The equation of the tangent to the given curve x = t⁴ + 3 , y = t³ + t at the corresponding point is y = x - 2 .
In the question ,
it is given that ,
the parametric equation is x = t⁴ + 3 , y = t³ + t ,
differentiating with respect to t ,
we get ,
dx/dt = 4t³ and dy/dt = 3t² + 1
On dividing dx/dt by dy/dt to get the slope ,
we get
dy/dx = (3t² + 1)/ (4t³)
Substituting in t=1
dy/dx = (3 + 1)/4 = 1
Slope (m) = 1 ;
Substituting t = 1 , in the parametric equation ,
we have , x = 4 and y = 2 .
So , (y - 2) = 1(x - 4)
y - 2 = x - 4
y = x - 2
Therefore , the equation of the tangent is y = x - 2 .
The given question is incomplete , the complete question is
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t⁴ + 3 , y = t³ + 3 ; t = 4 ?
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Do You Know How?
3. Estimate 452 ÷ 21.
4. Complete.
21)4 52
-
R
Remember
to check that
your answer is
reasonable.
452 ÷ 21 is equal to [tex]$21 \frac{11}{21}$[/tex].
What is Quotient?
When we divide a number, the result we ultimately obtain is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally split. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.
[tex]$\frac{452}{21}=21$[/tex] Remainder 11
Convert to mixed number: Quotient= [tex]$\frac{\text { Remainder }}{\text { Divisor }}$[/tex]
[tex]$\frac{452}{21}=21 \frac{11}{21}$[/tex]
[tex]$=21 \frac{11}{21}$[/tex]
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David needs a wood board with an area of 5/12 square yard to complete a project. If the wood board is 2/3 yard wide, how long must the board be?
The area of the board is 5/12 yard², then the length of the board will be equal to 5/8 yard.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Area of board = 5/12 yard²
Width, W = 2/3 yard
Use the equation of area,
A = LW
5/12 = L(2/3)
L = (5/12)×(3/2)
L = 5/8 yard.
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Tyshawn took a taxi from his house to the airport. The taxi company charged a pick-up fee of $2.50 plus $3.50 per mile. The total fare was $79.50, not including the tip. Which equation could be used to determine mm, the number of miles in the taxi ride?
Answer: m = 22
Step-by-step explanation:
First, you subtract $2.50 from the total of $79.50 (because that is the static fee) to get $77.00. Now, because every mile is $3.50 and we want to find the number of miles, we divide $77 by $3.50 to get 22. (An easy way to do this mentally is to divide 77 by 7 and multiply by 2.) Therefore, m = 22.
The base of a square prism has an area of 16 in.2 The
height of the prism is 6 in. What is the surface area
of the square prism?
Answer:
idek
Step-by-step explanation:
Write the explicit and recursive rules for a geometric sequence given a table of values.
(a) The Explicit Rule for f(n) is 0.1 × 3n The Recursive Rule for f(n) is f(n-1) × 3. (b) The Explicit Rule for f(n) is 100 × 0.1ⁿ The Recursive Rule for f(n) is f(n-1) × 0.1
What is Explicit rule ?The explicit rule states that the value of the sequence at each term is 0.1 multiplied by 3 raised to the power of n. The recursive rule states that the value of the sequence at each term is equal to the value of the preceding term multiplied by 3. This can be seen in the table of values where each value is 3 times the preceding value.
Given,
n = 0,1,2,3,4…
f(n) = 0.1,0.3, 0.9, 2.7, 8.1
(b) The Explicit Rule for f(n) is 100 × 0.1ⁿ, The Recursive Rule for f(n) is f(n-1) x 0.1
Given,
n= 0,1,2,3,4..
f(n) = 100, 10, 1,0.1, 0.01
The explicit formula is the formula to calculate the value of the sequence directly without using any previous terms. The recursive formula uses the previous term to calculate the value of the current term.
In this example, the explicit formula is 100 × 0.1ⁿ and the recursive formula is f(n) = f(n-1) × 0.1. This means that each term in the sequence is equal to the previous term multiplied by 0.1.
For example, the third term in the sequence is 1, so the fourth term is 1 × 0.1 = 0.1.
