The set of vectors spanning the null space of A is {(0,0,z)}.
A set of vectors spanning the null space of a matrix A is a set of vectors that, when multiplied by the matrix A, result in the zero vector. In other words, these vectors are in the null space of A because they are mapped to the zero vector under the transformation represented by A.
To find a set of vectors spanning the null space of matrix A, you can use the following steps:
Write the matrix A in row-reduced echelon form.Identify the pivot columns in the matrix. These are the columns that contain the leading 1's in the row-reduced echelon form.For each pivot column, assign a variable to the corresponding pivot row.For each pivot column, set the variables corresponding to all other rows in the column equal to 0.For each non-pivot column, set the variables corresponding to the rows in the column equal to a free variable.The set of vectors formed by the values of the variables is a set of vectors spanning the null space of A.To find a set of vectors spanning the null space of the matrix A= 1 1 2 -1 2 3 6 -2 -2 1 2 2 0 -2 -4 0:
Write the matrix A in row-reduced echelon form:
1 1 2 | -1
0 0 0 | 0
0 0 0 | 0
The pivot columns are the first and second columns, which contain the leading 1's.
Assign variables x and y to the pivot rows:
1 1 2 | -1
0 0 0 | 0 x
0 0 0 | 0 y
Set the variables corresponding to all other rows in the pivot columns equal to 0:
1 1 2 | -1
0 0 0 | 0 0
0 0 0 | 0 0
Set the variables corresponding to the rows in the non-pivot column equal to a free variable z:
1 1 2 | -1
0 0 0 | 0 0 z
0 0 0 | 0 0 z
The set of vectors spanning the null space of A is {(0,0,z)}.
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What is a degree 4 function called?
Answer:
Quartic function
Step-by-step explanation:
Answer: Quartic function
Step-by-step explanation:
How do you graph 4 lines?
To graph four lines, you will need to plot at least four points for each line and then draw a line through these points.
A general procedure you can use is as follows:
Identify the equation of each line. You will need the equation of each line in slope-intercept form (y = mx + b) to graph the line.Choose at least four points to plot on each line. You can choose these points based on the x-values you want to use or by substituting different values for x into the equation of the line and solving for y.Plot the points on the graph. Use a ruler to draw a line through the points for each line.Give the graph a title and identify its axes. Make sure to include units of measurement on the axes if necessary.It can be helpful to use a different color or style (such as a solid line or a dotted line) for each line to make it easier to tell them apart.
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What is the product of five and 85
Answer:
[tex]5 * 85 = 425[/tex]
Step-by-step explanation:
⭐ What is the product of 2+ numbers?
The product of 2+ numbers is the answer you get when multiplying 2+ numbers.To get the product of 5 and 85, multiply them!
You can multiply them using a calculator, or manually multiply them just like how I showed in the image attached:
Solve the equation with the help of laplace transform (d^2y+dx=2 ,when x(0)=3, x’(0)=1, where d=d/█(dtà)
Correct Question:-
Solve the following differential equation using Laplace transformation.
[tex]\rm{x''(t)+x'(t)=2,\quad x(0)=3,\quad x'(0)=1}[/tex]
where [tex]\rm{x'(t)=\dfrac{dx}{dt},\quad x''(t)=\dfrac{d^2x}{dt^2}.}[/tex]
[tex]\quad[/tex]
Solution:-
Let,
[tex]\cal{L}\{\rm{x(t)}\}=X(s)[/tex]
[tex]\cal{L}^{\rm{-1}}\{\rm{X(s)}\}=x(t)[/tex]
Given,
[tex]\longrightarrow\rm{x''(t)+x'(t)=2}[/tex]
We take Laplace transformation of both sides of the equation.
