The maximum area of the rectangle inside the ellipse is 2ab.
Given that,
Ellipse = x2 / a2 + y2 / b2 = 1
we know the general coordinates of any point in an ellipse of the equation
x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)
So, we take general vertices of rectangles as
(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)
So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ
So, its area will be ab4sinθcosθ (Length x Breadth)
Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A
Now A=2absin2θ
Now as the area is the maximum given in the question, we have to differentiate it with respect to θ
dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)
Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ = π / 2 and θ=π / 4
So now we to put θ=π / 4 in the equation of area which is A=2absin2θ
We get as A=2absin2π / 4=2absinπ / 2=2ab
Hence the max area of the rectangle inside the ellipse is 2ab.
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What literary devices are used in The Importance of Being Earnest?
Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.
What is The Importance of Being Earnest?
Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.
It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.
The characters maintain false personae to avoid onerous social duties.
The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.
In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.
Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.
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Which of these is true?
a) Some ordered pairs of real numbers are not points in the Cartesian coordinate system.
b)Only integer ordered pairs are allowed in the coordinate system.
c)There is no point in the coordinate system with the ordered pair (T, Tt)
d)all of the above are false
9514 1404 393
Answer:
d) all of the above are false
Step-by-step explanation:
Every ordered pair of real numbers is a point in the Cartesian coordinate system.
The various statement saying otherwise are all false.
3. ) Mary is the director of the Washington Performing Arts Center. Her employer offers a pension. Mary’s employer uses a formula to calculate the pension. Marina is planning on retiring at the end of this year after 30 years of employment. A retiring employee receives 1. 6% of his or her average salary for the last 5 years of employment multiplied by the number of years worked. Mary would receive this amount each year until her death. Her salaries for the last 5 years are $80,900; $90,200; $95,000; $99,000; and $104,000. Calculate Marina’s pension
Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.
1.6% x $80,900 = $1,282.40
1.6% x $90,200 = $1,444.32
1.6% x $95,000 = $1,520.00
1.6% x $99,000 = $1,584.00
1.6% x $104,000 = $1,664.00
Total = $7,604.72
Pension amount = $7,604.72 x 30 years
= $228,141.60
Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.
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I NEED HELP PLS PSSSSSSSSSSSSSSS
Answer:
240
Step-by-step explanation:
The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday
Answer:
278
Step-by-step explanation:
average = sum/count
count = 7 (7 days)
monday = 150
tuesday = 250
wednesday = 200
thursday = 250
friday = 350
saturday = 450
sunday = 300
sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950
mean = 1950/7 = 278.571428571 ≈ 278
A chef that manages two restaurants buys seven bags of rice and six bags of flour.
Restaurant A receives four bags of rice and two bags of flour for a total cost of
$78. Restaurant B receives three bags of rice and four bags of flour for a total
cost of $71.50. What is the cost of each bag of rice and each bag of flour?
Answer:
- A bag of rice is $16.9
- A bag of flour is $5.20
Step-by-step explanation:
Let R and F stand for the price of a bag of Rice and Flour, respectively.
We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)
A) 4R + 2F = 78 [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.
B) 3R + 4F = 71.5 [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50
We have 2 equations and 2 unknowns. We can use substitution to find the answers. Take one of the equations and reorganize it to isolate one of the variables (R or F). We'll take the equation for A and isolate F
---
A) 4R + 2F = 78
2F = 78-4R [subtract 4R from both sides]
F = 39-2R [divide both sides by 2]
We've isolated F, and we can use this definition of F in the second equation:
===
B) 3R + 4F = 71.5
3R + 4(39 - 2R) = 71.5 [Use the definition of F derived above. In this manner, we have legally eliminated one of the two variables. (Sneaky, effective, and fun)]
3R + 156 - 8R = 71.5 [Multiply, combine like terms, and simplify]
-5R = -84.5 [Isolate R]
R = $16.9 A bag of rice costs $16.9
Now use the price of rice (R=$16.9) in one of the equations. Since the rearranged equation we used above is already conveniently written for F, we'll use it:
F = 39 - 2R
F = 39 - 2(16.9)
F = 39 - 33.8
F = $5.20 A bag of flour costs $5.20
===
CHECK:
Do these two prices satisfy both equations we first formulated?
