The area of the enclosed loop of the curve y^2 = x^2(x 3) is 56√3/15.
To find the area of the enclosed loop of the curve y^2 = x^2(x 3), we need to first sketch the curve to see what it looks like. The equation can be rewritten as y^2 = x^2(x-3), which means that the curve is symmetric about the x-axis and passes through the origin.
Next, we can find the x-intercepts of the curve by setting y=0: 0^2 = x^2(x-3), which simplifies to x=0 and x=3. So the curve intersects the x-axis at (0,0) and (3,0).
To find the area of the enclosed loop, we need to integrate the curve from x=0 to x=3 and subtract the area below the x-axis. We can do this by setting up the integral as follows:
A = ∫[0,3] y dx - ∫[0,3] -y dx
We can solve for y by taking the square root of both sides of the equation y^2 = x^2(x-3):
y = ± x√(x-3)
To find the bounds of the integral, we can set the two functions equal to each other and solve for x:
x√(x-3) = -x√(x-3)
x=0 or x=3
So our integral becomes:
A = ∫[0,3] x√(x-3) dx - ∫[0,3] -x√(x-3) dx
We can simplify the integral by making the substitution u = x-3, which gives us:
A = ∫[0,3] (u+3)√u du - ∫[0,3] -(u+3)√u du
Simplifying further, we get:
A = 2∫[0,3] (u+3)√u du
This integral can be evaluated using integration by parts, which gives us:
A = 2/3 [2(u+3)(2u+3)√u - ∫(2u+3)√u du] from 0 to 3
Simplifying, we get:
A = 2/3 [(54√3/5) - (2/5)(18√3) + (2/3)(4√3)]
A = 56√3/15 DETAIL ANS
Therefore, the area of the enclosed loop of the curve y^2 = x^2(x 3) is 56√3/15.
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1) Marisol works for a florist that sells two types of bouquets, as shown below. On Monday, Marisol used
96 tulips to make the bouquets. On Tuesday, she used 192 tulips to make the same number of Spring Mix
bouquets as Monday, but 3 times as many Garden Delight bouquets.
a. Write a system of equations that you can use to find how many bouquets of each type Marisol made.
b. Find the total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday.
To calculate how many flowers of each kind Marisol created, use the formulae x+y=96 and x+3y=192. Marisol used 48 tulips in total to produce Garden Delight bouquets on Monday and Tuesday.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Let x be Spring Mix bouquets and y be the Garden Delight bouquets.
x+y=96
x+3y=192
2y=96
y=48
x=48
The system of equations that you can use to find how many bouquets of each type Marisol made is x+y=96 and x+3y=192. The total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday is 48.
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What is the value of sin^2A
Answer:
Solution: Sine is a trigonometric function of an angle defined as the ratio of the length of the perpendicular(opposite) side to the hypotenuse. Thus, the value of sin 2A = √3 / 2.
(Two-Step Linear Inequalities MC)
Which graph represents the solution to the inequality 2(b + 2) > 24?
number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right
The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left
What is an inequality?You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal. The graph is a diagram that illustrates the statement.
The given inequality is 2(b + 2) > 24
Opening the brackets to get
2b+4≥24
2b≥24-4
This implies that 2b≥20
Making b the subject
b≥20/2
b≥10
Conclusively the graph is a number line with closed point at 10 with arrow pointing left
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While working a summer job, Jaxon earned $983.40 in 33 hours. Find the rate of change.
5 starts and a thanks+brainliest
find the slope of the line passing through the point and perpendicular to the given line [tex](-5,2) 4x-3y=12[/tex]
options: -3/4 or -4/3
The slope of the line passing through the equation 4x - 3y = 12 is given by Slope m = -3/4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
4x - 3y = 12 be equation (1)
Now , on simplifying the equation , we get
Adding 3y on both sides of the equation , we get
3y + 12 = 4x
Subtracting 12 on both sides of the equation , we get
3y = 4x - 12
Divide by 3 on both sides of the equation , we get
y = ( 4/3 )x - 4
It is of the form y = mx + b where m is the slope and b is the y-intercept
So , slope m₁ = 4/3
Now , the line is perpendicular to the line y = ( 4/3 )x - 4
So , the product of their slopes is -1
And , m₁ x m₂ = -1
Substituting the values in the equation , we get
m₂ = ( 3/4 ) x -1
m₂ = -3/4
Hence , the slope of the line is -3/4
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How do you describe the motion of an object in terms of distance or displacement?
Distance is a measure of how far an object has traveled from a starting point. Displacement is the change in position from the starting point.
It is the total distance an object has moved and is the sum of all the displacements an object has made. The formula for calculating distance is distance = speed x time. For example, if a car has traveled at a speed of 50 km/h for 4 hours, then the distance traveled is 200 km (50 km/h x 4 h = 200 km).