[tex]\longrightarrow\cal{L}\{\rm{x''(t)+x'(t)}\}=\cal{L}\{\rm{2}\}[/tex]
[tex]\longrightarrow\cal{L}\{\rm{x''(t)}\}+\cal{L}\{\rm{x'(t)}\}=\cal{L}\{\rm{2}\}[/tex]
We have,
[tex]\cal{L}\{\rm{x''(t)}\}=\rm{s^2\,X(s)-s\,x(0)-x'(0)}[/tex]
[tex]\cal{L}\{\rm{x'(t)}\}=\rm{s\,X(s)-\,x(0)}[/tex]
[tex]\cal{L}\{\rm{2}\}=\rm{\dfrac{2}{s}}[/tex]
Then,
[tex]\small\text{$\longrightarrow\rm{\big[s^2\,X(s)-s\,x(0)-x'(0)\big]+\big[s\,X(s)-x(0)\big]=\dfrac{2}{s}}$}[/tex]
[tex]\longrightarrow\rm{s(s+1)\,X(s)-(s+1)\,x(0)-x'(0)=\dfrac{2}{s}}[/tex]
Given that [tex]\rm{x(0)=3}[/tex] and [tex]\rm{x'(0)=1.}[/tex] Then,
[tex]\longrightarrow\rm{s(s+1)\,X(s)-3(s+1)-1=\dfrac{2}{s}}[/tex]
[tex]\longrightarrow\rm{s(s+1)\,X(s)-3s-4=\dfrac{2}{s}}[/tex]
[tex]\longrightarrow\rm{s(s+1)\,X(s)=\dfrac{2}{s}+3s+4}[/tex]
[tex]\longrightarrow\rm{X(s)=\dfrac{2}{s^2(s+1)}+\dfrac{3s+4}{s(s+1)}}[/tex]
[tex]\longrightarrow\rm{X(s)=\dfrac{3s^2+4s+2}{s^2(s+1)}\quad\dots(1)}[/tex]
We will factorise this expression by partial fractions.
Assume,
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{As+B}{s^2}+\dfrac{C}{s+1}}[/tex]
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{(As+B)(s+1)+Cs^2}{s^2(s+1)}}[/tex]
[tex]\longrightarrow\rm{3s^2+4s+2=(As+B)(s+1)+Cs^2}[/tex]
[tex]\longrightarrow\rm{3s^2+4s+2=(A+C)s^2+(A+B)s+B}[/tex]
Equating corresponding coefficients,
[tex]\rm{A+C=3}[/tex]
[tex]\rm{A+B=4}[/tex]
[tex]\rm{B=2}[/tex]
Solving each equation we get,
[tex]\rm{A=2}[/tex]
[tex]\rm{B=2}[/tex]
[tex]\rm{C=1}[/tex]
Therefore,
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{2s+2}{s^2}+\dfrac{1}{s+1}}[/tex]
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{2}{s}+\dfrac{2}{s^2}+\dfrac{1}{s+1}}[/tex]
Then (1) becomes,
[tex]\longrightarrow\rm{X(s)=\dfrac{2}{s}+\dfrac{2}{s^2}+\dfrac{1}{s+1}}[/tex]
Now we will inverse Laplace transformation to obtain the solution.
[tex]\longrightarrow\cal{L}^{\rm{-1}}\{\rm{X(s)}\}=\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{2}{s}+\dfrac{2}{s^2}+\dfrac{1}{s+1}}\right\}[/tex]
[tex]\small\text{$\longrightarrow\rm{x(t)}=\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s}}\right\}+\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s^2}}\right\}+\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s+1}}\right\}$}[/tex]
[tex]\small\text{$\longrightarrow\rm{x(t)}=\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s}}\right\}+\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1!}{s^{1+1}}}\right\}+\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s-(-1)}}\right\}$}[/tex]
We have,
[tex]\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s}}\right\}=\rm{1}[/tex]
[tex]\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1!}{s^{1+1}}}\right\}=\rm{t}[/tex]
[tex]\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s-(-1)}}\right\}=\rm{e^{-t}=\dfrac{1}{e^t}}[/tex]
Hence,
[tex]\longrightarrow\rm{\underline{\underline{x(t)=2+2t+\dfrac{1}{e^t}}}}[/tex]
This is the solution to our differential equation.
[tex]\quad[/tex]
Some results of Laplace Transformation:-
[tex]\boxed{\begin{array}{c|c}&\\\rm{x(t)}=\cal{L}^{\rm{-1}}\{\rm{X(s)}\}&\rm{X(s)}=\cal{L}\{\rm{x(t)}\}\\\\=============&==================\\\\\rm{\dfrac{d^nx}{dt^n}}&\rm{s^n\,X(s)}-\displaystyle\sum_{\rm{r=0}}^{\rm{n-1}}\rm{s^{n-r-1}\,\dfrac{d^rx}{dt^r}(t=0)}\\\\----------&--------------\\\\\rm{x'(t)}&\rm{s\,X(s)-x(0)}\\\\----------&--------------\\\\\rm{x''(t)}&\rm{s^2\,X(s)-s\,x(0)-x'(0)}\\\\----------&--------------\\\\\rm{a}&\rm{\dfrac{a}{s}}\\\\----------&--------------\\\\\rm{t^n,\ n}\in\mathbb{N}&\rm{\dfrac{n!}{s^{n+1}}}\\\\----------&--------------\\\\\rm{e^{at}}&\rm{\dfrac{1}{s-a}}\\&\end{array}}[/tex]
What is y =- 3 on a graph?
