No, All equilateral triangles need not to be always congruent with one another .
Justification of answer:
The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .
Properties of an equilateral triangles:1. All 3 side of an equilateral triangles have same length .
2. All 3 angles of an equilateral triangles have same measure.
3. Each angles of an equilateral triangles is 60 degree .
4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} * a^2[/tex]
5 . Perimeter of an equilateral triangles = 3*a
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HELP PLSSS I NEED TO SHOW WORK ALSO … The band has at most $3000 for its annual trip to Six Flags. The budget consisted of $1000 for travel cost, and $25 for each student's expenses. Write an inequality that represents the maximum number of sudents, x, that would be able to attend the trip. ( i’ll give you 50 points)
Answer: The maximum students that would be able to attend the trip is 40 students. Because 25 multiplied by 40 is = 1,000 and the budget is only 3,000 the answer is 40 students
Step-by-step explanation: Hope this helps =)
7. Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a
flight had 52 passengers who paid $1360, how many first class and tourist class passengers were
there?
Answer:
12 first class and 40 tourist
Step-by-step explanation:
Answer:
40 tourist class passengers, and 12 first class passengers.
Step-by-step explanation:
Here's my explanation:
We let X be the number of passengers booking for the tourist class.
If there were 52 passengers who paid 1360, then to find the number of passengers who booked first class, we write:
52-x
And if the airline fares are 30 per first class and 25 dollars for tourist class, you would say 30.00(first class)+25.00(tourist class)=1360
Using substitution, plug-in 52-x for the first class:
30(x)+25(52-x)=1360
30x+1560-25x=1360
1360-1560 =25x-30x
-200=-5x
x=40
Plug in 40 for x,
52-40=12
So, 40 tourist class passengers, and 12 first class passengers.
If a and b are real numbers then a+b is a real number.This law is called ?
Step-by-step explanation:
This law is called the closure property of real numbers. It states that if a and b are real numbers, then their sum, a + b, is also a real number. This is because the set of real numbers is closed under addition, which means that any operation performed on real numbers will result in another real number.
For example, if a = 3 and b = 4, then a + b = 7, which is a real number. Similarly, if a = -2 and b = 3, then a + b = 1, which is also a real number.
The closure property of real numbers holds for many other mathematical operations as well. For example, the product of two real numbers is also a real number, as is the quotient of two real numbers (assuming that the divisor is not zero). The set of real numbers is also closed under subtraction and negation.
find the equation of tangent normal to the curve y=3x-x^3 at points where it cuts the x-axis
Correct Question:-
Find the equations of lines normal to the curve [tex]\rm{y=3x-x^3}[/tex] at points where it cuts the x axis.
[tex]\quad[/tex]
Solution:-
The given curve,
[tex]\longrightarrow\rm{y=3x-x^3}[/tex]
Differentiating wrt x we get,
[tex]\longrightarrow\rm{\dfrac{dy}{dx}=3-3x^2}[/tex]
This term is slope of tangent on the curve at a point (x, y).
Taking reciprocal,
[tex]\longrightarrow\rm{\dfrac{dx}{dy}=\dfrac{1}{3-3x^2}}[/tex]
and multiplying by -1,
[tex]\longrightarrow\rm{-\dfrac{dx}{dy}=\dfrac{1}{3x^2-3}}[/tex]
Now this term is slope of normal on the curve at a point (x, y).
[tex]\longrightarrow\rm{n(x)=\dfrac{1}{3(x^2-1)}}[/tex]
[tex]\quad[/tex]
The points where the curve [tex]\rm{y=3x-x^3}[/tex] cuts x axis is obtained by equating y = 0.
[tex]\longrightarrow\rm{0=y}[/tex]
[tex]\longrightarrow\rm{0=3x-x^3}[/tex]
[tex]\longrightarrow\rm{0=x(3-x^2)}[/tex]
[tex]\longrightarrow\rm{0=x(\sqrt3-x)(\sqrt3+x)}[/tex]
[tex]\Longrightarrow\rm{x\in\left\{-\sqrt3,\ 0,\ \sqrt3\right\}}[/tex]
So the points where the curve cuts x axis are (-√3, 0), (0, 0) and (√3, 0).
