The vectors [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]] are linearly independent.
To determine if the vectors are linearly independent, we can use the determinant of the matrix formed by the vectors. If the determinant is not equal to 0, then the vectors are linearly independent.
The matrix formed by the vectors is:
\begin{bmatrix}
4 & 9 & 6\\
0 & 3 & 6\\
0 & -6 & -18
\end{bmatrix}
The determinant of this matrix is:
\begin{vmatrix}
4 & 9 & 6\\
0 & 3 & 6\\
0 & -6 & -18
\end{vmatrix} = 4\begin{vmatrix}
3 & 6\\
-6 & -18
\end{vmatrix} - 9\begin{vmatrix}
0 & 6\\
0 & -18
\end{vmatrix} + 6\begin{vmatrix}
0 & 3\\
0 & -6
\end{vmatrix} = 4(-54-(-36)) - 9(0-0) + 6(0-0) = 4(-18) = -72
Since the determinant is not equal to 0, the vectors are linearly independent. Therefore, the vectors [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]] are linearly independent.
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Question 16(Multiple Choice Worth 3 points)
(01.04 MC)
A forensics expert analyzes the ink of handwriting on a piece of paper. The ink has yellow, red, and blue pigments in it. The size of ink particles is measured in
nanometers (nm). Here is a chart of the size of each molecule: image below
If the forensics expert performs chromatography on the ink sample, in what order from the bottom to the top would the ink pigments appear on the chromatography
paper?
O Red, blue, yellow
O Blue, red, yellow
O Yellow, blue, red
O They will all be on the same line.
The order of the colors is Red, blue, yellow
What is chromatography?
Chromatography is a laboratory technique used to separate and analyze mixtures of different compounds based on their physical and chemical properties. It involves passing a mixture through a stationary phase, which may be a solid or a liquid, and a mobile phase, which may be a liquid or a gas.
As the mixture passes through the stationary phase, the different compounds in the mixture interact with the stationary phase to varying degrees, causing them to separate. The mobile phase carries the separated components through the stationary phase, and the separated components are detected and analyzed using a detector, such as a spectrophotometer.
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Solve :-7x-6y=4
When x=-3y+8
Mr. Lucy has 10 1/4 feet of rope. If he needs 1/8 OF the rope
for a project, how many feet of rope will he use?
The amount of rope used by Mr.Lucy is given by equation A = 1.28125 feet of rope
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the amount of rope used be represented as A
Now , the equation will be
The total amount of feet of rope Mr.Lucy has = 10 1/4 feet
So , total amount of feet of rope Mr.Lucy has = 10.25 feet
Now , the amount of rope used = ( 1/8 ) of the total amount
On simplifying , we get
The amount of rope used A = ( 1/8 ) x 10.25 feet
The amount of rope used A = ( 41 / 32 ) feet
The amount of rope used A = 1 9/32 feet
The amount of rope used A = 1.28125 feet of rope
Hence , the amount of rope used is A = 1.28125 feet of rope
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Write a polynomial function, P(x), 34. Quadratic Function Zero: 3-4i Additional Zero:
The polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).
A polynomial function, P(x), is a function that can be written in the form P(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a non-negative integer and an, an-1, ..., a1, a0 are real numbers. A quadratic function is a polynomial function of degree 2, which means it can be written in the form P(x) = ax2 + bx + c.
If a polynomial function has a zero of 3-4i, then it must also have a zero of 3+4i, since complex zeros always come in conjugate pairs. This means that the polynomial function must have factors of (x - (3-4i)) and (x - (3+4i)). Multiplying these two factors together gives us (x - 3 + 4i)(x - 3 - 4i) = x2 - 6x + 25.
If the polynomial function also has an additional zero, then it must have a factor of (x - additional zero). Multiplying this factor with the previous one gives us P(x) = (x2 - 6x + 25)(x - additional zero).
So, the polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).
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5. Martin is a telemarketer and receives $75 every day he works. He make a baseline of 35 calls (c) every hour. For every call he makes over 35 in one hour, Martin receives a bonus of $5.50 per call. Martin works for 4 hours every day and makes the same number of calls every hour. Write a function to express the total amount of money Martin will make as a function of the number of calls he makes. If Martin makes a total of 45 calls every hour, how much money will Martin make for the day?