Answer:
A line.
Step-by-step explanation:
Graphing y = -3 will give you a horizontal line 3 units below the x-axis.
To imagine this, we can create a bunch of points, each with a y coordinate of -3. For example: (-2, -3), (-1, -3), (3, -3), (6,-3). Graphing these will lead to a horizontal line!
which two figures of the following labels correctly refer to the angels shown in the figure?
A.
B.
C.COD
D.
a certain identification code is a list of five symbols: s sub 1s sub 2d sub 1d sub 2d sub 3 each of the first 2 symbols must be one of the 26 letters of the english alphabet, and each of the last 3 symbols must be one of the 10 digits. (repeated letters and digits are allowed.) what is the total number of different identification codes?
676000 is the required total number of different identification codes.
The total number of possible combinations here is computed as:
= Product of the many ways to select each of the characters
= 262*103 = 676000 is the required number of total ways here.
Note that there are 26 possible ways to select each of the first 2 letters and there are 10 ways to select each of the 3 digits here.
Identification Code is a randomly generated set of alpha-numeric symbols supplied by the Bank at the time the Agreement was executed and used as a personal security measure to identify the Customer in communications between the Bank and the Customer via the Customer Service Desk.
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What are the 4 ways to write a solution to an inequality?
How do you find the sum of numbers from 1 to 100 in Java?
The sum of all natural numbers from 1 to 100 is 5050. The total number of natural numbers in this range is 100. So, by applying this value in the formula: S = n/2[2a + (n − 1) × d], we get S=5050.
In Java, finding the sum of two or more numbers is very easy. First, declare and initialize two variables to be added. Another variable to store the sum of numbers. Apply mathematical operator (+) between the declared variable and store the result. So you simply make this: sum=sum+num; for the cycle. For example sum is 0, then you add 5 and it becomes sum=0+5 , then you add 6 and it becomes sum = 5 + 6 and so on.
Thus, the sum of all natural numbers 1 to 10 can be calculated using the formula, S= n/2[2a + (n − 1) × d], where, a is the first term, d is the difference between the two consecutive terms, and n is the total number of natural numbers from 1 to 10. Therefore, the sum of the first ten natural numbers is 55.
public class T35{
public static void main(String[] args) {
int nmb;
for(nmb= 1; nmb<= 100; nmb++){
System.out.println(nmb);
}
}
}
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The difference between a number p and 6 is -14
Equation:
Solution:p=
The value of p in the equation p - 6 = -14 is -8.
What is the value of p in the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, the difference between a number p and 6 is -14.
It should be noted that the equation van be illustrated as:
p - 6 = -14
Collect like terms
p = -14 + 6
p = -8
The value of p is -8.
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15 m
50 m
B
X
A
30 m
Ra
KY
18 m
Assuming that figure A is the original figure,
state the scale factor. Write your answer as
a simplified fraction.
Answer:
5/3
Step-by-step explanation:
The scale factor is the ratio of the side length of the image to the corresponding side in the preimage.
So, the scale factor is [tex]\frac{50}{30}=\frac{5}{3}[/tex].
Help!! My question is : One species of frog can grow up to a maximum length of 12.4 millimeters. What is the maximum length of this frog species in centimeters? My notes are that if you are converting longer to shorter units, multiply if your doing the opposite (shorter to longer) you divide. Lmk if u need the metric units of length (helps w/ solving the problem) and customary units of length
It can reach a length of 12 inches. The smallest frog can grow to be about 4% the size of the goliath.
12.4 millimeters = 1.24 centimeters is the answer.
what are metric length units?To convert units of length in the metric system of measurement
The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter. The prefix “centi-“means one hundredth.