[tex]\quad[/tex]
Consider the point (-√3, 0).
The slope of normal at this point is,
[tex]\longrightarrow\rm{n(-\sqrt3)=\dfrac{1}{3((-\sqrt3)^2-1)}}[/tex]
[tex]\longrightarrow\rm{n(-\sqrt3)=\dfrac{1}{6}}[/tex]
Then equation of normal at this point is,
[tex]\longrightarrow\rm{y-0=\dfrac{1}{6}(x+\sqrt3)}[/tex]
[tex]\longrightarrow\bf{x-6y+\sqrt3=0}[/tex]
[tex]\quad[/tex]
Consider the point (0, 0).
The slope of normal at this point is,
[tex]\longrightarrow\rm{n(0)=\dfrac{1}{3((0)^2-1)}}[/tex]
[tex]\longrightarrow\rm{n(0)=-\dfrac{1}{3}}[/tex]
Then equation of normal at this point is,
[tex]\longrightarrow\rm{y-0=-\dfrac{1}{3}(x-0)}[/tex]
[tex]\longrightarrow\bf{x+3y=0}[/tex]
[tex]\quad[/tex]
Consider the point (√3, 0).
The slope of normal at this point is,
[tex]\longrightarrow\rm{n(\sqrt3)=\dfrac{1}{3((\sqrt3)^2-1)}}[/tex]
[tex]\longrightarrow\rm{n(\sqrt3)=\dfrac{1}{6}}[/tex]
Then equation of normal at this point is,
[tex]\longrightarrow\rm{y-0=\dfrac{1}{6}(x-\sqrt3)}[/tex]
[tex]\longrightarrow\bf{x-6y-\sqrt3=0}[/tex]
[tex]\quad[/tex]
Hence the equations of lines normal to the curve [tex]\rm{y=3x-x^3}[/tex] at points where it cuts x axis are,
[tex]\longrightarrow\left\{\begin{array}{ll}\bf{x-6y-\sqrt3}&\bf{=0}\\\bf{x+3y}&\bf{=0}\\\bf{x-6y+\sqrt3}&\bf{=0}\end{array}\right.[/tex]
A construction worker is pouring concrete stairs. The first step requires 1. 8 cubic feet of concrete, and the first 5 steps require a total of 27 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 12 steps? 259. 2 cubic feet 43. 2 cubic feet 156 cubic feet 140. 4 cubic feet.
We can follow Arithmetic series, then the number of cubic feet concrete is required for the first 12 steps = 140.4 cubic feet.
Given that,
The first step requires 1. 8 cubic feet of concrete,
The first 5 steps require a total of 27 cubic feet.
An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. Following is a simple formula for finding the sum: Formula 1: If [tex]S_{n}[/tex] represents the sum of an arithmetic sequence with terms , then. This formula requires the values of the first and last terms and the number of terms.
For an arithmetic series
[tex]a , a+d , a+2d , a+3d , .......[/tex]
where a is the first term and d is the common difference, the sum of n terms equals,
[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex] (Equation-1)
Since the first step requires 1.8 cubic feet of concrete, a = 1.8.
Now, the first 5 steps require 27 cubic feet of concrete, that is,
[tex]S_{5}[/tex] = 27
a = 1.8
n = 5
We can substitute values in equation-1,
[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + [tex](\frac{5(5-1)}{2} )d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + [tex](\frac{5*4}{2} )d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + [tex]\frac{20}{2} d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + 10 d
[tex]S_{5}[/tex] = 9 + 10 d
Then, [tex]S_{5}[/tex] = 27
27 = 9 + 10d
27 - 9 = 10d
18 = 10d
d = [tex]\frac{18}{10}[/tex]
d = 1.8
Find the concrete required for 12 steps.