(c) The Explicit rule for f(n) is 1000 × 0.1⁽ⁿ ⁻ ¹⁾, The Recursive rule for f(n) is f(n-1) x 0.1
To solve,
f(5) = 1000 × 0.1⁽⁵ ⁻ ¹⁾(5-1)
= 1000 × 0.1⁴
= 1000 × 0.0001
= 0.1
Given,
n= 1,2,3,4,5…
f(n) = 1000, 100, 10, 1, 0.1
The explicit and recursive rules for this geometric sequence are both written as f(n) = 1000 × 0.1⁽ⁿ ⁻ ¹⁾. This means that the value of the sequence at any given point n will be equal to 1000 multiplied by 0.1 raised to the power of n-1. This means that the value of the sequence decreases by a factor of 0.1 for every increase in n.
In this case,
f(5) = 1000 x [tex]0.1^4[/tex]
= 0.1.
(d) The Explicit Rule for this geometric sequence is f(n) = 10⁽⁵⁰ ⁻ ³ⁿ⁾, where n is the term number of the sequence.
The Recursive Rule for this geometric sequence is f(n) = f(n-1) ÷ 10³, where f(n) is the value for the nth term of the sequence and f(n-1) is the value for the (n-1)th term of the sequence.
Given,
n= 1,2,3,4,5..
f(n) = 10⁵⁰,10⁴⁷, 10⁴⁴, 10⁴¹, 10³⁸….
The value for the 5th term of the sequence is f(5) = 10⁽⁵⁰ ⁻ ³⁽⁵⁾⁾ = 10³⁸. The explicit rule for this geometric sequence is f(n) = 10⁽⁵⁰ ⁻ ³ⁿ⁾, where n is the term number of the sequence. This means that the value of each term is determined by taking 10 to the power of 50 minus 3 multiplied by the term number.
The recursive rule for this geometric sequence is [tex]\frac{f(n-1)}{10^3}[/tex] which means that the value of each term can be calculated by dividing the previous term by 10 cubes. We can use
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Which of the following inequalities matches the graph? (1 point) −6x + y < 3 6x + y < 3 6x − y < −3 The correct inequality is not listed
6x − y < −3 , inequality matches the graph.
Step 1:
Find the equation of the line
we have A(0,3) , B(1,9)
The formula to calculate the slope between two points is equal to
m = (y₂-y₁) / (x₂-x₁)
Substitute the values:
m = (9-3) / (1-0)
m = 6/1
m = 6
The equation of the line into slope intercept form is equal to
y = mx + c
where
m is the slope
b is the y-intercept
In this problem we have
m = 6
b = 3 ----> the y-intercept is the point B
Substitute the values:
y = 6x + 3
Step -2
Find the equation of the inequality
we know that:
The solution is the shaded area above the dashed line
so, the inequality is equal to
y > 6x + 3
rewrite
-6x + y > 3
6x - y < -3
Step 3
Using a graphing tool
The x-intercept is the point
The y-intercept is the point
The slope of the dashed line is positive, the graph in the attached figure.
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I have a hard time with these questions. Make sure your answer is rounded to nearest hundredth. Explain. Thank you in advance
(a) The printer will print 3.5 pages per minute.
(b) It will plant 0.13 acres of seed per pound.
What is a unit rate?
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.
(a) If a color printer prints 14 pages in 4 minutes.
So it will print = 14/4
= 3.5 pages per minute
(b) If it takes 23 pounds of seed to completely plant a 3 - acre field
So it can plant = 3/23
= 0.13 acres per pound.
Hence,
(a) The printer will print 3.5 pages per minute.
(b) It will plant 0.13 acres of seed per pound.
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What is the classification of each system? Drag the answers into the boxes to match each system. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. {4x+y=8 x+3y=8 consistent independent
The given system of equations has a solution (16/11, 24/11), so they are consistent and independent.
The given system of equations are 4x+y=8 and x+3y=8.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here, 4x+y=8 ----------(I) and x+3y=8 ----------(II)
Multiply equation (I) by 3, we get
12x+3y=24 ----------(III)
Now, subtract equation (II) from (III), we get
12x+3y-(x+3y)=24-8
11x=16
⇒ x=16/11
Substitute x=16/11 in equation (II), we get
16/11 +3y=8
⇒ 3y=8- 16/11
⇒ 3y=72/11
⇒ y=24/11
If equation as one solution, then they are consistent and independent.
Therefore, the given system of equations has a solution (16/11, 24/11), so they are consistent and independent.
