Answers
Answer:
Take the picture you uploaded.
Click the rotate 'button' once.
Change the x to y and y to x on the graph. (axis labels)
Done
J (0, -1)
K(-4,-3)
I ( -4,-1)
Related Questions
A flight leaves the airport at 22:00 hours. It is an 11 hours and 45 minutes flight. There is a 2-hour time difference. What time will they arrive at their destination, assuming the time difference is 2 hours ahead
Answers
Answer:
It's on the next day at 11.45am
Step-by-step explanation:
I hope it helps
Based on the time the plane left, the length of the flight, and the time difference, the plane will arrive at 11 : 45 am the next day.
Because the time is 2 hours ahead, adjust the departure time by 2 hours:
= 22:00 + 2
= 00:00
With the plane leaving by 12 am, the time of arrival is:
= 00:00 + 11 hours 45 mins
= 11 : 45 am
In conclusion, the plane will arrive at 11:45 am.
Find out more at https://brainly.com/question/25150454.
Leora wants to paint the nursery in her house. The nursery is an 8–by–10–foot rectangle, and the ceiling is 10 feet tall. There is a 3–by–6.5–foot door on one wall, a 3–by–6.5–foot closet door on another wall, and one 2–by–3.5–foot window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?
Answers
Answer:
The correct answer is - 242 ft^2
Step-by-step explanation:
Given:
one door : 3*6.5 => 19.5 ft^2
other door: 3*6.5 => 19.5 ft^2
a window: 2*3.5 => 7 ft^2
total = 46 ft^2
area of all four walls: 2h (l+b)
= 2(8) (10+8)
= 16 (18)
= 288 ft^2
paint required excluding doors and window:
=> area of your wall - (area of doors and window)
=> 288 - 46
= 242 ft^2
A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $100,000 with a standard deviation of $10,000. Assume that salaries follow a bell-shaped distribution. Use the empirical rule:
a. Approximately what percentage of the salaries fall between $90,000 and $110,000?
b. Approximately what percentage of the salaries fall between $80,000 and $120,000?
c. Approximately what percentage of the salaries are greater than $120,000?
Answers
Answer:
a) 68%
b) 95%.
c) 2.5%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 100,000, standard deviation of 10,000.
a. Approximately what percentage of the salaries fall between $90,000 and $110,000?
90,000 = 100,000 - 10,000
110,000 = 100,000 + 10,000
Within 1 standard deviation of the mean, so approximately 68%.
b. Approximately what percentage of the salaries fall between $80,000 and $120,000?
80,000 = 100,000 - 2*10,000
120,000 = 100,000 + 2*10,000
Within 2 standard deviations of the mean, so approximately 95%.
c. Approximately what percentage of the salaries are greater than $120,000?
More than 2 standard deviations above the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean, so approximately 5% are more than 2 standard deviations from the mean.
The normal distribution is symmetric, which means that 2.5% are more then 2 standard deviations below the mean, and 2.5% are more than 2 standard deviations above the mean, which means that 2.5% of the salaries are greater than $120,000.
7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken. a. What is the probability that 10 or fewer customers choose the leading brand
Answers
Answer:
0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The leading brand of dishwasher detergent has a 30% market share.
This means that [tex]p = 0.3[/tex]
A sample of 25 dishwasher detergent customers was taken.
This means that [tex]n = 25[/tex]
a. What is the probability that 10 or fewer customers choose the leading brand?
This is:
[tex]P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001[/tex]
[tex]P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014[/tex]
[tex]P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074[/tex]
[tex]P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243[/tex]
[tex]P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572[/tex]
[tex]P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030[/tex]
[tex]P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472[/tex]
[tex]P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712[/tex]
[tex]P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651[/tex]
[tex]P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336[/tex]
[tex]P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916[/tex]
Then
[tex]P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021[/tex]
0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand
Mis directly proportional to r?