Then, we can substitute n = 12
So,
We can write,
[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + [tex](\frac{12(12-1)}{2} )d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + [tex]\frac{12*11}{2} d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + [tex]\frac{132}{2} d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + 66 d
[tex]S_{12}[/tex] = 21.6 + 66 d
We can substitute d = 1.8
[tex]S_{12}[/tex] = 21.6 + 66 (1.8)
[tex]S_{12}[/tex] = 21.6 + 118.8
[tex]S_{12}[/tex] = 140.4
Therefore,
We can follow Arithmetic series, then the number of cubic feet concrete is required for the first 12 steps = 140.4 cubic feet.
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What are the six steps of copying an angle?
Angle can be copied by following 6 steps.
How to copy an angle?These are the steps to copy an angle:
1.Make point B the center of the working line (l).
2.Create an arc (A, r) that intersects the two sides of angle A at locations S and T by setting your compass to any radius r.
3.Create an arc (B, r) with a point V where it intersects the line l.
4.Build an arc (S, ST).
5.Create an arc at point W where (V, ST) intersects (B, r).
6.You're done after you draw line BW.
Angle can be copied by following 6 steps.
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What is ten more than twenty?
10 more than 20 will be Addition of 10 and 20 which is supposed to be 10 plus 20 = 30.
Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.
The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.
We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 20 to add 10 to 20. Therefore, the answer is 30 once more.
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What are the 3 types of real numbers?
Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.
What is Real number?A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).
whole = 0,1,2,3,4,5,6,7,8,9...….
rational = 1,2,3,3/4,5/6,...…
irrational = [tex]\sqrt{8}[/tex], etc
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The population of a city has increased by 27% since it was last measured. If the current population is 63,500 , what was the previous population?
Answer:
50000
Step-by-step explanation:
We know it increase 27% since it was last measured
100% + 27% = 127%
We have to find 1%
We take 63500 divided by 127 = 500
500 times 27 = 13500
Now we have to take 63500 and subtract by 13500 to find the previous population.
63500 - 13500 = 50000
So, the previous population is 50000
How do you write numbers in Excel?
Go to the Home tab and choose Number from the drop-down menu. In addition, you have the following choices: When choosing Number, press CTRL + 1. Right-click the cell or cell range, choose Format Cells..., then choose Number.
what are numbers ?To calculate and represent a quantity, a number, an arithmetic value, is needed. Numbers are represented by mathematical inscriptions, such the letter "3." Using logical symbols or digits to represent numbers is known as a number system.
here ,
The cells you want to format should be selected.
Place your cursor over the Dialog Box Launcher next to Number on the Home tab.
Click Fraction in the Category list.
Select the desired fraction format type from the Type list by clicking it.
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How do you know when a graph is inequality?
Observing the graph and the lines drawn, The graph is inequality is known if it is showing the region for which the inequality exists. Usually it is shown with arrows at the end of the line.
What do you mean by inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities.
What do you mean by graph?The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
Using a given graph,
We know that the graph is inequality if it is showing the region where the inequality exists,
It is usually shown using arrows at the end of the line towards the direction where the inequality is satisfied.
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What are the factors of the expression 2x² 5x 12?
The factors of the expression 2[tex]x^{2}[/tex] -5x -12 are (x - 4) and (2x+3)
given that
2[tex]x^{2}[/tex] -5x -12 =0
in the above equation
a = 2[tex]x^{2}[/tex]
b =-5x
c = -12
now we need to multiply a and c
a * c = 2[tex]x^{2}[/tex] * -12 = -24[tex]x^{2}[/tex]
now split b into two terms such that sum is equal to -5x and their product is -24
-5x = -8x +3x
2[tex]x^{2}[/tex] -5x -12 =0
2[tex]x^{2}[/tex] -8x + 3x -12 =0
2x(x - 4)+3(x-4) =0
(2x+3)(x-4) =0
The factors of the expression 2[tex]x^{2}[/tex] -5x -12 are (x - 4) and (2x+3)
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How many rows and columns are there in Excel 2007?
A maximum of 1,048,576 rows are allowed in Microsoft Excel 2007. 15,384 columns. Columns and rows make up an Excel spreadsheet.
what are columns and rows ?The arrangement of items next to or horizontally across one another is referred to as a row. As a vertical grouping of items according to category, a column can be said to exist. Left to right is the direction of arranging. From top to bottom, the set up is made. At far right is where the total is displayed.
here
Numbers 1, 2, 3, and 4 are used to designate the rows, which are horizontally oriented.