Restaurant A: 4R + 2F = 78?
4(16.9) + 2(5.20) = 78 YES
Restaurant B: 3R + 4F = 71.5?
3(16.9) + 4(5.20) = 71.5 YES
These are the correct answers.
Wht is the missing part of 1/7 of ... 1/35
The missing part is 1/5. The complete expression is 1/7 of 1/5 is 1/35.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
We have the expression:
1/7 of (...) = 1/35
To find the missing fraction:
Let n be the number.
So,
1/7(n) = 1/35
n = 7/35
n = 1/5
Therefore, 1/5 is the missing part.
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Jaidyn’s family drinks a total of 10 gallons of milk every 5 weeks . How many gallons of milk does the family drink per week? How many weeks does it take the family to consume one gallon of milk?
Answer:
2 gallons of milk per week
0.35 weeks(3.5 days) to consume 1 gallon
Step-by-step explanation:
Jaidyn's family drinks 10 gallons of milk every 5 weeks, which is a ratio of
10:5
To find how many gallons of milk they drink per week, you'd have to divide 10/5
10 ÷ 5 = 2
Considering that 1 week is 7 days, it would take them 0.35 weeks to consume 1 gallon of milk, which is the same as 3 and a half days.
A student solved a quadratic using the Quadratic Formula and got:
X=4+-(square root)-14/3
Shown in picture
How many solutions did they get?
Answer:
2 solutions
Step-by-step explanation:
the plus or minus sign makes there be 2 solutions
[tex] \frac{4 + i \sqrt{14} }{3} [/tex]
and
[tex] \frac{4 - i \sqrt{14} }{3} [/tex]
Can someone please help me with math.
Answer:
Answer C 2,799.159
Step-by-step explanation:
[tex]v=\pi r^{2} h[/tex]
which statement is true about the equation 4x - 4x - 5 = -5
it has no solution
it has one solution has
two solutions
it has infinitely many solutions
Answer:
It has infinitely many solutions. The 4x's cancel themselves out and you are left with -5=-5, which is a true statement.
Step-by-step explanation:
branliest please
(5 points) 2. The coordinates of the vertices of ARST are R(1, 6), S(5, 3), and T(3,-2). Triangle R'S'T' is the image of ARST after a reflection in x = -1. Graph and state the coordinates of the vertices of AR'S'T'.
The coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each otherGiven are the coordinates of the vertices of ΔRST are R(1, 6), S(5, 3), and T(3,-2).
The rule for a reflection over the x -axis is (x, y) →(x, −y). Now we can write the coordinates of the reflection as -
R' (1, -6)
S' (5, -3)
T' (3, 2)
The graph is attached.
Therefore, the coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.
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If you could buy 500 individual nerd candies for $5 or 186 g of individual nerd candies for $5, which would be the better deal
The better deal would be 500 individual nerds candy for $5.
One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. The equal partition of bigger groupings into smaller parts is referred to as division.
The order of work assigned to and completed by the team of employees in order to optimize efficiency is known as the division of labor.
The splitting down of a job into multiple separate parts that make up the total is referred to as the division of labor. 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.
Thus, The better deal would be 500 individual nerds' candy for $5 since you will have more candy and it will last longer.
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can anyone help me answer this? please and thanks!
9514 1404 393
Answer:
7/5
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the tangent ratio is ...