When r= 2, M= 14
a) Work out the value of M when r= 12.
b) Work out the value of r when M = 224.
Answers
Answer:
M = 84 , r = 32
Step-by-step explanation:
Given M is directly proportional to r then the equation relating them is
M = kr ← k is the constant of proportion
To find k use the condition when r = 2, M = 14 , then
14 = 2k ( divide both sides by 2 )
7 = k
M = 7r ← equation of proportion
(a)
When r = 12
M = 7 × 12 = 84
(b)
When M = 224 , then
224 = 7r ( divide both sides by 7 )
32 = r
Find the distance between the two points.
(3,-9) and (-93,-37)
Answers
Answer:
100
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(-93 - 3)² + [-37 - (-9)]
√(-96)² + (-28)²
√9216 + 784
√10000
= 100
Find the volume
h=9cm
8cm
8cm
Answers
Answer: (8x8x9)/3=192
11
5
у
х
Find the value of x.
A) 4rad5
B) 8rad5
C) 6
D) 16
Answers
Answer:
Option A, 4rad5
Step-by-step explanation:
x² = 5*(5+11)
x² = 5*16
x² = 80
x = 4√5
Answered by GAUTHMATH
the blueprint dimensions of the playground are 23/147 yd x 3/14 yd after reducing them by the factor of 2/147 what are the original dimensions if the playground in yards
Answers
Answer:
The original dimensions of the park are:
(23/2) yards by 7 yards.
Step-by-step explanation:
Suppose that you have a given dimension X
if you want to reduce that dimension by a scale factor k, such that:
0 < k < 1
The reduced dimension is just:
X' = k*X
Now let's solve the problem:
We know that the dimensions on the blueprint are:
(23/147)yd by (3/14)yd
And the original dimensions are:
A yd by B yd
We know that, to get the blueprint dimensions, we reduced the original dimensions by a factor of 2/147
Then we just have that:
(2/147)*A = 23/147
(2/147)*B = 3/14
Now we just can solve these two equations for A and B
A = (23/147)*(147/2) = 23/2
B = (3/14)*(2/147) = (3/7)*(1/147) = 49/7 = 7
Then the original dimensions of the park are:
(23/2) yards by 7 yards.
Please help me with the question; It is attached in the image
Answers
Answer:
The function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].
Step-by-step explanation:
Firstly, we integrate the function by algebraic substitution:
[tex]\int {x^{2}\cdot e^{2\cdot x^{3}}} \, dx[/tex] (1)
If [tex]u = 2\cdot x^{3}[/tex] and [tex]du = 6\cdot x^{2} dx[/tex], then:
[tex]\int {e^{2\cdot x^{3}}\cdot x^{2}} \, dx[/tex]
[tex]\frac{1}{6}\int {e^{u}} \, du[/tex]
[tex]f(u) = \frac{1}{6}\cdot e^{u} + C[/tex]
[tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} + C[/tex]
Where [tex]C[/tex] is the integration constant.
If [tex]x = 0[/tex] and [tex]f(0) = 0[/tex], then the integration constant is:
[tex]\frac{1}{6}\cdot e^{2\cdot 0^{3}} + C= 0[/tex]
[tex]C = -\frac{1}{6}[/tex]
Hence, the function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answers
line up is rise
line across us run
rise over run = 13 up over 10
so 13/10
The catch-up effect says that low-income countries can grow faster
higher income countries. However, in statistical studies covering many countries
differences, we do not observe the catch-up effect unless we control for the
other variables affecting productivity. Consider the factors that determine productivity, list and solve
I like the reasons why a poor country can't keep up with rich countries.
Answers
worldwide markets are already established with bis stakeholders like McD, Appe, MS, Aldi Car Manufacturers etc.
so seeing a big corporation emerging from an underdeveloped country would be kind of a suprising thing to happen.
also, economically developed countries are likely to have stable trade relationships with other countries. giving them an edge over outsiders.