A, B, C, D, etc., are used to denote the letters that run horizontally along the columns.
Cells are what happen when a column and row intersect.
A maximum of 1,048,576 rows are allowed in Microsoft Excel 2007. 15,384 columns.
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Braden salazar was deployed in a combat zone for all of 2021. He is married and has two children. Braden's nontaxable combat pay in 2021 is $14,000. His wife worked part-time while braden was deployed and earned $7,000. What is the maximum amount of earned income the salazars can report for eitc purposes in 2021?.
The amount of earned income the Salazars can report for EITC purposes in 2021 is $21,000.
The maximum amount of earned income the Salazars can report for EITC purposes in 2021 is $21,000. This is calculated by adding Braden's nontaxable combat pay ($14,000) and his wife's earned income ($7,000).
Formula:
Maximum Earned Income for EITC = Braden's Nontaxable Combat Pay + Wife's Earned Income
Maximum Earned Income for EITC = $14,000 + $7,000
Maximum Earned Income for EITC = $21,000
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Which is not a solution to the inequality: 3x+13= -8.
A. -8
B. -7
C. -6
D.-5
Answer:
All the options except for option B.
Answer:
A,C and D are not.
where as B is solution
Solve this system of equations by graphing. First graph the equations, and then type the solution.
The graph of the equation given is mentioned below.
What is plot point in graph ?
Whenever we draw a point on our grid, we'll call it "plotting a point." The grid is really called a "graph" and the points we plot are called "coordinates." These are really locations on a plane -- we're just finding and labeling them.
Equation given,
y = 3/5x - 1 ----eq(i)
y = 2/5x -----eq(ii)
Now, for this two equation we infinite points for real numbers.
Now, take some points to plot the graph.
First for the eq(i)
Put x = 0, so y = -1
Put x = 5, so y = 2
Points for eq(i) is (0, -1) and (5, 2)
Now, for eq(ii)
Put x = 0, so y = 0
Put x = 5, so y = 2
Points for eq(ii) is (0, 0) and (5, 2)
Common point is (5, 2)
Now, plot this point on graph.
Hence, for more clarity graph of the equation given is mentioned below.
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How do you find the vertical asymptotes of the following function?
The vertical asymptotes of a function can be found by setting the denominator equal to zero and solving for x. This will give the x-values that the function cannot approach as it approaches infinity.
The vertical asymptotes of a function can be found by setting the denominator equal to zero and solving for x. This will give the x-values that the function cannot approach as it approaches infinity.In other words, a vertical asymptote is a line that the graph of a function approaches but never touches. This line is the result of the denominator of a rational function becoming equal to zero. When this happens, the function is undefined at that value of x. To find the vertical asymptotes of a function, one must first factor the denominator and set each factor equal to zero. Then, solve each factor for x to get the x-values of the vertical asymptotes. It is important to note that a vertical asymptote can also appear if the numerator of a rational function is equal to zero. In this case, the vertical asymptote is the x-value at which the numerator is equal to zero. The vertical asymptotes of a function can help us to understand the behavior of the function and its graph.
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please help me with this question
step by step please
Answer:
[tex]36.77150[/tex], or 37 (rounded)
Step-by-step explanation:
1. [tex]\sqrt{97} = 9.84885[/tex]
2. [tex]9.84885[/tex] + [tex]8.169178744[/tex] = [tex]18.01803[/tex]
3. [tex]\frac{18.01803}{0.49}[/tex]
4. = [tex]36.77150[/tex]
You can simplify 36.77150 to 37
... Hope this helped! Have a wonderful New Year!
The value of the equation is A = 36.77
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( √97 + 2.014³ ) / 0.49 be equation (1)
On simplifying the equation , we get
√97 = 9.8488578
2.014³ = 8.169178744
Substituting the values in the equation , we get
A = ( 9.8488578 + 8.169178744 ) / 0.49
A = 18.018036544 / 0.49
A = 36.77150
Therefore , the value of A is 36.77
Hence , the equation is A = 36.77
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I'm giving all the points I got man, pls help me with this geometry question
Answer:
Vertex = (0,0)
Focus = (0, -1/8)
Axis of symmetry; x = 0
directrix, y = 1/8
graph: (attached picture)
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer:
Vertex = (0,0)
Focus = (0, -1/8)
Axis of symmetry; x = 0
directrix, y = 1/8
Step-by-step explanation:
A runner sprinted for 198 yards . How many feet is this?