Answer: The function to express the total amount of money Martin will make as a function of the number of calls he makes is:
Total Money = (Number of hours worked x Base pay per hour) + (Bonus pay per hour x Number of bonus calls)
Where:
Number of hours worked = 4
Base pay per hour = $75 / 4 = $18.75 (since he works for 4 hours every day and receives $75)
Bonus pay per hour = ($5.50 x (Number of bonus calls)) / 4 (since he works for 4 hours every day and receives a bonus of $5.50 per call over 35 in one hour, which is equivalent to $5.50 / 4 per call)
Number of bonus calls = (Total calls - (Number of hours worked x Baseline calls per hour))
Using this formula, we can calculate how much money Martin will make for the day if he makes a total of 45 calls every hour:
Number of bonus calls = (45 - (4 x 35)) = 5
Bonus pay per hour = ($5.50 x 5) / 4 = $6.875
Total Money = (4 x $18.75) + (4 x $6.875) = $75 + $27.50 = $102.50
Therefore, if Martin makes a total of 45 calls every hour, he will make $102.50 for the day.
Step-by-step explanation:
Find all the zeros. Write the answer in exact form. c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24
The exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.
To find all the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24, we need to find the values of x that make c(x)=0. One way to do this is by using the Rational Root Theorem, which states that if a polynomial has rational zeros, then they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The factors of the constant term, 24, are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of the leading coefficient, 3, are ±1 and ±3. Therefore, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.
Using synthetic division, we can test these possible zeros to see if they are actually zeros of the polynomial. After testing, we find that the zeros are -4, -3/2, 2, and 1.
So, the exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.
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4/5x + 3 =7
What is x?
Answer: 5
Step-by-step explanation:
To solve 4/5x + 3 = 7 for x, we must isolate x on one side of the problem.
To begin, remove 3 from both sides to get:
4/5x = 4
Hence, we can multiply both sides by 5/4 to isolate x:
x = 5
As a result, the answer to the equation 4/5x + 3 = 7 is x = 5.
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The length of an arc RV of circle M with a radius of 6 units is 3pi/2 units. What is the approximate measure of angle RMV?
the options are
A- 15
B- 45
C-66
D-231
Answer:
The formula for the length of an arc of a circle is given by:
length of arc = (central angle/360) x 2πr
where r is the radius of the circle and the central angle is measured in degrees.
In this problem, we know the length of arc RV is 3π/2 units and the radius of circle M is 6 units. Therefore, we can solve for the central angle using the formula above:
3π/2 = (central angle/360) x 2π(6)
3π/2 = (central angle/180) x π x 6
3/2 = (central angle/180) x 6
central angle = (3/2) x (180/6) = 45 degrees
So the approximate measure of angle RMV is 45 degrees, which corresponds to option B.
A book sold 38,100 copies in its first month of release. Suppose this represents 7.1% of the number of copies sold to date. How many copies have been sold to date?
The book sold 38,100 copies in its first month of release. then approximately 537,324 copies have been sold to date.
What is the percentage?
A percentage is a ratio, fraction, or portion of a whole which is represented as 100.
Let "x" be the total number of copies sold to date.
According to the problem, 38,100 is 7.1% of x, which can be written as:
38,100 = 0.071x
To find x, we can solve for it by dividing both sides of the equation by 0.071:
x = 38,100 / 0.071
x = 537,323.94 (rounded to the nearest whole number)
Therefore, approximately 537,324 copies have been sold to date.
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. The table shows the number of people, n, who went to see musical
The average rate of change for the week is calculated by subtracting the first day's attendance (1,534) from the last day's attendance (2,394) and then dividing by the number of days (7).
What is Number?Number is an abstract concept used to describe a quantity or amount of something. It is used to measure, count, and label objects, people, places, and other things. Numbers can be used to describe size, shape, location, and many other concepts. They are also used to represent data, money, and other mathematical operations. Numbers are the cornerstone of mathematics, and they are used in a variety of ways in everyday life.