1 centimeter=1 one-hundredth of a meter
kilo- = 1000 1 kilometer (km) = 1000 meters (m)
hecto- = 100 1 hectometer (hm) = 100 m
deca- = 10 1 decameter (dam) = 10 m 1 meter (m) = 1 m
deci- = 0.1 1 decimeter (dm) = 0.1 m
centi- = 0.01 1 centimeter (cm) = 0.01 m
milli- = 0.001 1 millimeter (mm) = 0.001 m
In the metric system, converting length units involves moving the decimal point to the right or left. Listing the units in ascending order will show how many places to move the decimal point and in which direction.
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How do you draw asymptotes?
To draw asymptotes, first determine the equation of the line of the asymptote. Then use the equation to plot points and draw the line. For vertical asymptotes, use the x-intercept and for horizontal asymptotes, use the y-intercept.
To draw asymptotes, first you need to determine the equation of the line of the asymptote. The equation of the asymptote is usually in the form of y = ax + b or x = ay + b. The a and b coefficients allow you to determine the slope and intercept of the line. Once you have the equation, use it to plot points and draw the line. For vertical asymptotes, use the x-intercept and for horizontal asymptotes, use the y-intercept. Then, connect the points with a smooth line. Make sure the line does not intercept the graph at any point as this would not be an asymptote. Once you have drawn the line, check to make sure it is indeed an asymptote by comparing it to the given equation. If it matches, you have successfully created an asymptote!
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How many solutions will the linear equation 2x 5y 7 has?
The linear equation 2x + 5y = 7 has infinitely many solutions.
In this question we need to determine the number of solutions of the linear equation 2x + 5y = 7.
We know that an equation of the form ax + by + c = 0, where a, b and c are real numbers such that a ≠ 0 and b ≠ 0, is called as a linear equation in two variables.
Also as we know a linear equation in two variables has infinitely many solutions. The graph of linear equation in two variables is a straight line. Every point on the straight line represents a solution of the linear equation.
Here we have a linear equation in two variables 2x + 5y = 7.
By rearranging given linear equation we get,
5y = 2x - 7
y = (2x - 7)/5
Here we will get different values of y for different values of x
Therefore, the linear equation has infinitely many solutions.
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Solve the systems of equations below using substitution.
Answer:
(24, 41 )
Step-by-step explanation:
y = 3x - 31 → (1)
y = - 2x + 89 → (2)
substitute y = 3x - 31 into (2)
3x - 31 = - 2x + 89 ( add 2x to both sides )
5x - 31 = 89 ( add 31 to both sides )
5x = 120 ( divide both sides by 5 )
x = 24
substitute x = 24 into either of the 2 equations and solve for y
substituting into (1)
y = 3(24) - 31 = 72 - 31 = 41
solution is (24, 41 )
Answer:
(24,41)
Step-by-step explanation:
Set the 2 equations equal to each other.
3x - 31 = -2x + 89 Add 2x to both sides of the equal sign
3x + 2x -31 = -2x + 2x + 89
5x -31 = 89 Add 31 to both sides of the equal sign
5x -31 + 31 = 89 + 31
5x = 120 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{120}{5}[/tex]
x = 24 This is your x value.
Substitute 24 for x into either of the two original equations to solve for y.
y = 3x -31
y = 3(24) - 31
y = 72 - 31
y = 41 This is your y value.
Check:
y = 3x -31
41 = 3(24) - 31
41 = 72 -31
41 = 41 Checks
y = -2x + 89
41 = -2(24) + 89
41 = -48 + 89
41 = 41 Checks.
Is 12345 divisible by 3?
Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility for three.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
here
add all the numbers,
1 + 2+ 3 + 4+ 5 = 15
and 15/3 = 5
so it is divisible by 3
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we want to determine the probability of obtaining at most 4 successful operations in 10 independent surgical operations where the probability of success is the same for each operation. the appropriate formula to be used is
Using (D) the binomial formula, which is used to determine probability when independent events are known, we will get the probability in the scenario.
What is the binomial formula?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).
The binomial probability is nCx⋅px⋅(1−p)n−x if the likelihood of success on a single trial is p.
When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."
So, in the given situation we will find the probability with help of the binomial formula which is used to calculate the probability when independent events are given.
Therefore, using (D) the binomial formula, which is used to determine probability when independent events are known, we will get the probability in the scenario.
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Complete question:
We want to determine the probability of obtaining at most 4 successful operations in 10 independent surgical operations where the probability of success is the same for each operation. The appropriate formula to be used is
(A) the mean of the binomial distribution.
(B) the hypergeometric formula.
(C) the mean of the hypergeometric distribution.