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Refer to Figure 18-12. If the world price of a baseball is $3 and a tariff of 51 per baseball is imposed in the United States, which area represents the aim tariff revenue the United States government collects?
a. a
b. b
c. e
d. f
The area represents the aim tariff revenue the United States government collects is D. f
What is a tariff?Tariffs are taxes levied by the government of a country or a supranational union on goods imported or exported. Import duties, in addition to being a source of revenue for the government, can also be a form of foreign trade regulation and policy that taxes foreign products in order to encourage or safeguard domestic industry.
Tariffs serve three primary functions: they generate revenue, they protect domestic industries, and they correct trade distortions (punitive function). The revenue function stems from the fact that tariff revenue provides governments with a source of funding. This was illustrated as f in the diagram.
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What is the mass of an object that
weighs -68.6 N?
Answer:
7 kg
Step-by-step explanation:
Newton's second law tells us that Force = Mass * Acceleration, also known as F = ma.
The downward acceleration due to gravity on Earth is usually taken to be 9.8 ms^-1.
Substitute the values into the equation:
68.6 = m * 9.8
Rearrange and simplify:
m = 68.6 / 9.8
m = 7 kg
mean of 8,7,11,15,3,4
Answer:
8
Step-by-step explanation:
The mean of numbers is the sum of the numbers divided by the number of numbers. By this definition, we first have to add up all of these numbers. If we do, we get 48. Now, we figure out the number of numbers, which is 6. Finally, we divide 48 by 6 to get 8.
Find the x-intercept of the line 2x–4y= – 12.
The x-intercept of the given line having equation 2x–4y= -12 is -6
How to find x-intercept of a line?
An x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system.
To find x-intercept of a line, put y = 0 in the given equation of line
According to the given question:
The equation of line is 2x - 4y = -12
Putting y = 0 in the above equation we get
2x - 4(0) = -12
2x = -12
x = -6
Therefore, x-intercept of the line 2x–4y= -12 is -6
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Estimate a 10 % tip on a bill of $159.67 by first rounding the bill amount to the nearest ten dollars.
Answer: $180
Step-by-step explanation: To calculate the total tip, you would add 10% to the bill,
Total bill = $159.67 x 1.10+ 175.637 or $175.64
$175.64 rounded to the nearest $10 dollars is $180 as the number in the 1s column is greater than 5. Because of this, you round up to get the nearest $10.
Total bill equals $180
What is Q(1.5) if ()=cos() f(x)=cos(x) and Q(x) is centered at /2? Round your answer to 4 decimals, for example, 0.1234.
Step-by-step explanation:
Hello. Can you repost the question and just for clarification is this Taylor, Maclaurin Series?
Consider the following methods, which appear in the same class.
public int function1(int i, int j)
{return i + j;}
public int function2(int i, int j)
{return j - i;}
Which of the following statements, if located in a method in the same class, will initialize the variable x to 11?
A int x = function2(4, 5) + function1(1, 3);
B int x = function1(4, 5) + function2(1, 3);
C int x = function1(4, 5) + function2(3, 1);
D int x = function1(3, 1) + function2(4, 5);
E int x = function2(3, 1) + function1(4, 5);
Option A , if located in a method in the same class, will initialize the variable x to 11 i.e, int x = function2(4, 5) + function1(1, 3).
function2(4, 5) = 5-4 = 1
function1(1, 3) = 3+1 = 4
function2(4, 5) + function1(1, 3) = 5
On initializing the function with 11 ,
the output will be 5
A function is a set of statements that take inputs, do some specific computation, and produce output. The idea is to put some commonly or repeatedly done tasks together and make a function so that instead of writing the same code again and again for different inputs, we can call the function.
In simple terms, a function is a block of code that only runs when it is called.
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Fig the function shown in the table below, which of the following is its average fate of change ever the interval 2≤x≤10
1.3/4
2.-2
3.-1/2
4.-3./2
2. What is the average rate of change of g(x)=x² on the interval 3≤x≤9
(1) 8
(3) 15
(2) 12
(4) 18
3. Given the function f(x) shown graphed below, what is its average rate of change from } x=1 to x=7 ?
(1) -1
(2) -4/3
(3) 8
(4) 3/5
4. A function h(x) has an average rate of change equal to 7 on the interval 5 ≤ x≤ 9. If h(5)=12, then which of the following must be the value of h(9) ?
