I would choose both I and II for accomplishing the task of "When you want to Add or Remove Filters, you select Data in the ribbon, and then Filter. You would prefer to do this with one click, so you decide to add Filters to the Quick Access Toolbar."
What is filters?Click the Commands Not in the Ribbon option in the Customize Quick Access Toolbar dialog box. Click Filter in the list of commands. Select the Add option. Press the OK button. You may use the FILTER function to filter a set of data depending on criteria you provide. The Filter option makes it simple to narrow down your search field.
Here,
I would choose both I and II to complete the task of "When you wish to Add or Remove Filters, go to the Data ribbon, then Filter. You'd prefer to do this with a single click, so you add Filters to the Quick Access Toolbar."
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im not sure how to answer thank you
The value of x in the triangle WXY is 27°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠VWY + ∠XWY = 180° (sum of angle in straight line)
6x + ∠XWY = 180°
∠XWY = 180 - 6x
∠XYW + ∠ZYW = 180° (sum of angle in straight line)
∠XYW + 4x = 180°
∠XYW = 180 - 4x
∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)
(180 - 6x) + (180 - 4x) + 90 = 180
450 - 10x = 180
10x = 270
x = 27°
The value of x is 27°
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Make a box plot for the given data : 17,29 ,32,30,14,9,39,10,32,23
Answer:
It can't add a plot for those numbers-
Step-by-step explanation:
Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 mililiters of water in each test tube. How many full test tubes can Russel fill with water? 1. Describe one way to estimate the solution to this problem. 2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable? Explain
The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.
How to Know Cylinder Volume ?Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.
Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?
1. Describe one way to estimate the solution to this problem.
By dividing the amount of milliliters of water in the baker by 16.5 ml
2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?
No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.
Therefore, the correct answer should be 36 test tubes.
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TRANSLATE EACH PHRASE INTO AN ALGEBRAIC EXPRESSION
1) 4 times a number,increased by 11.
2) 8 times the sum of a number and 7.
3) 1 less than twice a number.
4) the sum of a number and 3 times that number.
5) 12 more than 5 times a number.
6) 16 increased by 1 more than a number.
7) 20 decreased by 5 less than a number.
8) 6 less than a number increased by 15.
Answer:
Step-by-step explanation:
Let the number be x then,
1) 4 * x + 11
2) 8 * (x + 7)
3) 2x - 1
4) x+ 3x
5) 5x + 12
6) 16 + 1 + x = 17 + x
7) 20 - ( x - 5) = 20 - x + 5 = 25 - x
8) x - 6 + 15 = x +9
Which of the following statements is not equivalent to the others?
16-34
|34 -16|
34-16
|16 -34
Answer:
the one that is not equivalent to the others would be 116-34
Step-by-step explanation:
because its 116 and the others dont have anything to do with 116 :)
Answer: The statement that is not equivalent should be D. |16-34
Angel missies 4% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 55
Answer:
Step-by-step explanation:
55 times 25, making Angel attempt 1375 free throws
Answer:
Step-by-step explanation:
Its 700% because 7x3 = 11
Share $60S in the ratio 4:5:7:
Answer:
15:18.75:26.25
Step-by-step explanation:
4:5:7
Total=16
60/16 = 3.75
4 x 3.75 = 15
5 x 3.75 = 18.75
7 x 3.75 = 26.25
15:18.75:26.25
Answer: $15 : $18.75 : $26.25
Step-by-step explanation:
4 + 5 + 7 = 16
4/16 × $60 = $15
5/16 × $60 = $18.75
7/16 × $60 = $26.25
In the story "How Tacos Conquered America" and "The Story of Spaghetti and
Meatballs" have a lot of similarities and differences. Read more to find out what they
have in different and what they have in common. Although the stories had a lot of
similarities it also had a lot of differences for reference Where do these beloved foods
have their roots Tacos were Originated in mexico where a owner of taco bell
"There was just one problem. The cooks at the restaurant hated making them! Each cornmeal tortilla shell had to be
individually fried in scalding oil. The cooks had to turn each tortilla by hand until it was perfectly crispy. The process
was dangerous and painful. The cooks had the burns to prove it ".Juvencio Maldonado was going to
change that. He got to work and made his Mechanical fryer which made up to 7 tacos at a time
and no more burns.
Dose this sound good
A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag.
13. The number of pictures your printer
can print are shown in the table. Find
the rate in pictures per minute.
Minutes 2 4 6
8
Pictures 16 32 48 64
15.
