The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances.
We have to explain the separatrix separation.
When in motion, a pendulum can either swing from side to side or rotate continuously. The separatrix, which marks the transition from one type of motion to another, can typically be determined under straight forward circumstances. But when the pendulum is pushed at a nearly constant rate, the math breaks down.
A pendulum in motion has two possible motions: a continuous circle or a side-to-side swing. The separatrix—the point at which it switches from one kind of motion to another—can be estimated in the majority of straight forward circumstances. However, the mathematics breaks down when the pendulum is pushed at a nearly constant velocity.
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5. Solve the system using substitution.
{4x + 5y = 7
{
{y= 3x + 9
What variable in the top equation will you substitute the bottom equation into? (x or
y)
6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation? (This is what it looks like BEFORE you simplify it.)
7. Using the equation you came up with for question 6, what does it look like simplified?
8. What is the solution to the equations from question 5?
Answer:
x= -2, y= 3
Step-by-step explanation:
5. Solve the system using substitution.
4x + 5y = 7
y= 3x + 9
What variable in the top equation will you substitute the bottom equation into? y
6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation?
4x + 5(3x+9) = 7
7. Using the equation you came up with for question 6, what does it look like simplified?
4x+5(3x+9) = 7, distribute 5 over the sum in parenthesis
4x+15x+45 = 7, subtract 45 from both sides of the equation
4x+15x+45-45 = 7-45, combine like terms
19x = -38, divide both sides by 19
x = -2
8. What is the solution to the equations from question 5?
y= 3x+9, substitute x for -2
y = 3(-2) +9
y = -6+9
y = 3
The solution for the system of equations
4x + 5y = 7
y= 3x + 9
is x= -2, y= 3
This means that the point (-2, 3) is the intersection of line 4x+5y=7 and line y=3x+9 and that point belongs to both lines.
Answer:
Below in bold.
Step-by-step explanation:
5. 4x + 5y = 7
y= 3x + 9
Substitute for y from the top equation.
5y = -4x + 7
y = (-4x + 7)/5
Substituting:
(-4x + 7)/5 = 3x + 9
6. Substituting from bottom equation, we get:
4x + 5(3x + 9) = 7
7. Simplifying the above:
4x + 15x + 45= 7
19x = -38
8. Solving equations from part 5:
(-4x + 7)/5 = 3x + 9
-4x + 7 = 15x + 45
-38 = 19x
x = -2.
Now substitute x = -2 into y = 3x + 9
y = 3(-2) + 9
= 3.
Solution is x = -2, y = 33
Find the maximum value of the quadratic function.
Answer:
-49.
Step-by-step explanation:
Convert to vertex form:
f(x) = -7x^2 - 14x - 56
= -7(x^2 + 2x + 8)
= -7 [(x + 1)^2 - 1 + 8)
= 7(x + 1)^2 - 49
- so the maximum value is -49.
Beth wanted to go to the school dance but we only had 25$ people to spend . If the ticket costs 5$, how many cookies could Beth buy at the dance if each cookie costs 1.25
The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match. A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies
Explain about Equation?The classification of various types of functions can be done using four primary categories. depending on a factor Onto function, one-to-one relationship, many-to-one relationship, and into function are all examples of relationships between function.
A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.
Equations' true strength is in their ability to explain numerous aspects of the world in a highly accurate manner. (This is why, if one can be found, an equation's solution can be helpful.)
Hence, A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies
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Thank you to who ever helps
Applying the transitive property of congruency and other postulates, lines l and m are proven to be parallel as explained below.
What is the Transitive Property of Congruency?The transitive property of congruency states that when two angles are sides are congruent to another third angle or side, then the three sides or angles are all congruent to each other.
For example, if <A = <C, and <B = <C, then <A = <B.
The proof that shows that lines l and m are congruent is explained below:
Statement Reason
1. r║s, <5 is congruent to <6 1. Given
2. <5 is supplementary to <4 2. Same-side interior angles theorem
3. <4 is supplementary to <6 3. Transitive property of congruency
4. l║m 4. Converse of same-side interior <s theorem
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IIIO GEOMETRYVolume of a sphereThe radius, R, of a sphere is 6.2 m. Calculate the sphere's volume, V.Use the value 3.14 for n, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The formula for calculating the volume of a sphere is expressed as
Volume = 4/3 x pi x radius^3
From the information given,
pi = 3.14
radius = 6.2
By substituting these values into the formula, we have
Volume = 4/3 x 3.14 x 6.2^3
Volume = 997.7999
Rounding to the nearest tenth,
Volume = 997.8 m^3
Suppose that 19 inches of wire costs 76 cents.
At the same rate, how many inches of wire can be bought for 64 cents?