Displacement is the change in position from the starting point. It is the shortest distance between the starting point and the final point and does not take into account the direction of motion. The formula for calculating displacement is displacement = final position – initial position. For example, if a car starts at point A and travels to point B, the displacement is the distance between A and B (B – A).
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What lessons do we get from books that discuss applied regression analysis and other multivariable methods?
The lessons we get from book that discuss applied regression analysis and other multivariable is that it can be used in real-life problems such as prediction and forecasting.
As a very effective and practical statistical technique, regression analysis has numerous applications to the field of nursing science. It allows scientists to explain, forecast, and quantify the correlations between variables, and form credible conclusions about the underlying causes of any phenomenon under study.
Regression analysis is a reliable way for determining which variables have an impact on a particular topic of interest. The method of doing a regression allows you to safely establish which elements are most important, which factors may be ignored, and how these factors influence each other.
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What is the missing reason in step 6
Answer:
triangle angle sum theorem
If one addend is 7 and the sim is 21, what is the other addend?
The other addend is from the arithmetic operation is 14
What is an addend in arithmetic operations?The act of combining two or more objects is known as an addition. The process of computing the sum of two or more integers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently utilized in daily life.
The addends are the figures that are added. Between the addends is the plus sign (+), which represents addition.
Given that:
7 + x = 21
Then;
x = 21 - 7
x = 14
Therefore, we can conclude that if one addend is 7, the other will be 14 to make a sum of 21.
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What is the difference between ⤠and �
⤠is the symbol for the euro, while ⥠is the symbol for the Japanese yen.
The euro, represented by the symbol â¤, is the official currency of 19 of the 28 member states of the European Union. It was introduced in 1999, and is the second-most traded currency in the world after the US dollar. The euro is managed and administered by the European Central Bank and the Eurosystem.
The Japanese yen, represented by the symbol â¥, is the official currency of Japan and is the third most traded currency in the world. It is issued and managed by the Bank of Japan, the country's central bank. The yen is used as a reserve currency by central banks and is often seen as a safe-haven asset during times of economic or political uncertainty.
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Find the measure of the indicated angle in each triangle (all questions) Please include how you solved them!!
Answer:
A step to step solution
Step-by-step explanation:
The measure of all these angles is just adding up the remote interior angles (the 2 angles that are shown in every triangle in this worksheet)
Find the sum, and that is your answer.
The first solution is 49+80 = 129
Therefore, the answer for #1 is 129 degrees
PLEASE HELP ASAP *VERY IMPORTANT* I WILL GIVE BRAINLIEST
Answer:
parallelogram
6. Describe some of the advantages and disadvantages to additional schooling.
Answer: you learn more, and it looks good on job applications, but you have to go to more school and use up more of your time
Step-by-step explanation:
IM NOT SURE IF THIS IS RIGHT CAN SOMEONE PLEASE HELP MEEEEE!!!!!
when written in symbols the product of r and s raised to the foruth power is represented as
The product of r and s to the fourth power is written as
(rs)⁴What is exponent?In math, the term exponent refers to the number of times a certain number multiplies it self.
The number that is being multiplies is referred to as the base number while the number of times it multiplies itself is the exponents
In the problem, the multiplication of r and s is done as follows
= r * s
= rs
In this case, the base number is rs and raise to the fourth power implies that rs multiplies it self four times
= rs * rs * rs * rs
= (rs)⁴
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Answer:
(rs)^4
Step-by-step explanation:
find the volume of figure B
Answer: 75m^3
Step-by-step explanation:
First, find the scale factor:
5/2 = 2.5
Multiply figure A's volume by the scale factor:
2.5 * 30
= 75 m^3
what am I supposed to do for this ?
What is R in the formula A πr2?
r is called as radius in the formula A=πr^2
A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.
Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).
A model is, for example, the method for the area of a circle, πr2.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
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A tree that is 3 feet tall is growing at a rate of 1 foot per year. A 5-foot tree is growing at a rate of 0. 75 foot per year. The ordered pair (t, h) represents the time in years, t, at which the trees are at height, h. Which ordered pair represents the number of years elapsed when the trees are at the same height?.
the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5). We were then asked to find the number of years elapsed when the trees are at the same height.
In this problem, we were given two different trees, one that is 3 feet tall and growing at a rate of 1 foot per year, and another that is 5 feet tall and growing at a rate of 0.75 feet per year. The ordered pair (3,1) represents the 3-foot tall tree growing at a rate of 1 foot per year and the ordered pair (5,0.75) represents the 5-foot tall tree growing at a rate of 0.75 feet per year.
To find the number of years elapsed when the trees are at the same height, we need to solve the equation:
3 + 1t = 5 + 0.75t
t = (5 - 3)/(1 - 0.75) = 2/0.25 = 8
So the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5).