16
Answer: The table shows the number of pictures that a printer can print at different intervals of time (measured in minutes). To find the rate in pictures per minute, we need to divide the number of pictures printed by the number of minutes it took to print them.
For example, at 2 minutes the printer printed 16 pictures. The rate of pictures printed per minute is 16 pictures / 2 minutes = 8 pictures/minute.
Similarly, at 4 minutes the printer printed 32 pictures. The rate of pictures printed per minute is 32 pictures / 4 minutes = 8 pictures/minute
And, at 6 minutes the printer printed 48 pictures. The rate of pictures printed per minute is 48 pictures / 6 minutes = 8 pictures/minute.
And, at 8 minutes the printer printed 64 pictures. The rate of pictures printed per minute is 64 pictures / 8 minutes = 8 pictures/minute.
From this it can be seen that the printer has a constant rate of 8 pictures per minute, independent of the number of minutes, it is producing 8 pictures/min.
The value 15 is not related to the table, so it's not the rate, and 16 is not the rate either, it is the number of pictures printed at 8 minutes.
Step-by-step explanation:
another one 2 more after this
A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters. Find the area of the parking lot. *
The area of the parking lot is 2,025 .81 meter2.
How do you calculate a triangle's area?In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters.
Triangle Height Determination Using Area
Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height.
s = a + b+ c /2
90 + 54 + 128 / 2 = 136
A = [tex]\sqrt{s (s-a) (s-b) (s-c)}[/tex]
A = [tex]\sqrt{136(136-90)(136-54)(136-128}[/tex])
A = 2,025 .81
The area of the parking lot is 2,025 .81 meter2.
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Quadrilateral ABCD is similar to quadrilateral A'B'C'D'. Write 2 equations that could be used to solve for missing lengths?
2 equations that could be used to solve for missing lengths are:
[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]
Now, According to the question:
Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
Quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
ABCD ~ A'B'C'D'
So,
[tex]\frac{AB}{A'B'} = \frac{BC}{B'C'}\\ \\ \frac{CD}{C'D'} = \frac{AD}{A'D'}[/tex]
Hence, 2 equations that could be used to solve for missing lengths are:
[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]
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Write and solve an equation to find the value of x.
Answer:
x = 60
Step-by-step explanation:
Let the two opposite angles be equal and let's call them y.
Because of the theory of angles on a straight line 120 +y = 180
y = 60
Because of the theory of angles on a straight line 2x + y = 180
2x + 60 = 180
2x = 120
x = 60
Alternatively. (also a lot easier)
120 and 2x are opposite angles so they are equal and so;
2x = 120
x = 60
Please mark as brainliest if this answer is helpful.
4x + 4y = -8
-2x - 2y = 4
Answer: To solve this system of equations, you can use the substitution method.
First, you can solve one of the equations for one of the variables in terms of the other. For example, you can solve the first equation for y:
y = (-4x - 8)/4
Then, you can substitute this expression for y into the second equation to find the value of x:
-2x - 2((-4x - 8)/4) = 4
-2x + 4x + 8 = 4
2x = -4
x = -2
You can then substitute this value of x back into the first equation to find the value of y:
y = (-4(-2) - 8)/4 = (8 - 8)/4 = 0
Thus, the solution to the system of equations is x = -2 and y = 0.
Step-by-step explanation:
1. A school held several events last month- a music concert, a basketball game, a drama play, and
literacy night. The music concert was attended by 250 people. How many people came to each of
the events? 250 people attended the events.
a. The attendance to the basketball game was 30% of attendance at the concert. 75 people
attended the basketball game.
b. Attendance at the drama play was 140% of attendance at the concert.
C. Attendance at the literacy night was 44% of the attendance at the concert.
70% of those who went to the music concert and the play also did so.
What is meant by percentage?A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The word "%" stands in for it.
In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.
We know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
We know that 250 people attended the music concert.
The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%
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70% of those who went to the music concert and the play also did so.
Hence, the option A is correct.
What is meant by percentage?In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to get the percentage of a given number, divide the number by the total and multiply by 100. The percentage is a chunk out of one hundred. One out of 100 is referred to as a percentage. The symbol for it is "%".
A % is a number that, in addition to being expressed as a decimal or a fraction, also specifies how many out of 100 it is. For the price of one, get three! To convert a percentage to a fraction, just enter the% as the numerator and 100 as the denominator.
We know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
We know that 250 people attended the music concert.