Is the system of linear equations 2x 3y 9 0 and 4x 6y 18 consistent justify your answer?
Consistency exists inside the linear equation system.
To determine whether a system of linear equations is consistent, you can try to solve the system to find the values of the variables that satisfy all of the equations. The system is consistent if it has at least one solution. If the system has no solutions, then it is inconsistent.
In this case, the system of linear equations is 2x + 3y - 9 = 0 and 4x + 6y - 18 = 0.
To solve this system, you can use algebraic methods such as substitution or elimination. Using substitution, you can solve one of the equations for one of the variables in terms of the other, and then substitute this expression into the other equation to solve for the other variable. For example, you could solve the first equation for y:
2x + 3y - 9 = 0
3y = 9 - 2x
y = (9 - 2x)/3
Then, you could substitute this expression for y into the second equation to solve for x:
4x + 6((9 - 2x)/3) - 18 = 0
4x + (54 - 12x)/3 - 18 = 0
(12x - 54)/3 + 4x - 18 = 0
(12x - 72)/3 = 0
12x - 72 = 0
12x = 72
x = 6
Substituting this value for x back into the first equation, you can solve for y:
2(6) + 3y - 9 = 0
12 + 3y - 9 = 0
3y = -3
y = -1
Therefore, the solution to this system of equations is x = 6 and y = -1. Since there is at least one solution, this system is consistent.
The complete question is:-
Is the system of linear equations 2x+3y-9=0 and 4x+6y-18=0 consistent? justify your answer.
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What stays the same when you perform a rigid motion transformation?
When a point or object is moved but its size and shape don't change, it is said to have undergone rigid motion, sometimes referred to as a rigid transformation.
What is rigid motion transformations?The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped.
When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.
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plss hellppp, I've been stuckk on this questionn
Answer:
we can conclude that there are 3 solid combined in this
a + b + c = d as the total volume
[(6)(6)(2)] + [(6)(3)2)] + [(6)(2)(2)]
= 72 + 36 + 24
= 132 ft³
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Which series of transformation would create a congruent shape?
A series of transformations that would create a congruent shape would include any combination of rotations, reflections, and translations that preserve the size and shape of the original figure.
For example, rotating a square by 90 degrees and then reflecting it across a line of symmetry would create a congruent square. Similarly, translating a triangle to a new location on the plane while preserving its orientation would also create a congruent triangle.
What is transformation, why is it important, etc.?The structures, cultures, and business models of an institution must be realigned in order to create a learning environment that produces substantial and equitable increases in outcomes and educational value. Transformation describes this procedure.
What is the transformational process?Any activity or collection of activities that takes one or more inputs, changes and adds value to them, and produces outputs for consumers or clients is referred to as a transformation process.
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find the probability with which bob plays l in the mixed strategy equilibrium (round your answer to the 4th decimal).
The probability with which bob plays l in the mixed strategy equilibrium = 0.9090
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here suppose Alice plays U with probability P and D * with probability ( 2 - P)
Therefore, when Bob plays L, Bob gets payoff 8 with probability P and (2) with probability ( 2 - P). Hence
= 8 * P + 2 * ( 2 - P)
= 8P +4 - 4P
= 4 + 8P
Also, when Bob plays R, Bob gets pay off 4 with probability P and 7 probability (2-P). Hence expected payoff is
= 4*P+7(2-P)
= 4P+14-7P
=14-3P
At mixed strategy nash equilibrium the expected payoffs are equal. hence,
4 +8P = 14-3P
3P+8P = 14-4
11P = 10
P = 10/11
P = 0.9090
In the mixed strategy equilibrium, Bob's chances of playing l are equal to 0.9090.