(D) the binomial formula.
Find the missing length.
c = √√ [?]
C
2
C
11
e
How many different possible outcomes are there when two six sided dice are rolled?
Answer:
36 different ones
Step-by-step explanation:
When two dice are rolled, there are now 36 different and unique ways the dice can come up. This figure is arrived at by multiplying the number of ways the first die can come up (six) by the number of ways the second die can come up (six)
How do you do linear graphs in math?
Linear graph equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
How do one express the standard form of a linear equation?A linear equation has the following standard form: ax + by + c = 0.
Here, variables x and y and constants a, b, and c are used.
Also, a ≠ 0, and b ≠ 0.
For linear equations, the slope-intercept formula is: y=mx+b
Where m stands for the line's slope and b represents the y-intercept.
The three types of linear equations are point-slope, slope-intercept, and standard form.
When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.
Steps of drawing linear graphs are described below:
Step 1: Using the provided linear equation, determine the value of y with respect to x.
Step 2: Arrange these data in a table format.
Step 3: Create a graph using the points from the database.
Step 4: Connect the points to form a straight line.
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NEED HELP!!!
The graph shows a linear relationship between y, the number of bicycles, and x, the number of tires.
Which statement is true?
Select TWO correct answers.
A. Range: {0, 1, 2, 3, 4, 5}
B. Domain: {0, 1, 2, 3, 4, 5}
C.Range: {0, 2, 4, 6, 8, 10}
D. Domain: 0 ≤ x ≤ 5
E. Domain: {0, 2, 4, 6, 8, 10}
F. Range: 0 ≤ y ≤ 10
The Range={0, 1, 2, 3, 4, 5}
Domain={0, 2, 4, 6, 8, 10}
So, options A and E are correct.
What is meant by range and domain?Its arguments are a group of values that can be plugged into a function's domain. This set includes the x values for a function like f(x). Its range refers to the set of digits that the function considers. The function prints these values in the order they are entered after the insertion of an x value.
Another approach to defining the scope and range of functions is through the use of graphs. Since "domain" refers to the set of possible input values, the full set of input values shown on the x-axis is the domain of a graph. On the y-axis, the range's varied output values are visible.
From the graph the points are (0, 0), (1, 2), (2,4), (3,6), (4,8), (5,10)
So, Range={0, 1, 2, 3, 4, 5}
Domain={0, 2, 4, 6, 8, 10}
Therefore, options A and E are correct.
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Is the equation 3x² 7y 13 a linear equation in 2variables?
This is not a two-variable linear equation.
If an equation is written in the form axe + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., When both a and b, in turn, do not equal zero, an equation with two variables is said to be linear. Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation.
Given equation,
[tex]3x^{2} -7y=13[/tex]
In this case, the variable x's degree is 2.
Hence, this is not a two-variable linear equation.
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1.5(x-5)=1 solve for x
Answer: 5.66
Step-by-step explanation:
1.5(x-5)= 1
1.5x - 7.5 = 1
Add 7.5 on both sides
1.5x = 8.5
Divided 1.5 into both sides
x = 5.66
How do you find the maximum of a quadratic function on a calculator?
Positive is the leading coefficient. The parabola is hence downward. The maximum vertex form value will then be a negative four.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = − x² + 2x − 5
Convert the equation into a vertex form. Then we have
y = − x² + 2x − 5
y = − x² + 2x − 1 − 4
y = − (x² − 2x + 1) − 4
y = − (x − 1)² − 4
The leading coefficient is positive. So, the parabola is downward. Then the maximum value of vertex form will be negative 4.
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The complete question is given below.
How do you find the maximum of a quadratic function on a calculator?
y = − x² + 2x − 5?
what is the 95% confidence interval for the difference in the two means (construction site minus undisturbed location)?
The 95% confidence interval for the difference in the two means = (-2.56 , 0.16)
What is Confidence Interval?