This yields an average rate of change of +77.71 people per day.
This average rate of change is only a good measure for how the number of people changed throughout the week if the number of people changed in a consistent manner. If the attendance was relatively stable from day to day, then the average rate of change would accurately reflect the number of people who attended. However, if the attendance changed drastically from day to day, the average rate of change would not accurately reflect the attendance for the entire week.
Complete questions as follows-
The table shows the number of people, n, who went to see musical , on the duh day of April. What is the average rate of 'change for the number of people from day to day 7? 1,534 2,324 2,418 b. Is the average rate of change a good measure for how the number of people changed throughout the week? Explain your reasoning; ''. ` 2,281 2,350 2,394 1,720 weight (02) 369 Algebra 1".
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You are asked to estimate the average height of black spruce trees in a 1,000 ha plot. How large must your sample be to have 99% confidence that your estimate is within 0.5 m? A study conducted last year, in a nearby location determined that the standard deviation of tree heights is 1.10 m.
To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, you need a sample size of at least 19. This is based on the standard deviation of tree heights in a nearby location of 1.10 m as determined in a study conducted last year.
To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, we can use the formula for sample size calculation:
n = (z² × σ²) / E²
Where:
n = sample size
z = z-score for the desired confidence level (99% confidence level corresponds to a z-score of 2.576)
σ = standard deviation (1.10 m)
E = margin of error (0.5 m)
Plugging in the values into the formula, we get:
n = (2.576² × 1.10²) / 0.5²n = 18.15.
Therefore, the sample size must be at least 19 black spruce trees to have 99% confidence that the estimate is within 0.5 m.
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Find the lateral area and total surface area of the rectangular prism. 12in, 7in, 5in
Answer:
The lateral area of the prism is 190 square inches and the total surface area is 358 square inches.
Step-by-step explanation:
To find the lateral area and total surface area of a rectangular prism, we need to use the following formulas:
Lateral Area = perimeter of the base x height
Total Surface Area = 2 x base area + lateral area
Where the base area is simply the product of the length and width of the rectangular prism.
Let's apply these formulas to the rectangular prism with dimensions 12in x 7in x 5in:
Lateral Area:
To find the perimeter of the base, we add up the lengths of all four sides of the rectangle:
Perimeter of the base = 2(length + width) = 2(12in + 7in) = 2(19in) = 38in
Now, we multiply the perimeter of the base by the height of the prism:
Lateral Area = 38in x 5in = 190in^2
Therefore, the lateral area of the rectangular prism is 190 square inches.
Total Surface Area:
To find the base area, we simply multiply the length and width of the rectangular prism:
Base Area = length x width = 12in x 7in = 84in^2
Now, we can use the formula for total surface area:
Total Surface Area = 2 x base area + lateral area
Total Surface Area = 2(84in^2) + 190in^2
Total Surface Area = 168in^2 + 190in^2
Total Surface Area = 358in^2
Therefore, the total surface area of the rectangular prism is 358 square inches.
So the lateral area of the prism is 190 square inches and the total surface area is 358 square inches.
A city will soon be voting on a bond issue which will provide the necessary funds for a new middle school. The school board wants to know how likely it is that the bond issue will pass. They randomly sample three groups of 200 people and ask each person whether they are for or against the bond issue. The results are recorded in the table below.
For Against
Sample #1 221 79
Sample #2 114 186
Sample #3 210 90
Based on the collected data, do you think the bond issue will pass or fail? How confident are you? Explain your reasoning using complete sentences.
Using the mean of the samples, approximately how many of the 16,000 voters would you expect to vote against the bond issue?
Approximately 11,800 of the 16,000 voters would be expected to vote against the bond issue.
What is data in math?Data in math is information that can be quantified and organized. It can include numeric values, words, dates, and other types of data. Data is used to analyze relationships and make predictions. Data can be used to create charts, graphs, and tables that display trends, patterns, and relationships. Data can also be used to inform decisions and help solve problems.