Already existing infrastructure might also be a concern to keep in mind when planning your business. It's nice to have mobility, internet, electricity, water at you tap.
I guess there could even be some kind of language barrier for many countries with an insufficient educational system. that might hinder individuals to participate in the global market and community.
PUWID, du then solve.
Timothy's father will build a shed for his tools. It will be a square with a
1 side that measures 8 m. What is the area of the shed?
1. What is asked?
testy
Answers
Answer:
The area of the shed=[tex]64m^2[/tex]
Step-by-step explanation:
We are given that
Side of square =8m
We have to find the area of the shed.
To find the area of shed we will find the area of square.
We know that
Area of square=[tex]side\times side[/tex]
Using the formula
Area of square=[tex]8\times 8[/tex]
Area of square=[tex]64m^2[/tex]
Area of shed=Area of square
Area of shed=64 square m
Hence, the area of the shed=[tex]64m^2[/tex]
Write the expression in complete factored form.
5n(x - 2) + 8(x - 2) =
Answers
x − 2 out of 5n ( x −2 ) + 8 ( x − 2) . ( x − 2 ) ( 5 n + 8 )
I hope this is correct and helps!
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5n(x - 2) + 8(x - 2) =}[/tex]
[tex]\large\text{DISTRIBUTE 5 and 8 WITHIN the PARENTHESES}[/tex]
[tex]\large\textsf{= 5n(x) + 5(-2) + 8(x) + 8(-2)}[/tex]
[tex]\large\textsf{= 5nx - 10n + 8x - 16}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf (x - 2)(5n + 8)}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find m<1. Please answer by tomrrow
Answers
Answer:
59
Step-by-step explanation:
Just get the supplement of 121.
So angle 1 is 180-121 = 59 degrees
Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 25% of the time, four events 30% of the time, three events 20% of the time, two events 15% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for less than three events each month. P (x < 3) = 2 Find the expected number of events Javier volunteers in a month. 3.6 It is given that x must be below a certain value, which limits the rows to use in the PDF table. What is the sum of the probabilities of those rows?
Answers
Answer:
[tex]P(x < 3) = 25\%[/tex]
[tex]E(x) = 3[/tex]
Step-by-step explanation:
The given parameters can be represented as:
[tex]\begin{array}{ccccccc}x & {5} & {4} & {3} & {2} & {1}& {0} & P(x) & {25\%} & {30\%} & {20\%} & {15\%} & {5\%} & {5\%} \ \end{array}[/tex]
Solving (a): P(x < 3)
This is calculated as:
[tex]P(x < 3) = P(x = 0) + P(x = 1) + P(x =2)[/tex] ----- i.e. all probabilities less than 3
So, we have:
[tex]P(x < 3) = 5\% + 5\% + 15\%[/tex]
[tex]P(x < 3) = 25\%[/tex]
Solving (b): Expected number of events
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 5 * 25\% + 4 * 30\% + 3 * 20\% + 2 * 15\% + 1 * 5\% + 0 * 5\%[/tex]
[tex]E(x) = 125\% + 120\% + 60\% + 30\% + 5\% + 0\%[/tex]
[tex]E(x) = 340\%[/tex]
Express as decimal
[tex]E(x) = 3.40[/tex]
Approximate to the nearest integer
[tex]E(x) = 3[/tex]
plz help with the task my child is trying to do
Answers
Answer:
7
Step-by-step explanation:
First, add all the cards.
[tex]2 + 5 + 7 + 8 + 9 = 31[/tex]
If we remove one card, the remaining four cards average will be 6, this means that the 4 remaning cards will average total will be at 24 because 6×4=24. So we need to find a value that will equal 24 if we remove that card.
The answer is 7 because
[tex] \frac{2 + 5 + 8 + 9}{4} = 6[/tex]
9514 1404 393
Answer:
remove 7 to make the total be 6×4 = 24.
Step-by-step explanation:
The description "mean average" is redundant to no apparent purpose. "Mean" and "average" are the same thing: the total divided by the number of contributors.