1. Average rate of change of function over the interval is d. -3/2
2. Average rate of change of function over the interval is 2. 12
3. Average rate of change of function over the interval is 1. -1
4. h(12) has the value of 61
What is the average rate of change of function?
The average rate of change function is defined as the average rate at which one quantity is changing with respect to something else changing.
Formula ----- A(x) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Solution:
1.Given a = 2, b = 10
A(x) = [tex]\frac{f(10)-f(2)}{10-2}[/tex]
A(x) = [tex]\frac{-3-9}{8}[/tex]
∴A(x) = -[tex]\frac{3}{2}[/tex]
2. Given a= 3, b = 9
f(x) = x²
A(x) = [tex]\frac{9^{2}-3^{2} }{9-3}[/tex]
A(x) = [tex]\frac{72}{6}[/tex]
∴ A(x) = 12
3. Given a = 1, b = 7
f(x) = Given graph
f(7) = 0, f(1) = 6
A(x) = [tex]\frac{0-6}{7-1}[/tex]
A(x) = -1
4. Given h(5)= 12, a=5, b=9, A(x) = 7
To find: h(12)=?
A(x) = [tex]\frac{h(12)-h(5)}{12-5}[/tex]
7 = [tex]\frac{h(12)-12}{12-5}[/tex]
h(12) = 7×7 + 12
∴ h(12) = 61
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1. Average rate of change of function over the interval is d. -3/2
2. Average rate of change of function over the interval is 2. 12
3. Average rate of change of function over the interval is 1. -1
4. h(12) has the value of 61
What is the average rate of change of function?
The average rate of change function is defined as the average rate at which one quantity is changing with respect to something else changing.
Formula ----- A(x) = (f(b)-f(a))/b-a
Solution:
1.Given a = 2, b = 10
A(x) = -3-9/10-2
∴A(x) = -3/2
2. Given a= 3, b = 9
f(x) = x²
A(x) = 81-9/9-6
∴ A(x) = 12
3. Given a = 1, b = 7
f(x) = Given graph
f(7) = 0, f(1) = 6
A(x) = 0-6/7-1
A(x) = -1
4. Given h(5)= 12, a=5, b=9, A(x) = 7
To find: h(12)=?
A(x) = (f(b)-f(a))/b-a
7 = h(12) = 7×7 + 12
∴ h(12) = 61
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The price of a share of stock changed by -$19.20
over a 5-day period. What was the average daily
change in the price of a share of the stock?
Answer:3.9
Step-by-step explanation:
Divide -19.50 by 5
=3.9
what are the domain and range of the function f(x) = 3/4 x + 5
Answer:
Domain: (−∞,∞)
Range: (−∞,∞)
Step-by-step explanation:
This equation has no bounds of domain or range, so the answer to both is all real numbers.
A circle with center C has equation x²+y²- 2x + 10y-19 = 0
It can be shown that center C is (1,-5) and that the radius is √45.
Find the equation of the tangent to the circle at the point (7,-2), giving your answer in the form ax + by + c=0, where a, b and c are integers.
Answer:
2x + y - 12 = 0
Step-by-step explanation:
The Tangent line will Always be perpendicular to the radius of a circle.
1. Find the slope of the radius that goes from the Center to the given point:
[tex]m=\frac{-2--5}{7-1}=\frac{3}{6}=\frac{1}{2}[/tex]
2. The slope of the Tangent at (7,-2) is the Negative (opposite) Reciprocal of the slope of the radius: [tex]\frac{1}{2}= > -2[/tex]
3. Write the equation of the Tangent in Point Slope Form:
[tex]y+2=-2(x-7)[/tex]
4. Distribute and rewrite in the form ax + by + c = 0
[tex]y+2=-2(x-7)\\y+2=-2x+14\\2x+y-12=0[/tex]
(a) Complete the statements below about the graphs of y=-1/3 x and y=x .