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Here suppose Alice plays U with probability P and D * with probability ( 2 - P)
Therefore, when Bob plays L, Bob gets payoff 8 with probability P and (2) with probability ( 2 - P). Hence
= 8 * P + 2 * ( 2 - P)
= 8P +4 - 4P
= 4 + 8P
Also, when Bob plays R, Bob gets pay off 4 with probability P and 7 probability (2-P). Hence expected payoff is
= 4*P+7(2-P)
= 4P+14-7P
=14-3P
At mixed strategy nash equilibrium the expected payoffs are equal. hence,
4 +8P = 14-3P
3P+8P = 14-4
11P = 10
P = 10/11
P = 0.9090
In the mixed strategy equilibrium, Bob's chances of playing l are equal to 0.9090.
in example 11.3 (p. 270), when bob jumps on the cart, what kind of collision is this?
Since Bob jumps on the cart in example 11.3 (p. 270), a kind of collision which this represents is: d) Perfectly inelastic.
What is an elastic collision?An elastic collision can be defined as a type of collision between two objects wherein the total kinetic energy of the two objects remains the same after the collision. This ultimately implies that, there isn't a net loss of momentum and kinetic energy within the system due to the collision.
What is an inelastic collision?An inelastic collision can be defined as a type of collision between two objects wherein the total kinetic energy of the two objects changes the same after the collision. This ultimately implies that, there is a net loss of momentum and kinetic energy within the system due to the collision.
In this context, we can reasonably infer and logically deduce that the coefficient of restitution would be equal to zero (0) when bob jumps on the cart, resulting in a perfectly inelastic inelastic collision.
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Complete Question:
In example 11.3 (p. 270), when Bob jumps on the cart, what kind of collision is this?
a) Inelastic, but not perfectly inelastic
b) Rigid
c) Elastic
d) Perfectly inelastic.
Is equidistant the same as parallel?
In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.
A point is said to be equally far from a group of objects if there is an equal distance between it and each member of the group.
The perpendicular bisector of two specified (different) points is their location in two-dimensional Euclidean geometry. The locus of points equidistant from two provided points in three dimensions is a plane, and generalizing further, the locus of points equidistant from two given locations in n-dimensional space is a (n1)-space.
The circumcenter of a triangle is a location that is equally spaced from each of the three vertices.
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The coordinate 2 has a weight of 2,
the coordinate 3 has a weight of 2,
and the coordinate 10 has a weight of 1.
Find the weighted average.
The coordinates' weighted average is 4
How is the weight average calculated?The "weighted average" is the average of a group of numbers, each of which has a unique "weight" or value. Add the results after dividing each number by its weight to obtain the weighted average. A weighted average or mean is one in which, as opposed to considering each item equally, each item being averaged is multiplied by a number (weight) based on the item's relative importance.The given parameters are:
Coordinate 2 has a weight of 2
Coordinate 3 has a weight of 2
Coordinate 10 has a weight of 1
The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
So, we have:
Weight average = (2 × 2 + 3 ×2 + 10 × 1)/(2 + 2 + 1)
Evaluate the quotient
Weight average = 4
Hence, the weight average of the coordinates is 4.
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Which is a list of all the roots of
x3 −x2 =4−4x?
F {−1,2,−2} H {−1,2i,−2i}
G {1,2,−2} J {1,2i,−2i}
Answer:
J
Step-by-step explanation:
[tex]x^3-x^2+4x-4=0 \\ \\ x^2(x-1)+4(x-1)=0 \\ \\ (x^2+4)(x-1)=0 \\ \\ (x-2i)(x+2i)(x-1)=0 \\ \\ x=1, 2i, -2i[/tex]
3.6432 rounded to the nearest hundredth
Answer: 3.64
Step-by-step explanation:
3.64
What is the Nearest Hundredth?
Nearest hundredth is the second digit after the decimal point.
How to Calculate Rounding to the Nearest 100th?
If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit. Example
124.586
The third digit of right of decimal point is 6
The second digit after decimal point is 8 which is greater than 5
So add 1 to 8
Result = 124.59
its 3.6400 I believe since you are rounding to the nearest hundredth which would be in the 2nd place value to the right of the decimal and 32 would round down to 0.