Based on the collected data, it is likely that the bond issue will pass. Out of the three samples, only one showed a majority of people against the bond issue, and the other two samples showed a majority of people in favor. This indicates that there is a strong likelihood of the bond issue passing. I am confident in this assessment because the samples are representative of the same population, and there is a clear majority of people in favor of the bond issue.
Using the mean of the samples, approximately 11,800 of the 16,000 voters would be expected to vote against the bond issue.
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Which expression uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16)?
A. (-3/4)x(-16)x1/5
B. (-16)x1/5x(-3/4)
C. (-3/4)x5/1x(-16)
D. (4/3)x(-16)x1/5
The expression which uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16) is (-3/4)x(-16)x1/5) which is therefore denoted as option A.
What is Commutative property?
This states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
In the expression (-3/4)x1/5x(-16) , there is the need to arrange them so as to make it easier for them to be reduced to their lowest factor which is why -16 was put close to the (-3/4).
(-3/4)x(-16)x1/5 = 12 × 1/5 = 12/5
This is therefore the reason why option A was chosen as the correct choice.
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please answer quick i will give u free branliest.
The expression when simplified is (d)
How to determine the expressionFrom the question, we have the following representation that can be used in our computation:
Black triangle = -xWhite triangle = xBlack square = -1White square = 1Using the above as a guide, we have the following:
The given expression is
3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square
This gives
-3x + 2x - 2 + 1
Evaluate the like terms
-x - 1
This means
1 Black triangle and 1 Black square
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HELPPPPPP DUE TONIGHTTT
The scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 23 students.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the money spent on entertainment for a student who works 10 hours.
Note that you can use the graphing tools to help you approximate the line.
Answer:
Step-by-step explanation:
A is y=x+4
b is y=14
Part C What does the mapping found in part B tell you about the relationship between the two circles? Explain your reasoning.
In conclusion, the mapping in part B informs us that the two circles are equation congruent, i.e., that their size and shape are the same and that the mapping preserves all of their geometrical characteristics.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The mapping in part B informs us that the points on the two circles correspond exactly to one another. In other words, there is exactly one point on the bigger circle for every point on the smaller circle, and vice versa.
In conclusion, the mapping in part B informs us that the two circles are congruent, i.e., that their size and shape are the same, and that the mapping preserves all of their geometrical characteristics.
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6a +5a + 1 =12
What is a?
Answer:
a = 1
Step-by-step explanation:
6a + 5a + 1 = 12
Subtract one to both side leaving a by itself.
6a + 5a = 12 - 1
Now simply by add or subtracting, multiply or dividing.
11a = 11
Divide 11 to both side leaving a = ?
a = 1
Answer:
a= 1
Step-by-step explanation:
6a + 5a + 1 = 12
(-1) + 6a + 5a +1 = 12 -1
6a + 5a = 11
11a = 11
11a/11 = 11/11
a= 1
A deli owner has room for 65 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total of 400 oz of cheese. If 5-oz containers sell for $7 and 10-oz containers sell for $13, how many of each should he sell to maximize his revenue? What is his maximum revenue?
He should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
What is cοntainer?A cοntainer is a standard unit οf sοftware that packages up cοde and all its dependencies sο the applicatiοn runs quickly and reliably frοm οne cοmputing envirοnment tο anοther. Cοntainers are a sοlutiοn tο the prοblem οf hοw tο get sοftware tο run reliably when mοved frοm οne cοmputing envirοnment tο anοther. This cοuld be frοm a develοper’s laptοp tο a test envirοnment, frοm a staging envirοnment intο prοductiοn, and perhaps frοm a physical machine in a data center tο a virtual machine in a private οr public clοud.
Corner point (x, y) Value of 8x+14y
0(0,0) 0
A(65,0) 520
B(50, 15) 610
C(0,40) 560
So, the maximum value is 610
Therefore, the maximum point is B(50, 15)
∴ x = 50, y = 15
So, the maximum value is
Therefore, the maximum point is
Hence, he should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
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What would be the answer to this?
Benjamin's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=8x+57 where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y = 98?
When the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.
What is the linear equation in two variables?
A linear equation in two variables is an equation of the form:
ax + by = c
where x and y are variables, a, b, and c are constants, and a and b are not both zero. The graph of a linear equation in two variables is a straight line, and any point on the line satisfies the equation.