The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes?
work pls/ explain
Answer:
$68
Step-by-step explanation:
So, we will start off by putting our original price as a variable, x. Now, we will need an equation to show the relationship between the current price and three-fourths of the original price. The equation will look like this:
[tex]\frac{3}{4} x = 51[/tex]
Then, we will multiply both sides by 4 to get rid of the fraction, giving us:
3x = 204
Finally, we will divide by 3 to find the original price of the sneakers:
x = 68
So the pair of shoes originally cost $68.
Hope this helped!
The question is in the picture I would appreciate if you could explain how to get the answer thank you.
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
The slope of an equation:
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.
The slope intercept form of a line is y = mx + c
Where, c - y-intercept and m - the slope of the line
Given that
The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.
4 minutes of internet costs $ 3
8 minutes of internet costs $ 4
[ We can represent the given situation as given below ]
And the coordinates formed are (4, 3) and (8, 4)
The slope of the line formed = (4 - 3)/(8 - 4) = 1/4
Let y = mx + c be the equation to the model situation
=> y = (1/2)x + c
=> 2y = x + c ---- (1)
As we know (1) will pass through (4, 3)
=> 2(3) = 4 + c
=> 6 = 4 + c
=> c = 6 - 4
=> c = 2
=> 2y = x + 2
=> x - 2y + 2 = 0
Therefore,
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
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The point Q has coordinates (2,3) The point R has coordinates (a,b) A line perpendicular to QR is given by the equation 5x+2y=9 Find an expression for b in terms of a
B = (2a + 11)/5 is an expression for b when expressed in terms of a.
What exactly are slopes and lines?
We are aware that lines might have several kinds of equations; the typical form is
The equation of a line in slope-intercept form is Ax + By + c = 0, and
y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept, or (0,b), is the point where the line crosses the y-axis when x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.
Given:
Coordinates of point Q = (2,3)
Coordinates of point R = (a,b)
The equation of the line is 5x + 2y = 9 ⇒ 2y = - 5x + 9
Therefore, y = (-5/2)x + 9/2.
We know slope m = (y2 - y1) / (x2 - x1)
∴ m = (b - 3)/(a - 2).
∴ (2/5) = (b - 3).(a - 2).
2(a - 2) = 5(b - 3).
2a - 4 = 5b - 15.
2a + 11 = 5b.
b = (2a + 11)/5.
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What is the difference of the two polynomials 9x2 8x 2x2 3x?
The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.
What is polynomials?A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.
Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).
To find the difference between
(9x² + 8x) - (2x² + 3x)
We do calculation
= 9x² + 8x - 2x² - 3x
= 9x² - 2x² + 8x - 3x
= 7x² + 5x
Thus, the difference between the polynomials is 7x² + 5x.
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what is the distance between (-3,5) and (4,5)
Answer: 7
Step-by-step explanation:
Distance (d) = √(4 - -3)2 + (5 - 5)2
= √(7)2 + (0)2
= √49
= 7
ΔX = 4 – -3 = 7
ΔY = 5 – 5 = 0
y = 0x + 5
When x=0, y = 5
Answer:
Step-by-step explanation:
D = SQRT(x 2 - x 1) 2 + (y 2 - y 1) 2
X2 Y2
(-3,5)
X1 Y1
(4,5)
D= SQRT (-3-4)^2 + (5-5)^2
D= SQRT 49
D=7
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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Consider sequences of positive real numbers of the form , in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of does the term 3000 appear somewhere in the sequence ?
a. 1
b. 2
c. 3
d. 4
e. more than 4
No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.
What is meant by sequences?An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.
To estimate a few terms of the sequence in order to obtain a feel how it looks like.
In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].
This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].
We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:
[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]
[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]
[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]
[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]
[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]
At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.
Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].
As [tex]$a_2=2000$[/tex], we only have four possibilities left.
Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.
The equation [tex]$a_4=2001$[/tex]
solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]
There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.
Therefore, the correct answer is option (D) 4.
The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........ in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?
(A) 1
(B) 2
(C) 3
(D) 4
(E) more than 4
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Divide the following polynomials, then place the answer in the proper location on the grid. Use synthetic division. Write the answer in descending powers of x. (3x^2 +7x - 18)/(x - 3)
Use synthetic division to divide (3x2 + 7x - 18) by (x - 3).The result of the division is (3x + 5)/(x - 3).
The first step is to write out the dividend and the divisor, and put a 0 in the box below the dividend.