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On a highway a wreck occurred and caused a 10 mile traffic jam on one sicle of the road.
Assuming the average car is 13.5 feet in length, how many vehicles are stuck in the traffic jam?
Calculating the total VMT or VKT for all road segments during a certain time period by multiplying the daily traffic volume on each segment by its length.
How many cars in a mile of traffic jam?The average automobile is around 15 feet long, so if you multiply 5280 by this number, you get about 350 cars, assuming they are all touching. Just over 284 million automobiles were on the road in the second quarter of 2022 in the United States. Though estimating the overall number of automobiles on the planet is not a precise science, the number is rising quickly.
Given that the ACS estimated there were 150 million workers in 2016, there are at least 115 million automobiles and trucks on American roads every day. Congestion is expected to be so bad during morning and afternoon rush hours. A balance between the demand for using the system and the infrastructure's capabilities can be achieved by creating digital twins of the transportation system and using them to optimise flows.
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What is 2y + 8x =
HELP ME!
The solution of equation: 2y + 8x = 2(y + 4)x.
Define the term common factor?A whole number that is a multiplier of at least two numbers is referred to as a common factor. The largest factor that would divide into two or so more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).In mathematics, the term "common factors" refers to the common divisors that are used when two or more integers are precisely divided by the identical number or numbers.For the stated equation:
= 2y + 8x
As. 2y and 8x both are divisible by 2 .
So, Taking two common from both.
= 2(y + 4x)
Thus, the solution of the equation becomes: 2(y + 4x).
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Determine whether each sequence has a negative common difference. Clearly explain your reasoning.
a). The sequence as represented in question a). is not an arithmetic sequence and hence, does not have a common difference.
b). The sequence formed by recording the daily odometer reading of a car after driving 15 miles each day does not have a negative common difference.
Which sequence has a negative common difference?It follows from the task content that the sequence which has a negative common difference be determined.
It follows that the common difference, by definition is the difference between successive terms a (n) of the sequence.
Therefore, common difference is usually given by; a (n) - a (n-1).
a). Since the given sequence is; 64, 32, 16, 8, ....
Since The common difference is; 32 - 64 ≠ 16 - 32 ≠ 8 - 16.
Hence, the sequence does not have a common difference and hence, is not an arithmetic sequence.
b). For a sequence involving the daily odometer reading of a car after driving 15 miles every day.
It follows that the recursive function for such a sequence would take the form; a (n) = a (n-1) + 15.
By comparison with the standard recursive function for arithmetic sequences, a (n) = a (n-1) + 15, it follows that the common difference, d = 15.
On this note, the common difference for the sequence is not a negative number.
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I need the awnsers to these 2 questions
The value of CE in the segment is 30 units.
The value of x in the segment is 1 units.
How to find the length in a line segment?A line segment is bounded by two distinct points on a line. Therefore, point D is located on the segment CE. Hence,
CD = 24 and DE = x
CE = 5x
Therefore, the measurement of the segment CE can be found as follows:
CE = CD + DE
5x = 24 + x
5x - x = 24
4x = 24
divide both sides of the equation by 4
x = 24 / 4
x = 6
Finally,
CE = 5(6) = 30
The segment XZ is bisected by the point Y. Hence,
XY = 12x
XZ = 18x - 6
Hence, let's find x
Therefore,
2XY = XZ
2(12x) = 18x - 6
24x = 18x - 6
24x - 18x = -6
-6x = -6
x = -6 / -6
x = 1
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A baker sells bread for $3 a loaf and rolls for $1 each. The baker needs to sell $27 worth of baked goods by
the end of the day.
Graph the linear equation 3b + r = 27, where b is the number of loaves of bread sold and r is the
number of rolls sold.
The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.
What is the slope-intercept form?
The slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept is the point at which the line crosses the y-axis, meaning the point at which the line intersects the y-axis when x = 0.
The given equation is in the form of y = mx + b where y =27, m = 3 and b = 1, is a linear equation and it can be represented as a straight line in a coordinate plane.
To graph this equation, we can use the following steps:
Plot the y-intercept, which is the point where the line crosses the y-axis. In this case, the y-intercept is (0, 27) since when b = 0 and r = 0, the left side of the equation equals 27.Identify the slope, m = 3. This tells us that the line rises 3 units for every 1 unit it moves along the x-axis.Using the slope and y-intercept, pick a second point on the line and plot it. Connect the two points with a straight line. The graph will be a straight line passing through the point (0,27) and (5,15)The graph will be the line with equation y = 3x + 1, where x is the number of loaves of bread sold and y is the total cost of the bread.The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.