Compared to the graph of y=x , the graph of y=-1/3 x is
Compared to the graph of y=x , the graph of y=1/3x intersects the y -axis at
The correct statements regarding the functions are given as follows:
a)
Compared to the graph of y = x, the graph of y = -1/3x is vertically compressed by a factor of 3 and reflected over the x-axis.Compared to the graph of y = x, the graph of y = -1/3x intersects the y-axis at the same place, which is the origin.b)
Compared to the graph of y = x, the graph of y = x - 2 is shifted right two units.Compared to the graph of y = x, the graph of y = x - 2 intersects the y-axis two units below.What are the transformations to the functionFor item a, the functions are given as follows:
y = x.y = -1/3x.The multiplication by -1/3 means that the vertically compressed by a factor of 3 and reflected over the x-axis, due to the multiplication by the negative number.
For item b, the functions are given as follows:
y = x.y = x - 2.The transformation is:
x -> x - 2, meaning that the function was shifted right two units.
The intersection with the y-axis is at the value of y when x = 0.
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Which of the following equations has an axis of symmetry with the equation x = 3?
y=x² + 6x-3
y= 2x² + 6x-3
y=x² - 6x +3
y=3x² + 6x-3
The equation which has an axis of symmetry with the equation x = 3 as required in the task content is; y = x² - 6x +3.
Which equation among the given answer choices has an axis of symmetry; x = 3?It follows from the task content that the equation which has an axis of symmetry; x = 3 be determined among the answer choices.
By expressing the equation; y = x² - 6x +3 in vertex form; y = ( x - h )² + k; where the axis of symmetry is given by; x = h; we have that;
y = ( x - 3 )² - 6
On this note, it can be concluded that the axis of symmetry of the considered equation; y = x² - 6x +3 is; x = 3.
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Two congruent parallelograms are joined along their base
to make the shape below.
18 cm
Work out the total area of the shape.
Optional working
11 cm
15 cm
The total area of the shape will be;
⇒ 721 cm²
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Two congruent parallelograms are joined along their base to make the shape below.
Now,
We know that;
2 identical parallelogram whose area = 2 (Base x Height)
And, 2 identical right triangle = base x height
And, 1 rectangle = length x width
So, We get;
In parallelogram;
Base = 15 cm
Height = 11 cm
Hence, We get;
Area = 2 (15 x 11)
= 330 cm²
And, Area of two identical right triangle;
Base = 11 cm
Height = 11 cm
Hence, Area = 11 × 11
= 121 cm²
Area of rectangle = 18 x 15 = 270 cm²
Thus, The total area of shape will be;
⇒ 330 + 121 + 270
⇒ 721 cm²
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7. Petal and Leaf florists currently have 30
roses, 36 carnations, and 54 tulips. How
many equal-sized bouquets can be made
using all of the flowers if the florists make
sure that each bouquet has the same
number of each type of flower?
The number of banquets that can be formed is 6 and total number of flowers are 2+3=5.
What is the greatest common divisor?
the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, and y.
We have given,
Petal and Leaf florists currently have 30 roses, 36 carnations, and 54 tulips
Since it is given that there are 75 rose and 45 lily flowers. Therefore,
Factorise 30 as follows:
30 = 2 × 3 × 5
Factorise 36 as follows:
36 = 2 × 2 × 3 × 3
Factorise 54 as follows:
54 = 2 × 3 × 3 × 3
We know that HCF is the highest common factor.
Since the common factor between the numbers 30, 36, and 54 is 2×3=6.
Hence, the number of banquets that can be formed is 6 and total number of flowers are 2+3=5.
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let be an matrix and an matrix so that the product is defined. suppose we know that the rref of both a and b have pivots in every column. explain why it follows that every column of rref(a b) also has a pivot in each column.
A pivot in every row means that the linear system A x=b has at least one solution, for every b.
If every column has a pivot, then the linear system A x=b has at most one solution.
If both hold (which can happen only if A is a square matrix), we get that the system A x=b has unique solution for every b.
A pivot in every row is equivalent to A having a right inverse, and equivalent to the columns of A spanning
[tex]$\mathbb{R}^m$ ( $m$[/tex] is the number of rows).
A pivot in every column is equivalent to A having a left inverse, and equivalent to the columns of A being linearly independent
A pivot means fundamentally changing the direction of a business when you realize the current products or services aren't meeting the needs of the market. The main goal of a pivot is to help a company improve revenue or survive in the market, but the way you pivot your business can make all the difference.
The first nonzero item of each row in a matrix in row-echelon form is known as a pivot, and the columns in which pivots appear are known as pivot columns.
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URGENT!
Translate the sentence into an equation.
The sum of 2 times a number and 3 is 9.