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given,
Sample statistics size(n) mean(x) s.d(s)
Construction site 16 x₁ = 5.584 1.812
Undistributed Location 16 x₂ = 6.789 1.945
Standard error = 0.665
Degree of freedom = 30
Critical T-value for 95% confidence interval is 2.0423
The 95% confidence interval for the difference in the two means
(construction site - undistributed location)
= x₁ -x₂ ± (t-value) (standard error)
= 5.584 - 6.786 ± (2.0423) (0.665)
= -1.2020 ± 1.358130
= (-1.2020 - 1.358130 , -1.2020 + 1.358130)
= (-2.56 , 0.156)
= (-2.56 , 0.16)
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Given,
Sample statistics size(n) mean(x) s.d(s)
Construction site 16 x₁ = 5.584 1.812
Undistributed Location 16 x₂ = 6.789 1.945
Standard error = 0.665
Degree of freedom = 30
Critical T-value for 95% confidence interval is 2.0423
The 95% confidence interval for the difference in the two means
(construction site - undistributed location)
= x₁ -x₂ ± (t-value) (standard error)
= 5.584 - 6.786 ± (2.0423) (0.665)
= -1.2020 ± 1.358130
= (-1.2020 - 1.358130 , -1.2020 + 1.358130)
= (-2.56 , 0.156)
= (-2.56 , 0.16)
For the polynomial function f(x) = -2x4 + 8x2 - 8, find all local and global extrema.
A.) No global extrema exist.
B.) The only extrema point is (0, -8).
C.)The local and global extrema are: (-√2.0), (0.-8) and (√2.0).
D.)No local extrema exist.
The derivative for [tex]y=eu(x)[/tex]; [tex]u(x)[/tex] is a function in terms of [tex]x[/tex] is [tex]\frac{dy}{dx}[/tex]=[tex]eu'(x)[/tex]+ [tex]u(x)e[/tex].
Definition of derivative-A derivative is the rate of change of a function with respect to a certain variable . Derivatives are fundamental to the solution of problems in calculus and differential equations.
There are certain rules of differentiation which help us to evaluate the derivatives of some particular functions. :
Power Rule.
Sum and Difference Rule.
Product Rule.
Quotient Rule.
Chain Rule.
Given: [tex]y=eu(x)[/tex]
Explanation:-This equation can be solved using the product rule of derivatives .
According to the product rule derivative of uv will be taken as -
u(v)' + v(u)'
where (') represents derivative of the variable.
Therefore accordingly, [tex]y=eu(x)[/tex]
Differentiating with respect to [tex]x[/tex],
[tex]\frac{dy}{dx} =e(u(x))'+u(x)(e')[/tex]
[tex]\frac{dy}{dx} =eu'(x)+u(x)e[/tex]
So, finally the derivative of the function in terms of x is [tex]\frac{dy}{dx}[/tex] = [tex]eu'(x)+[/tex][tex]u(x)e[/tex]
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what does 12 times a number g mean?
Answer:
The Answer is 12 g because 12* g =12g
Which is the graph of y 5?
The graph of y = 5 is a line parallel to the x-axis at a distance of 5 units from the origin.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
The y = 5 graph is a line that runs parallel to the x-axis at a distance of 5 units from the origin.
Assuming Y-axis as vertical line, X-axis as horizontal line
(see it in attached image)
Graph of y = 5 is the line where y is not changing or y always be 5, only x will change.
Graph of y is the straight line passing through 5 and parallel to X axis
Therefore, a line that is 5 units from the origin and parallel to the x-axis forms the graph of y=5.
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select all the true statements. if vertical angles are congruent, then two lines cut by a transversal are parallel. if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. points on a perpendicular bisector of a line segment are never equidistant from the segment’s endpoints.
Answer:
if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.Step-by-step explanation:
You want to identify the true statements regarding angles at a transversal crossing parallel lines, and perpendicular bisectors.
AnglesThe Corresponding Angles theorem tells you that corresponding angles are congruent where a transversal crosses parallel lines. Since vertical angles are congruent, and angles congruent to the same angle are congruent to each other, this also means that alternate interior angles are congruent.
Perpendicular bisectorA bisector of a segment passes through its midpoint, a point that is equidistant from the end points. When the bisector is perpendicular to the segment, all points on the perpendicular bisector are equidistant from the segment's endpoints.
Is algebra 8th or 9th grade?
Algebra is advised for ninth grade, and pre-Algebra is taught in eighth grade, according to the Common Core standards that California enacted two years ago and is just now starting to apply.
what is algebra ?In algebra, definite or fixed numbers with values like 2, 9, 0.068, etc. are used. Introduction to algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are only a few of the many sub-disciplines of algebra.
here ,
The option to take it in the eighth grade may be given to students who demonstrated extraordinary potential in the subject.
Algebra is often taught in the eighth grade in many schools today, while certain students who meet a certain threshold can finish the subject in the lower grades.
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