.
Answers
Answer:
y=-\frac{2}{5}x+\frac{19}{5}y=−52x+519
Further explanation:
We have to find the equation of the line first to graph the line.
The general form of slope-intercept form of equation of line is:
y=mx+by=mx+b
Given
m=-\frac{2}{5}m=−52
Putting the value of slope in the equation
y=-\frac{2}{5}x+by=−52x+b
To find the value of b, putting the point (-3,5) in equation
\begin{gathered}5=-\frac{2}{5}(-3)+b\\5=\frac{6}{5}+b\\5-\frac{6}{5}+b\\b=\frac{25-6}{5}\\b=\frac{19}{5}\end{gathered}5=−52(−3)+b5=56+b5−56+bb=525−6b=519
Putting the values of b and m
y=-\frac{2}{5}x+\frac{19}{5}y=−52x+519
HELPPP ME PLEASEEEEEE
Answers
Answer:
I would think the answer is 0
Step-by-step explanation:
this is a sort of division and any number divided by itself is always 0
PLSSSSS SOMEONE HELP ME!!!!!!!!
Subtract the polynomials (3^5 + 8^3) − (7^2 − 6^3). Show all work
Answers
Answer:
We can simplify each term in the polynomials and then perform the subtraction:
(3^5 + 8^3) − (7^2 − 6^3)
= 243 + 512 − 49 + 216
= 752 - 33
= 719
So, (3^5 + 8^3) − (7^2 − 6^3) = 719
Hello! :3
Correct Answer: 716
The answer below is incorrect! solved with 3^3 instead of 3^5! OOPS!!!
( 27 + 8^3) - (7^2-1x6^3)( 27 + 512 ) - (7^2-1x6^3) (539) - (7^2-1x6^3)(539) - (49-1x6^3)(539) - (49-1x216)539 - (49-216)539 - (-167)539 + 167706Hope this helps! :)
Write an inequality that represents the graph.
Answers
Answer:
\(y - 2x - 1 = 0\)
Step-by-step explanation:
the slope is :
\( \tan( \alpha ) = 4 \div 2 = 2\)
at a pt on graph , when
\(x = 1 \\ y = 3 \\ \)
therefore, coordinates are (1,3)
The equation is :
\((y - 3) = slope \times (x - 1) \\ (y - 3) = 2 \times (x - 1) \\ y - 3 = 2x - 2 \\ y - 2x - 1 = 0\)
A stock on the New York Stock Exchanged opened at $48on Monday.During the week,the stock lost $2 ,gained $1 ,gained$3 ,lost $1 and lost $4.What was the stock worth at the close of the businesson Friday?
Answers
The stock worth at the close is $45.00
A data form asks for applicants birth dates in the form mm/dd/yyyy. Find the probability that the number made up of the first two digits on a form is greater than 0
Answers
Answer:
P = 1
Explanation:
The first two numbers in the form will be the numbers related to the month. Since there is no month 00, the probability that the number made up is greater than 0 is 1.
It means that in all forms, the number made up of the first two digits will be greater than 0.
So, the answer is:
P = 1