The given equation is:
y = 8x + 57
where y is the quiz score and x is the hours spent on homework.
To find the meaning of the x-value when y = 98, we can substitute y = 98 into the equation and solve for x:
98 = 8x + 57
Subtracting 57 from both sides, we get:
41 = 8x
Dividing both sides by 8, we get:
x = 5.125
when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours. This suggests that students who spend around 5 hours and 7.5 minutes on homework per week can expect to score around 98 on their weekly quiz.
Therefore, when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.
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Please help, Progress reports for the semester coming out soon!!
(Look at screenshot) <33
Answer:
The graph will be parallel with x-axis and intersects y at -8
Step-by-step explanation:
For the function y = -8, whatever the x is, y is always -8.
x y
-10 8
-9 8
-3 8
-2 8
2 8
The graph will be parallel with x-axis and intersects y at -8
1. the variance for the following distribution of ungrouped
data to its right is:
a. 0.79 b. 2.01 c. 0.89 d.2.45
Dato (x) Frecuensia
3.2 3
1.3 4
2.4 2 2. the variance for the following distribution of ungrouped
data to its right is:
A.8.00
b. 65.60
c. 7.81
d. 62.57
edad (x) frecuencia (f) xf x^2 f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628
The correct answer is c. 7.81.
To find the variance for the distribution of ungrouped data, we need to use the formula:
Variance = (Σ(x^2)f - (Σxf)^2 / n) / n
Where x is the data value, f is the frequency of the data value, and n is the total number of data values.
For the first question:
1. The variance for the following distribution of ungrouped data to its right is:
Dato (x) Frecuencia (f) xf x^2f
3.2 3 9.6 30.72
1.3 4 5.2 6.76
2.4 2 4.8 11.52
Total 9 19.6 49
Variance = (49 - (19.6)^2 / 9) / 9
Variance = (49 - 42.46) / 9
Variance = 0.73
Therefore, the correct answer is a. 0.79.
For the second question:
2. The variance for the following distribution of ungrouped data to its right is:
Edad (x) Frecuencia (f) xf x^2f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628
Variance = (2628 - (328)^2 / 42) / 42
Variance = (2628 - 2570.29) / 42
Variance = 1.38
Therefore, the correct answer is c. 7.81.
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The length of a radius is three-fourths the height of a cone. The surface area is 3750
square units.
What are the height and the radius of the cone?
The height of the cone is approximately 28.867 units and the radius is approximately 21.65 units.
How to Find the Height and Radius of a Cone?Let's denote the height of the cone as "h" and the radius as "r".
From the problem statement, we know that:
r = (3/4)h ...(1) (given)
The surface area of the cone is given as 3750 square units. The formula for the surface area of a cone is:
Surface Area of Cone = πr(r + l),
where "l" is the slant height of the cone. Since the slant height is not given in the problem, we need to express "l" in terms of "r" and "h" using the Pythagorean theorem:
l² = r² + h²
l² = (3/4)² h² + h²
l² = (9/16)h² + h²
l² = (25/16)h²
l = (5/4)h
Substituting this expression for "l" and the expression for "r" from equation (1) into the surface area formula, we get:
3750 = πr(r + l)
3750 = π[(3/4)h] [(3/4)h + (5/4)h]
3750 = π (9/16 + 15/16) h²
3750 = π (24/16) h²
3750 = (3/2) π h²
h² = (2500/3π)
h ≈ 28.867
Substituting this value of "h" into equation (1), we get:
r = (3/4)h
r ≈ 21.65
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Answer: Radius 37.5 & height 50
Step-by-step explanation: correct in edmuntum/plato
Please help I'll mark brainliest !
Answer:
x = -3 to x = 2
Step-by-step explanation:
The function is decreasing where the slope is negative, seen when the y-values decrease as the x-values increase. Your answer is correct.
Answer:
X is - 3 to x is 2
Step-by-step explanation:
Look at the x axis, the point where the curve slopes down is the decreasing point
Where x is - 3 is a peak point, it begins to slope from there and rises when x is 3
Problem C:
A farmer has potatoes planted in a large garden.