Answer: 16 inches
Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.
Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents
i need helppppppppp plsssssssssssssssss
Answer:
Step-by-step explanation:
A!
Answer: Function A is faster by 1 meter per second.
Step-by-step explanation:
The first function has a greater speed because by taking the meters per second, you get 14 meters per second. Meanwhile, function B has only 13 meters per second, therefore function A is faster by 1 meter per second.
If f(x) = 1/5x - 11, what is f(−12)?
2x - 8 + 3x - 10 = 10x - 43
The value of variable x in the equation is 5.
How to solve for x in an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Therefore, let's solve for variable x in the equation below.
2x - 8 + 3x - 10 = 10x - 43
A variable is number represented with a letter in an equation.
Hence,
2x - 8 + 3x - 10 = 10x - 43
2x + 3x - 8 - 10 = 10x - 43
5x - 18 = 10x - 43
5x - 10x = - 43 + 18
-5x = - 25
divide both sides of the equation by -5
-5x / - 5= - 25 / -5
Therefore,
x = 5
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The location between the park and Ray's
home is indicated in the graph.
Each unit represents a mile.
What is the distance, in miles, from the
park to Ray's home, rounded to the
nearest tenth?
A 16.6
B 15.6
C 14.1
D 143
E 11.0
The answer to the question is A-
16.6
Answer:
A. 16.6
Step-by-step explanation:
d = sqrt{(x2 - x1)^2 + (y2-y1)^2}
so this is our distance formula
now we need the two points
(-6, -6) and (3, 8)
lets plug these into our formula
d = sqrt{(3 - (-6))^2 + (8 - (-6))^2}
lets simplify
d = sqrt{(9)^2 + (14) ^2}
d = sqrt{277}
d = 16.64 or 16.6
Problem 1
(3x - 4y = 0
(4x - 5y = k
Consider the following system of equations:
where k is a constant real number. Solve the system for (x, y) in terms of k. Do not replace
the constant k with a numerical value. Give your solution as an ordered pair in terms of k.
[For example: If you solve the system and obtain x = 2k and y = 5k + 1, then you would
write your solution as (2k, 5k + 1).]
The ordered pair is [4k , 3k]
In first equation, 3x - 4y = 0
∴ 3x = 4y
x = 4y/3. ----1
Placing the value of x in second equation:
4x - 5y = k
4[4y/3] - 5y = k
16y/3 - 5y = k
[tex]\frac{16y - 15y}{3}[/tex] = k
16y - 15y = 3k
y = 3k
Replacing the value of y in eq. 1, we get
x = 4k
∴ The ordered pair is [4k , 3k]
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what is(7x10^-6) (5x10^-6) in scientific notation?
Answer:
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11
Please help me with this question
Answer:
its A
Step-by-step explanation
i took this test
In a scale diagram, 0.15 inch represents 150 feet. How many inches represent 2.5 feet?
Answer:
.0025 inches
Step-by-step explanation:
[tex] \frac{.15}{150} = \frac{x}{2.5} [/tex]
[tex]150x = 3.75[/tex]
[tex]x = .0025[/tex]
Given: AABC, mzC = 90°
m2A = 30°, BC = 16
Find: AB and AC
Help fast
The most appropriate choice for trigonometry will be given by -
AB = 32
AC = [tex]16\sqrt{3}[/tex]
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin\theta,[/tex] [tex]cos\theta[/tex], [tex]tan\theta[/tex], [tex]cot\theta[/tex], [tex]sec\theta[/tex], [tex]cosec\theta[/tex]
[tex]sin\theta=\frac{perpendicular}{hypotenuse}\\\\cos\theta=\frac{base}{hypotenuse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The figure has been attached here.
Since this is a right angled triangle, trigonometry can be applied here,
Since ∠C = 90°, AB is the hypotenuse of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex] as the side opposite to 90° angle is the hypotenuse.
Let BC be the base of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex]
BC = 16
m∠B = 180 - (90 + 30)
= 180 - 120
= 60°
cos 60 = [tex]\frac{BC}{AB}[/tex]
[tex]\frac{1}{2} = \frac{16}{AB}\\AB = 16\times 2\\AB = 32[/tex]
sin 60 = [tex]\frac{AC}{AB}[/tex]
[tex]\frac{\sqrt{3}}{2} = \frac{AC}{32}\\\\AC = 32 \times \frac{\sqrt{3}}{2}\\\\AC = 16\sqrt{3}[/tex]
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when the product of 6 and 8 became 48, what must be done to write that in scientific notation ?
By definition, Scientific notation has the following form:
[tex]a\cdot10^n[/tex]Where the coefficient "a" is a number from 1 to 10, but not including 10 and the exponent "n" is an Integer. The base will be always 10.