3x2 +7x -18
x - 3 0
The next step is to divide the divisor into the first term of the dividend.
3x2 +7x -18
x - 3 0
3 -9
Next, we multiply the divisor by the result from the previous step and subtract it from the second term of the dividend.
3x2 +7x -18
x - 3 0
3 -9 5
Next, we multiply the divisor by the result from the previous step and subtract it from the third term of the dividend.
3x2 +7x -18
x - 3 0
3 -9 5 -15
Finally, we divide the last result by the divisor.
3x2 +7x -18
x - 3 0
3 -9 5 -15 3
The result of the division by synthetic division is (3x + 5)/(x - 3).
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What unit is equal to Avogadro's number ?
Avogadro's number is a unitless object. It represents a number.
What is unit?
The mass of a particular piece of metal or the length of a particular rod are examples of quantities (specific properties) of objects that have historically been used to define measurement units. An object that has no units is known as unitless.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The value of Avogadro's number is 6.02214076 × 10²³.
One mole of the chemical compound consists of 6.02214076 × 10²³ atoms.
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A(3,-1); y= 1/3x +10
write an equation of the line passing through the given point that is parallel to the given line
the equation of the desired line is x = 3y + 6.
To find the equation of a line that is parallel to the given line
y = 1\3x + 10
and passes through the point (3,-1), since parallel lines have the same slope.
Therefore, the slope of the desired line is also 1\3.
Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:
y - (-1) = 1\{3}(x - 3)
Simplifying, we get
y + 1 = 1\ 3x - 1
Multiplying both sides by 3, we get
3y + 3 = x - 3
Adding 3 to both sides, we get
3y + 6 = x
Therefore, the equation of the desired line is x = 3y + 6.
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Arithmetic sequence please help
10. a. The sequence is arithmetic as the difference between the next term and the previous term is constant.
b. The 200th term of the sequence is 1382.
c. 100 is not a member of the sequence.
11. a. u₁ is even and d is also even.
b. u₁ is odd and d is even.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, u₁ = - 12 and uₙ₊₁ = uₙ + 7.
So,
u₂ = u₁₊₁ = - 12 + 7 = - 5.
Similarly, u₃ = - 5 + 7 = 2 and u₄ = 9.
So, The terms have a common difference o 7 and hence it is an arithmetic sequence.
We know, uₙ = u₁ + (n - 1)d.
Therefore, u₂₀₀ = u₁ + (200 -1)×7.
u₂₀₀ = - 12 + 199×7.
u₂₀₀ = - 12 + 1393.
u₂₀₀ = 1382.
Now, Determining whether 1000 is a member of the sequence.
Let, 1000 = - 12 + (n - 1)×7.
1012 = 7n - 7.
1019 = 7n, Here is not completely divisible hence 1000 is not a member of the sequence.
11. When all the terms of an AP is even the first term u₁ is even and the common difference would also be even and when all the terms of an AP are odd the first term u₁ would be odd and the common difference d would e even, as odd - odd = even.
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The integral 1 π(y2−y4) dy 0 represents the volume of a solid. Describe the solid.
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the y axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.
In the cartesian coordinate system, a plane is divided into four areas by the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.Use washer method:The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.
As we have mentioned, the washer method is an extension of the disk method. This technique is established so that we can also calculate for the volume of the solid returned by rotating the region bounded by two curves over the x and y axis.[tex]$$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$[/tex]
Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.
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Determine whether y varies with x if so find the constant of variation and write the equation A. No b. Yes k= -2 and y= -2x
The equation is y = 2x and the constant of variation k = 2
Therefore, the correct answer is option d.
Here, we can clearly see that y varies directly with x, because as x increases, y increases with the same proportion and vice versa. The constant of variation, k, is the coefficient of proportionality between x and y. To find the constant of variation, we can divide the value of y by the value of x for any one of the given points.
For example, for the point (-2, -4) we have:
k = -4 / -2 = 2
So the equation relating x and y is: y = kx = 2x
Hence, the equation is y = 2x and the constant of variation k = 2
Therefore, the correct answer is option d.
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The complete question is -
Determine whether y varies directly with x. If so, find the constant of variation and write the equation.
x | y
-2 | -4
-4 | -8
-16 | -32
a. No
b. yes; k=-2 and y=-2x
c. yes; k=1/2 and y=1/2x
d. yes; k=2 and y=2x
b. Consider a circle with centre O and radius of 4 units. The distance of point P is 2 units from centre. Find the distance of inverse of point P' from the centre O.