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reflection across the y-axis
N(-3, 1), G(0, 4), B(-1, 1)
The required reflection of the points N(-3, 1), G(0, 4), B(-1, 1) across the y-axis are N(3, 1), G(0, 4), B(1, 1) .
Explain reflection across y-axis.Point (x, y) is reflected across the x-axis as (x, -y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse.
According to question:We have,
N(-3, 1), G(0, 4), B(-1, 1)
While, find reflected points we are considering y-axis as mirror,
Then,
Reflection of point N(-3, 1) across the y-axis
⇒ N(3, 1)
Reflection of point G(0, 4) across the y-axis
⇒ G(0, 4)
Reflection of point B(-1, 1) across the y-axis
⇒ B(1, 1)
Thus, required reflected points are N(3, 1), G(0, 4), B(1, 1) .
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How can I see my real face?
But to see one’s own face essential that the light emitted by it is either bounced back into our eyes (intimate a mirror - or something very much like it) - or that the light is recorded, captured and then played back into our eyes.
Did you know that shapes have a face? No, this face does not mean a face with two eyes, a nose, and a mouth. I mean a face of a shape, or the flat surface of a shape that you can trace and see. This face is known as a face in math.
Plane shapes in math mean any closed, flat, two-dimensional shape. All plane shapes have a face, because you can trace the shape of all plane shapes.
A triangle has a triangle face.
A rectangle has a rectangle face.
A diamond has a diamond face.
A circle has a circle face.
A square has a square face.
An oval has an oval face.
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A ball is launched from a 25.48-meter tall platform. The equation
for the ball's height h at time t seconds after launch is h (t) =
-4.9t2 +20.58t + 25.48, where his in meters. What is the
maximum height the ball achieves before landing?
Answer:
[tex]\boxed{47.089 \;meters} \\\\[/tex]
Step-by-step explanation:
For any function f(x), the maximum or minimum value can be determined by 1. Finding the first derivative f(x) with respect to x i.e. f'(x)
2. Setting this first derivative to 0, solving for x
3. Substituting for x in the original function to get the maximum/minimum value
[tex]\textrm{The equation for the function f(t) is }\\f(t) = -4.9t^2 + 20.58t + 25.48\\\\[/tex]
[tex]\textrm{The first derivative of this function with respect to t is }\\\\f'(t) = - 2\cdot 49t + 20.58\\= -9.8t + 25.48\\\\[/tex]
[tex]\textrm{Setting this first derivative equal to 0 gives:}\\\\-9.8t + 20.58 = 0\\\\-9.8t = -20.58 \;\;\;\;\;\textrm{(Subtracting 20.58 from both sides)}\\\\9.8t = 20.58 \;\;\;\;\;\; \textrm{ (Multiplying both sides by -1)}[/tex]
[tex]\textrm{Therefore }\\\\t = \dfrac{20.58}{9.8}\\\\t= 2.1 \textrm{ seconds}[/tex]
[tex]\textrm{Therefore, at = 2.1 seconds, the ball will reach its maximum height.}[/tex]
To find what this maximum height is, substitute t = 2.1 in the original equation and solve for h(t)
[tex]h(t)\;at\;t=2.1 \\h(2.1) = 4.9\cdot \:2.1^2+20.58\cdot \:2.1+25.48=47.089 \;meters\\\\[/tex]
[tex]\textrm{ The maximum height the ball achieves before landing is } \boxed{47.089 \;meters} \\\\[/tex]
[tex]\textrm {This occurs 2.1 seconds after launch }[/tex]
(xy−1)(xy+6)(xy−8)
Multiply the polynomials
Answer:
Step-by-step explanation:
just do - x + = -
- x - = +
so the answer is + i think
Three fifths of the students in the reading grouplike non-fiction books. If there are 25 students in the group, how many do not like non-fiction?
Answer choices
15 students
9 students
12 students
10 Students
When there are 25 students in the group, the number of people who not like non-fiction will be A. 15 people.
How to compute the value?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
From the information, three fifths of the students in the reading group like non-fiction books. If there are 25 students in the group, the number of people who not like non-fiction will be:
= 3/5 × 25
= 15
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A company rents paddleboards by charging a rental fee plus an hourly rate. Write an expression that represents the cost (in dollars) of renting a paddleboard for h hours.
The expression that represents the cost (in dollars) of renting a paddleboard for h hours is r + xh
How to determine the cost for h hoursFrom the question, we have the following parameters that can be used in our computation:
Cost of rents:
Charging a rental fee plus an hourly rate.
Using the above as a guide, we have the following:
Initial rental fee = r
Hourly rate = x
The cost for h hours can then be represented as
C(h) = Initial rental fee + Hourly rate * Number of hours
Substitute the known values in the above equation, so, we have the following representation
C(h) = r + x * h
Evaluate
C(h) = r + xh
Hence, the expression is r + xh
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