When you write a number in Scientific notation, the decimal point must be after the first digit of the coefficient.
In this case, you have:
[tex]6\cdot8=48[/tex]So, in order to write that product in Scientific notation, you must move the decimal point one space to the left. This must be represented in the exponent. If you move it just one space, to the left, then the exponent will be 1 and will be positive.
Therefore, you get that this is:
[tex]=4.8\cdot10^1[/tex]Therefore, you can determine that the answer is:
[tex]4.8\cdot10^1[/tex]What does it multiply too
0.88
X 1.2
Answer:
1.056
Step-by-step explanation:
The equation7y =хrepresents:neitherinverse variationdirect variation
The equation is:
[tex]y=\frac{7}{x}[/tex]If x grows then y is going to reduce, and if y gets smaller, then t grows. this means that is an inverse variation
when a number is added to 18 the answer is the same as 59 mins 20. what is the number?
Explain and correct the error in this calculation
-Picture below-
The error calculated is 2/5×3/8 = 3/20
What is error?An estimate or approximation of a true value and an error are two different things.
An error is defined as a mistake or a state of being incorrect. If you add 2+2 and get 5, that is an error. When a mistake causes you to believe the wrong conclusion about a collusion and you stick with it, that is an example of error.
Given
2/5×3/8 = 3/10
which is not possible, because 2×4 = 8 and the numerator and denominator is divided by 2 at the same time.
1/5×3/4 = 3/20
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Algebra 2 help
Ccfggggggggyytttt
The solution to the quadratic equation -3 = 4x² + 9x using quadratic formula is; x = (-9 + √33)/8 or (-9 - √33)/8
How to use the quadratic formula?The general form of any quadratic equation is written as;
ax² + bx + c = 0
The quadratic formula that is used to solve this is given by;
x = [-b ± √(b² - 4ac)]/(2a)
Now, we are given the quadratic equation as;
-3 = 4x² + 9x
It can be written as;
4x² + 9x + 3 = 0
Thus, using quadratic formula we have;
x = [-9 ± √(9² - (4 * 4 * 3))]/(2 * 4)
x = [-9 ± √(81 - 48)]/8
x = (-9 ± √33)/8
x = (-9 + √33)/8 or (-9 - √33)/8
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Solve the inequality r divided by negative 3.2 is greater than or equal to 7.6 for r.
r ≥ −24.32
r ≤ −24.32
r ≥ 2.375
r ≤ −2.375
Answer:
r ≤ -24.32
Step-by-step explanation:
r/-3.2 > 7.6
r /-3.2 × 3.2 > 7.6 × -3.2
r ≤ -24.32
Answer: r ≤ −24.32
Step-by-step explanation:
The inequality you provided is:
r/-3.2 >= 7.6
To solve for r, we can multiply both sides of the inequality by -3.2 to get:
r <= -24.32
Therefore, r is less than or equal to -24.32.
I hope this helps! Let me know if you have any other questions.
Solve the linear system using the elimination method. Type youranswer as an ordered pair in the form (#,#). 2x + 5y = 8-10x – 9y = -72
1 ) Let's solve this Linear System with the elimination method
Choose the x, as the first variable to be eliminated
2x + 5y = 8 Multiply by 5 the whole equation
-10x – 9y = -72
Adding both equations:
10x +25y=40
-10x -9y=-72
----------------------
0 16y=-32 Dividing both equations by 16
y=-2
2) Plugging into the simplest equation within that Linear System:
2x +5(-2) = 8
2x -10 = 8 Adding 10 to both sides
2x = 18 Dividing both sides by 2
x=9
3) So the answer is the pair (9,-2)
Fill in the blank. Using the number line below, the plotted number is
when rounded to the nearest thousand.
Answer:2000 will be the nearest thousand.
Step-by-step explanation:
Which situation can be represented by the expression 2.5 X
Given the expression:
2.5x
Let's determine the situation which best represents the expression.
Let's start from the first statement:
• A. The total amount of change received to pay for an item that cost $2.50:
The best representation for this is: C = A - 2.50
Where A is the amount paid, C is the amount of change.
• B. The area of a rectangle with side lengths 2.5 and x:
The best representation for this situation is:
2.5x
• C. The total cost of an item that is 2.50 more than x dollars:
T = 2.50 + x
• D. The total square footage of a yard when 2.50 yards is divided into equal parts:
This expression cannot be represented by 2.5x
Therefore, the situation which can be represented by the expression 2.5 is:
The area of a rectangle with side lengths 2.5 and x
ANSWER:
B. The area of a rectangle with side lengths 2.5 and x
A ribbon is 3 4/5 feet long. Each hair tie needs
2/5 feet. How many hair ties can you make?