Tan = Opposite/Adjacent
The side opposite angle A is BC, length 7. The side adjacent to angle A is AC, length 5. Then the tangent ratio is ...
tan(A) = BC/AC
tan(A) = 7/5
9. Samuel is comparing the average EPA ratings on 4 types of vehicles. He wants to drive a pickup truck, but he can see from the table below that he would use less gasoline if he drove a compact car. If Samuel
drives an average of 13,000 miles per year, how many more gallons of gas would he need to buy for a pickup truck compared to a compact car?
4-door Sedan
Compact Car
Pickup Truck
Small SUV
EPA rating: 26 mpg (combined city and EPA rating: 32 mpg (combined city EPA rating: 20 mpg (combined city and EPA rating: 22 mpg (combined city and
highway)
and highway)
highway)
highway)
O221.25 gallons
243.75 gallons
250.25 gallons
O261.75 gallons
Answer:
If Samuel drives a compact car, he would need to buy 243.75 gallons of gas per year. If he drives a pickup truck, he would need to buy 250.25 gallons of gas per year. So he would need to buy 6.5 more gallons of gas per year if he drives a pickup truck compared to a compact car.
Step-by-step explanation:
work out the length of x
show working out
Answer:
12.12
Step-by-step explanation:
the formula to find x in this case would be:
______
x=√14^2-7^2
x=√c^2﹣a^2=√14^2﹣7^2≈12.12436
how do i find the unit rate for 30 inches per 5 years
per year unit rate becomes 6 inches. This can be solved using the concept of unit rate.
What is an unit rate?A unit rate is a price for one of anything. This is expressed as a proportion with such a base of one. For instance, you would cover 7 yards on average every second if you covered 70 yards in 10 seconds. The ratios of 70 yards in 10 seconds and 7 yards in 1 second are both rates, however, the latter is a unit rate.
A rate is the ratio of two different measurement units, whereas a unit rate seems to be the ratio of two different units of measurement for just a single object.
unit rate for 30 inches per 5 years:
= 30 inches / 5 years
= 6 inches / 1 year
Thus, per year unit rate becomes 6 inches.
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Find the measure of the missing angles.
Answer:
Hello!
y = 90
x = 51
Hope that helps!
A rhombus with a perimeter of 24 units is graphed on a coordinate grid. The rhombus is dilated by a scale factor of 0.3 with the origin as the center of dilation.
If (x, y) represents the location of any point on the original rhombus, which ordered pair represents the coordinates of the corresponding point on the resulting rhombus?
A) (x, y) → (0.3x, 0.3y)
B) (x, y) → (24x, 24y)
C) (x, y) → (x ÷ 0.3, y ÷ 0.3)
D) (x, y) → (x + 0.3, y + 0.3)
Answer:
Step-by-step explanation:
It’s c
Why infinity is open interval?
The number line is drawn to find the open end point interval is infinity.
Number Line of an Open endpoint to the endpoint of number line =?
Selection of Open endpoint to the endpoint of the number line is fit for the following intervals as such determined below :
basically the intervals are mentioned as follow
( ), [ ], ( ], [ )
An open interval is mentioned (a, b), is an interval that does not contain its endpoints. When an interval involves infinity or negative infinity, hence the following rules for whether it is an open or closed interval. (a, and
(-a , a) are open intervals.
For instance [a,∞) doesn't contain all of its endpoints as mentioned . It's a real number where The interval has only one endpoint - a, so it contains all of its endpoints (however it only has one).
Secondly, the definition forgot to add that (−∞,∞) is also open
Take numbers as follows:
Final Answer as followed in intervals
(-2, 2)
[-2, 2]
(-∞, 2]
[2, ∞)
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25 points and brainiest badge
No Links
Select the correct answer.
What is the value of x in the figure?