Use the variable x for the unknown number.
The equation is 2x+3=9, x is the unknown number. After solving the equation, we get x=3.
What is equation?A mathematical expression shows the equality between two terms.
How can we find unknown value from an equation?In mathematics variables are used to denote any unknown number and equations are developed based on an expression. Finally, equations are solved, and unknown values are determined.
let, x is the unknown number. As per question the equation will be 2x+3=9
the equation is solved, and x is determined
2x=9-3
x=6/2
x=3
hence, x=3, 3 is the number.
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Answer:
[tex] \sf \: 2x + 3 = 9, \: x = 3[/tex]
Step-by-step explanation:
Given statement,
→ Sum of 2 times a number & 3 is 9.
Let the unknown number be,
→ [tex] \sf \pink{x}[/tex]
Forming the equation,
→ (2 × x) + 3 = 9
→ 2x + 3 = 9
Now the value of x will be,
→ 2x + 3 = 9
→ 2x = 9 - 3
→ 2x = 6
→ x = 6/2
→ [ x = 3 ]
Hence, the value of x is 3.
Sales Tax in Cities
City A 3%
City B 4.1%
City C 2.9%
City D 3.2%
2. How much will Tom's $30 sweater cost in
City B?
A $30.90
B $31.23
C $30.87
Answer: C
Step-by-step explanation:
30 x 1.029
30.87
P=a+3b+4c solve for a
the answer is
a=p-3b-4c
when the ___ calculates an increasing ___ ; the ___ may choose to decrease .
The answer that correctly fills the missing portions is option A.
The full sentence is: When the Bureau of Labor Statistics (BLS) calculates an increasing Consumer Price Index (CPI); the Federal Reserve (FED) may choose to Quantitative Easing.
Quantitative easing is a monetary policy operation in which a central bank buys government bonds or other financial assets to infuse monetary reserves into the economy in order to encourage economic activity.
The goal of QE is to level the playing field in order to make spending and investing money more enticing and accessible to people. Lower interest rates may improve the possibility that company and civilian borrowers will borrow to make purchases, promoting economic activity.
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Full Question:
When the ___ calculates an increasing ___ ; the ___ may choose to decrease______.
A) BLS, CPI. FED, QE
B) OECD, QE, BLS, CPI
C) BEA, GDP, BLS, CPI
D) BEA, CPI, OECD, GDP
Which property is shown in the matrix addition below?
-6
9
15 -2
0
-3
+
6
-9
-15 2
0
3
commutative property
associative property
Oinverse property
Oidentity property
0 0 0
0 0 0
For the given matrix the additive inverse property is shown.
What is additive inverse of matrix?
The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.
Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix
M = - M.
Consider the given matrix,
[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]
Here each element in first matrix is negative of the element of second matrix.
That is each element is inverse of the element in second matrix.
And the addition of elements is 0.
Hence, for the given matrix the additive inverse property is shown.
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tree with root vertex d that has a left edge to f, a center edge to b, and a right edge to a. b has a left edge to i, a center edge to h, and a right edge to e. a has a center edge to c. c has a center edge to g. (a) give the order in which the vertices of the tree are visited in a post-order traversal. (b) give the order in which the vertices of the tree are visited in a pre-order traversal.
Answer:
post-order: f, i, h, e, b, g, c, a, dpre-order: d, f, b, i, h, e, a, c, gStep-by-step explanation:
You want the (a) post-order, and (b) pre-order list of visited vertices in a traversal of the tree described by {root, left, center, right}: {d, f, {b, i, h, e}, {a, {c, g}}}.
(a) Post-orderA tree is traversed in post-order by visiting the left branch, center branch, and right branch before the root. This is accomplished recursively.
For the given tree, the root 'd' has left branch 'f' which has no branches. That means node 'f' is reported first.
The middle branch goes to 'b' which has three branches. Those are reported before their root 'b'.
The right branch from root 'd' goes to 'a', which has branch 'c' going to 'g'. So, 'g' is reported, then 'c', then 'a'.
Finally, 'd' is reported.
Hence, the post-order traversal is f, i, h, e, b, g, c, a, d.
(b) Pre-orderThe pre-order traversal reports the root node, then the left, center, and right nodes, recursively. The vertices are effectively visited in the order in which we have defined the tree above: d, f, b, i, h, e, a, c, g.