A ribbon is 3 4/5 feet long. Each hair tie needs 2/5 feet. Number of hair ties is 6
What is meant by fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction, Next, multiply the two numerators. Then, multiply the two denominators.
No of hair ties = 6
How to find number of hair ties :
Length of the ribbon = 3 4/5 feet
Length of each hair tie needed = 2/5 feet
To find how many ties , divide the total length of ribbon by 2/5
That is = [tex]\frac{3 (4/5)}{2/5}[/tex]
= 6 You can make 6 no. of hair tie from 3 4/5 feet ribbon.
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suppose the scores of students on an exam are normally distributed with a mean of 573 and a standard deviation of 72. then approximately 99.7% of the exam scores lie between the integers and , and the mean is halfway between these two integers.
The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between that is it will lie in the range.
We are given that the scores are normally distributed.
The mean of the data is 573.
The standard deviation of this data is 72.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
So,
We can write,
μ = 573
σ = 72
Then, the given expression is,
( μ - 3σ < x < μ +3σ ) = 99.7%
So,
μ - 3σ = 573 - 3*72
μ - 3σ = 573-216
μ - 3σ = 357
μ +3σ = 573 + 3*72
μ + 3σ = 573+216
μ + 3σ = 789
Hence, the mean is halfway between these two integers are = 357 and 789
Empirical rule states that for a normally distributed data that
about 68% data lies between μ + 1σ that is one standard deviation from mean.
about 95% data lies between μ + 2σ that is one standard deviation from mean.
about 99.7% data lies between μ + 3σ that is one standard deviation from mean.
Therefore,
The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between that is it will lie in the range.
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The table contains data on the number of people visiting a historical landmark over a period of one week.
From the data provided, we can consider the following function as a good approximation:
[tex]y=2.57+49.29x-3.86x^2[/tex]Therefore:
The answer is:
a quadratic function with a negative value of a
find five soultion linear eqation x+y=3
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.
What are Equations?Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. The given equation is x + y = 3Let the value of x = 0,then,0 + y = 3⇒ y = 3One of the solutions for x + y =3, is (0,3)Similarly, If x = 1,then,1 + y =3⇒ y = 3 - 1 = 2One of the solutions for x + y =3, is (1,2)If x = 2,then,2 + y = 3⇒ y = 3 - 2 = 1One of the solutions for x + y =3, is (2,1)If x = 3, then,3 + y = 3⇒ y = 3 - 3 = 0One of the solutions for x + y =3, is (3,0)If x = 4,then, 4 + y = 3⇒ y = 3 - 4 = -1One of the solutions for x + y =3, is (4, -1)Hence, five solutions of the equation x + y = 3, are:(0,3), (1,2), (2,1), (3,0) and (4, -1).Mathematical variables are used in even the most fundamental and straightforward algebraic equations. There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.To learn more about Equations, refer to:
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The five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).
What are Equations?Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.
A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.
What is the linear equation's general form?Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.
Let the value of
x = 0,
then,
0 + y = 3
⇒
y = 3
One of the solutions
for x + y =3, is =(0,3)
Similarly, If x = 1,
then,
1 + y =3 ⇒ y = 3 - 1 = 2
One of the solutions for x + y =3, is
(1,2)
If x = 2,
then,
2 + y = 3
⇒ y = 3 - 2 = 1
One of the solutions for x + y =3, is
(2,1)
If x = 3, then,
3 + y = 3
⇒ y = 3 - 3 = 0
One of the solutions for x + y =3, is
(3,0)
If x = 4,
then,
4 + y = 3
⇒ y = 3 - 4 = -1
One of the solutions for x + y =3, is
(4, -1)
Hence,
five
solutions of the equation x + y = 3, are:
(0,3), (1,2), (2,1), (3,0) and (4, -1).
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PLS HELP
Circle A has a diameter of 9 cm. Circle B has a radius of 6 cm.
a.) Which circle has the larger circumference? A or B?
b.) About how many centimeters larger is it?
cm larger
(NO PICTURE INCLUDED) (DONT ASK FOR PIC)
The circle that has the larger circumference is circle B. The difference in the circumference is 9.42 cm.
Which circle has the bigger circumference?A circle is a bounded object in which points from the center is equidistant to the circumference. The circumference of a circle is the perimeter of the circle. The diameter of a circle is a straight line that touches two opposite points on the circumference of a circle and also passes through the center. Radius is half the diameter of a circle.
The circumference of a circle = 2πr
Where:
π = pi = 22/7 r = radius = diameter / 2Circumference of Circle A = 22/7 x 2 x (9/2) = 28.29 cm
Circumference of Circle B = 22/7 x 2 x 6 = 37.71 cm
Difference in circumference = 37.71 - 28.29 = 9.42 cm
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