A. 70°
B. 80°
C. 120°
D. 150°
Answer:
70
Step by step explanation
Answer:
150°
Step-by-step explanation:
The 70° angle is on a straight line so to find the next angel for the triangle
180-70=110
Angles in a triangle adds up to 180
so
110+40=150
180-150=30
Therefore the angle near x in the triangle is 30
To find x
180-30=150°
Help with this question
Its about shapes
Answer:
a
Step-by-step explanation:
triangles are pyramids and it has 6 sides
Answer:
Hexagonal prism
Step-by-step explanation:
We can rule out B and D because if it was a pyramid, there would be a triangle in the net (The net of a 3D shape is what it looks like if it is opened out flat). We can also rule on C because it it was a cylinder, there would be a circle in the net. Therefore, our remaining answer is A.
Hello! could use some help. (answer all questions in one answer comment)
1. Draw 16 stairs. put them equally into 2 sets. how many stairs are in each set?
2. Abel Drew some Triangles, His drawing had 21 vertices. How many triangles did he draw? write a division equation to answer the question.
3. Equation: 30 ÷ 6 = 5. Write a related multiplication sentence.
4. Terrance tackled a total of 42 football players in the last 6 games. he tackled the same amount of players each game. how many players did Terrance tackle each game?
Answer:
1. 8
2. 21÷3=7
3. 5x6=30
4. 7
A researcher wants to set up a hypothesis test to determine if there is a difference in the mean exam scores of students who are visual learners, versus auditory learners, versus kinesthetic learners. What would be the correct setup for the null and alternative hypotheses for this test
On solving the provided question we can say that here in null hypothesis a negative relationship; as anxiety rises less items are remembered
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
here,
in null hypothesis a negative relationship; as anxiety rises less items are remembered
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A car travels 196 miles in 3.5 hours. A. 224 miles in 4 hours B. 356 miles in 6 hours C. 504 miles in 9 hours D. 392 miles in 7 hours
Answer:
A and D
Step-by-step explanation:
distance = rate x time
196 = 3.5r
r = 196/3.5
r = 56 mph
A) 56 x 4 = 224 Yes
B) 56 x 6 = 336 No
C) 56 x 9 = 494 No
D) 56 x 7 = 392 Yes
What is 21/4 X 1/3 can u help me please
Answer:
1 3/4
Step-by-step explanation:
1 3/4
Answer:
7/4
Step-by-step explanation:
Multiplying fraction is so easy just multiply the nominators with each other. Then the denominators.
21 *1 =21 and 4 *3=12
21/12 =7/4 just simplify
select all of the partial products of 5 x 1,234
[] 20
[] 150
[] 1,000
[] 10,000
Find volume of cylinder
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the cylinder on the image is:
v = 36,424 in³
So the correct option is the second one.
What is the volume of the cylinder?We know that for a cylinder of diameter D and height H, the volume is given by the formula:
V = pi*(D/2)²*H
Where pi = 3.14
Here we know that:
D = 40 inches.
H = 29 inches.
Replacing that in the formula for the volume we will get:
V = 3.14*(40 in/2)²*29 in = 36,424 in³
So the correct option is the second one.
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which point on the graph would best represent unemployment (underutilizing labor)?
Answer:
i think the right one is H
A ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km. Find the distance traveled from the starting point to the ending point
The distance traveled from the starting point to the ending point is 30.35 km.
What is a bearing?
A bearing tracks the rotation of an angle around the north line in a clockwise fashion. The line connecting the compass's centre to a location and measuring its bearing in degrees as it moves clockwise from north is known as the bearing.
The ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km.
The x-coordinate of the final point is -
50 cos (27°) + 140 cos (117°) = -19
The y-coordinate of the final point is -
50 sin (27°) + 140 sin (117°) = 23.67
The distance from (0,0) to the final point is as follows -
d = √(-19)^2+(23.6)^2)
= √(921.27)
= 30.35 km
Therefore, the distance traveled is 30.35 km.
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Hilda filled her aquarium with
water. On Monday, she put 8 cups
into the aquarium. On Tuesday she
put 2 pints. On Wednesday, she put
quarts. How many cups of water dic
she put into her aquarium in all?
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable. A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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