If the mean of 4 cards is 6, then we require ...
6 = (total of 4 cards) ÷ 4
24 = total of 4 cards . . . . . . . multiply both sides of the equation by 4
__
We note that the total of all the cards shown is ...
2 + 5 + 7 + 8 + 9 = 31
In order to make the total be 24, we need to remove a card that has a value of ...
31 -24 = 7
Removing 7 will bring the total to 2 + 5 + 8 + 9 = 24, and the average to 24/4 = 6.
_____
Additional comment
It is worthwhile to remember the relationship between the total and the average and the number of contributors. This shows up a lot in problems involving adjusting an average or finding a value to give a certain average.
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x
3
2
1
–1
y
8
2
0.5
0.125
a. No; the domain values are at regular intervals and the range values have a common factor 0.25. b. No; the domain values are not at regular intervals although the range values have a common factor. c. Yes; the domain values are at regular intervals and the range values have a common factor 4. d. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.
Answers
9514 1404 393
Answer:
b. No; the domain values are not at regular intervals although the range values have a common factor.
Step-by-step explanation:
The differences between x-values are ...
-1, -1, -1, -2 . . . . not a constant difference
The ratios of y-values are ...
2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference
The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.
Suppose you choose a marble from a bag containing 3 red marbles, 5 white marbles, and 4 blue
marbles. You return the first marble to the bag and then choose again. Find P (red and blue).
Answers
Answer:
P(red and blue) = 1/12
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of independent events:
If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each event happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
P (red and blue).
Probability of choosing a red marble, then a blue marble. The marbles are replaced, so the trials are independent.
Probability of a red marble:
3 out of 3 + 5 + 4 = 12. So
[tex]P(A) = \frac{3}{12} = \frac{1}{4}[/tex]
Probability of a blue marble:
4 out of 12, so:
[tex]P(B) = \frac{4}{12} = \frac{1}{3}[/tex]
P (red and blue).
[tex]P(A \cap B) = P(A)P(B) = \frac{1}{4} \times \frac{1}{3} = \frac{1}{4*3} = \frac{1}{12}[/tex]
So
P(red and blue) = 1/12
Standardized tests: In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 526 and the standard deviation was 101. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places. Part: 0 / 40 of 4 Parts Complete Part 1 of 4 Core for an ACT score of 16. The z-score for an ACT score of 16 is Jose's ACT score had a -score of . What was his ACT score?
Answers
Answer:
The z-score for an ACT score of 16 is -1.23.
His ACT score was of [tex]X = 22.5 + 5.3Z[/tex], considering that Z is his z-score.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
ACT:
Mean of 22.5, standard deviation of 5.3, so [tex]\mu = 22.5, \sigma = 5.3[/tex]
The z-score for an ACT score of 16 is
Z when x = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 22.5}{5.3}[/tex]
[tex]Z = -1.23[/tex]
The z-score for an ACT score of 16 is -1.23.
Jose's ACT score had a Z-score of Z. What was his ACT score?
This is X, considering Z his z-score. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - 22.5}{5.3}[/tex]
[tex]X - 22.5 = 5.3Z[/tex]
[tex]X = 22.5 + 5.3Z[/tex]
His ACT score was of [tex]X = 22.5 + 5.3Z[/tex], considering that Z is his z-score.
please solve both i have been struggling
Answers
Answer:
3
Step-by-step explanation:
make a column of x ,f, fx
then write income in x and no.of workers in f
andthen multiply both just like 100*3 ,100*2, 300*p, 400*2,500*1 write its answer fx
add the all fx and use this formula
mean =fx /n
260=adding total of fx divide by 5
Repeat same formula in no 2
22
Question 6 Multiple Choice Worth 1 points)
(04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation?
3x + y = 8
-x - 2y = -10
O-2y + 10
O 2y + 10
O 2y - 10
O-2y - 10
Answers
Answer:
-2y + 10
Step-by-step explanation:
Substitution method:
On the second equation of the system, we have to find x as a function of y.