The field is 14 yards long and 10-yards wide.
What is the area of the farmer's potato garden?
-
Answer:
140 square yards
Step-by-step explanation:
To calculate the area of the farmer's potato garden, we need to multiply the length by the width of the garden.
Area of the potato garden = Length x Width
Given that the length of the potato garden is 14 yards and the width is 10 yards, we can substitute the values into the formula and get:
Area of the potato garden = 14 yards x 10 yards
Area of the potato garden = 140 square yards
Therefore, the area of the farmer's potato garden is 140 square yards.
Answer:140[tex]yards^{2}[/tex]
Step-by-step explanation: to find the area you multiply two different lengths of the rectangle together to get 140
Please help find X on this
Step-by-step explanation:
11²+4²=X²121+16=X²137=X²X=[tex] x = \sqrt{137 \\ } [/tex]Problem \# 6: Let R^4 have the Euclidean inner product. Find a unit vector with a positive first component that is orthogonal to all three of the following vectors. u = (1,-1, 7, 0) ; v=(8,1,0,1) ; w=(1,0,6,1)
Problem \#6: Enter your answer symbolically, as in these Enter the four components of your vector, separated with commas.
To find a unit vector with a positive first component that is orthogonal to all three of the given vectors, we need to find a vector x = (x1, x2, x3, x4) that satisfies the following equations:
= 0
= 0
= 0
This means that:
x1 - x2 + 7x3 = 0
8x1 + x2 + x4 = 0
x1 + 6x3 + x4 = 0
We can solve this system of equations to find x. One possible solution is x = (1, -1, 0, 1). However, this is not a unit vector, so we need to divide each component by the length of the vector to get a unit vector:
x = (1, -1, 0, 1) / ||(1, -1, 0, 1)|| = (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3))
So, the unit vector with a positive first component that is orthogonal to all three of the given vectors is (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3)).
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Find the two values that x can have if 5x ^ 2 + 41 = 86
Answer:
x= 3 or x = -3
Step-by-step explanation:
We can see here that the two values that x can have if 5x² + 41 = 86 is -3 and +3.
How we arrived at the solution?To find the values of x that satisfy the equation 5x² + 41 = 86, we can start by isolating the term with the variable on one side of the equation. Here's the step-by-step solution:
Subtract 41 from both sides of the equation:
5x² + 41 - 41 = 86 - 41
5x² = 45
Divide both sides of the equation by 5:
(5x²) / 5 = 45 / 5
x² = 9
Take the square root of both sides of the equation:
√(x²) = √9
x = ±3
Therefore, the equation 5x² + 41 = 86 has two solutions: x = 3 and x = -3.
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Find the total surface area of a large round bowl (hollow hemisphere) with outer radius of 12 cm and thickness of 1 cm. 1cm 12cm
The total surface area of the hollow hemisphere is 1736.4 cm²
The total surface area of a large round bowl (hollow hemisphere) can be calculated by finding the surface area of the outer hemisphere and the surface area of the inner hemisphere and area of the ring and adding them together.
The formula for the surface area of a hemisphere is 2πr^2, where r is the radius of the hemisphere.
The outer radius of the bowl is 12 cm, so the surface area of the outer hemisphere is:
Surface area of outer hemisphere = 2π(12)^2 = 2π(144) = 288π
The inner radius of the bowl is the outer radius minus the thickness, which is 12 - 1 = 11 cm. So the surface area of the inner hemisphere is:
Surface area of inner hemisphere = 2π(11)^2 = 2π(121) = 242π
area of the concentric circle joining the outer surface and inner surface is π(12²-11²)= 23π
The total surface area of the bowl is the sum of the surface area of the outer hemisphere and the surface area of the inner hemisphere:
Total surface area = 288π + 242π + 23π = 553π
So the total surface area of the bowl is 530π cm^2.
then we can use the approximation π ≈ 3.14 to find the total surface area:
Total surface area ≈ 553*(3.14) ≈ 1736.4 cm^2
So the total surface area of the bowl is approximately 1736.4 cm^2.
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