-x - 2y = -10
We have to find x as a function of y, so:
[tex]-x = -10 + 2y[/tex]
Multiplying both sides of the equality by -1:
[tex]x = -2y + 10[/tex]
So -2y + 10 is the answer to this question.
See attached writing an equation for the graph
y=
Answers
Answer:
Step-by-step explanation:
-2*x +2
it is reveresed with a y interecept of 2
A mechanic charges $65 for an engine check and $20 per hour for his
services. Which of the following is a linear model of his charges.
y=20x+65
y=65x+20
y=3.25x+65
O y=3.25x+20
Question 5
Answers
Answer:
y = 65 + 20x
Step-by-step explanation:
Okay, when you're talking about linear equations try to find the fixed value, and then the changing one.
The fixed value will be by itself
The value that varies will have a variable next to it (x, y, z, whatever)
Then, the answer has to be
y = 65 + 20x
Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)
Answers
Answer:
[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]
Step-by-step explanation:
We are given the function:
[tex]Q(x)=2x^2+5x-3[/tex]
And we want to find and simplify:
[tex]Q(a+h)-Q(a-h)[/tex]
Substitute:
[tex]=[2(a+h)^2+5(a+h)-3]-[2(a-h)^2+5(a-h)-3][/tex]
Expand:
[tex]\displaystyle =[2(a^2+2ah+h^2)+5a+5h-3]-[2(a^2-2ah+h^2)+5a-5h-3][/tex]
Distribute:
[tex]=[2a^2+4ah+2h^2+5a+5h-3]-[2a^2-4ah+h^2+5a-5h-3][/tex]
Distribute:
[tex]=(2a^2+4ah+2h^2+5a+5h-3)+(-2a^2+4ah-2h^2-5a+5h+3)[/tex]
Rewrite:
[tex]=(2a^2-2a^2)+(4ah+4ah)+(2h^2-2h^2)+(5a-5a)+(5h+5h)+(-3+3)[/tex]
Combine like terms:
[tex]=8ah+10h[/tex]
Hence:
[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]
Please help me i will give you brainlest
Answers
Answer:
a speaker receive credibility is a combination of competence trustworthiness and caring
Study the table representing the price of different amounts of apples, in pounds, and then complete the sentences. The constant difference in the y-values is . The linear function is .
Answers
Answer: the first part is 1.25. The second part is y=1.25x
Step-by-step explanation: edge 2021
True or false: If you are changing a larger unit into a smaller unit, like cm into mm, the decimal is moved to the right because you are multiplying by a power of ten
Answers
Answer:true
Step-by-step explanation:
i dont know
Use the parametric equations of an ellipse, x=acosθ, y=bsinθ, 0≤θ≤2π , to find the area that it encloses.
Answers
Answer:
Area of ellipse=[tex]\pi ab[/tex]
Step-by-step explanation:
We are given that
[tex]x=acos\theta[/tex]
[tex]y=bsin\theta[/tex]
[tex]0\leq\theta\leq 2\pi[/tex]
We have to find the area enclose by it.
[tex]x/a=cos\theta, y/b=sin\theta[/tex]
[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]
Using the formula
[tex]sin^2x+cos^2x=1[/tex]
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
This is the equation of ellipse.
Area of ellipse
=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]
When x=0,[tex]\theta=\pi/2[/tex]
When x=a, [tex]\theta=0[/tex]
Using the formula
Area of ellipse
=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]
Using the formula
[tex]1-cos2\theta=2sin^2\theta[/tex]
Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]
Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]
Area of ellipse=[tex]\pi ab[/tex]
Does the equation 3x-6y=0 represent a direct variation? *
Answers
Answer:
yes
Step-by-step explanation:
if you change it to standard form, it would be
y=1/2x
because it's in the format of y=ax then it is direct variation