The correct option is B an algorithm. If the wrong password is put in more than five times, Owen's computer will lock for an hour. To prevent this, he is building a programme. An illustration of a "algorithm" is this collection of instructions.
Explain about the algorithm?An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms operate as a detailed sequence of instructions that carry out prescribed operations sequentially.
All aspects of information technology leverage algorithms extensively. A simple technique that resolves a recurring issue is typically referred to as an algorithm in computer science and math. Algorithms are essential to automated systems because they serve as specifications for processing data.An initial input and a list of instructions are used by algorithms. The input, which can be described as either words or numbers, is the first batch of information required to make judgements. The input data is subject to a number of calculations or instructions.Know more about algorithm
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what is the quadratic formula multiplied by pie divided by X?
The quadratic formula multiplied by π divided by x is: π(-b ± √(b² - 4ac)) / (2ax).
What is the Quadratic formula?
The quadratic formula is used to solve quadratic equations, and is given by: x = (-b ± √(b² - 4ac)) / 2a.
Pi otherwise denoted by the symbol π in real terms is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, although its decimal representation goes on infinitely without repeating.
Since the rational objective of every mathematical expression or problem is to simplify, we will leave Pi in it's symbolic form - π.
Thus, multiplying quadratic formula by π and dividing by x, we get:
π(-b ± √(b² - 4ac)) / (2ax)
Therefore, the quadratic formula multiplied by π divided by x is:
π(-b ± √(b² - 4ac)) / (2ax).
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Answer: π(-b ± √(b² - 4ac)) / (2ax)
Step-by-step explanation:
take the standard quadratic formula and plug in pi and x and you get you answer hope this helps
Write the gradient and y-intercept of each line
a. Y=10x+20
b. Y=10-20x
c. Y=-2. 5+0. 5x
The required gradient and y-intercept for the given lines is given by ,
1. gradient = 10 and y-intercept = 20
2. gradient = -20 and y-intercept = 10
3. gradient = 0.5 and y-intercept = 2.5
Equation of a line in slope-intercept form = y = mx + c.
where 'm' is the slope of the line
And 'c' is the y-intercept.
For the line Y = 10x + 20
Compare with standard form we get,
Slope of the line is 10 .
And the y-intercept is 20.
This implies,
gradient is 10 and the y-intercept is (0, 20).
For the line Y=10-20x
Compare with standard form we get,
Slope of the line is -20
And the y-intercept is 10.
This implies,
the gradient = -20
And the y-intercept = (0, 10).
For the line Y=-2. 5+0. 5x
Compare with standard form we get,
Slope of the line is 0.5
And the y-intercept is -2.5
This implies,
the gradient = 0.5
And the y-intercept = (0, -2.5)
Therefore, the gradient and the y-intercept for each line is equal to,
Y=10x+20 , gradient = 10 and y-intercept = 20
Y=10 -20x , gradient = -20 and y-intercept = 10
Y=-2. 5+0. 5x , gradient = 0.5 and y-intercept = 2.5
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Find a formula for the exponential function passing through the points (-2,768) and (2,3)
The formula for the exponential function passing through the points (-2,768) and (2, 3) is:
[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]
We have,
To find a formula for the exponential function passing through the points (-2, 768) and (2, 3), we can use the general form of an exponential function: y = a x [tex]b^x[/tex], where "a" is the initial value or y-intercept, and "b" is the base of the exponential function.
Let's start with the first point (-2, 768).
Plugging in the values, we have:
768 = a x [tex]b^{-2}[/tex]
Next, let's consider the second point (2, 3).
Plugging in the values, we have:
3 = a x b²
Now we have a system of equations:
768 = a x [tex]b^{-2}[/tex]
3 = a x b²
To solve this system, we can divide the second equation by the first equation:
3/768 = (a x b²) / (a x [tex]b^{-2}[/tex])
Simplifying further:
3/768 = [tex]b^4[/tex]
Taking the fourth root of both sides:
[tex](b^4)^{1/4} = (3/768)^{1/4}\\b = (3/768)^{1/4}[/tex]
Now we can substitute the value of b back into either of the original equations to solve for a.
Let's use the first equation:
[tex]768 = a \times b^{-2}[/tex]
Substituting [tex]b = (3/768)^{1/4}:[/tex]
[tex]768 = a \times ((3/768)^{1/4})^{-2}[/tex]
Simplifying:
[tex]768 = a \times (3/768)^{-1/2}[/tex]
Now, we can simplify the right-hand side:
[tex]768 = a \tmes (768/3)^{1/2}[/tex]
Simplifying further:
[tex]768 = a \times (256)^{1/2}[/tex]
Taking the square root of 256:
768 = a x 16
Solving for a:
a = 768 / 16 = 48
Therefore,
The formula for the exponential function passing through the points (-2,768) and (2, 3) is:
[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]
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What is the constant of proportionality between
�
yy and
�
xx in the graph?
The response to the given question would be that Hence, 2 is the proportionality constant between y and x.
what is proportionality?Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.
We must calculate the ratio of the change in y to the change in x in order to discover the constant of proportionality between two variables, x and y. The slope of the line that depicts the connection between x and y is another name for this.
The slope of the line, which is the change in y divided by the change in x, is therefore equal to the constant of proportionality between y and x. As we can see from the graph, y grows by 2 units for every unit rise in x. Hence, the line's slope is 2/1, or only 2.
Hence, 2 is the proportionality constant between y and x.
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The Pressure in the bulb of a constant volume gas thermometer 82cm at 0degree 105.2 cm at loo°c and 68.4cm. When the bulb is surrounded by solid Carbon(iv ) oxide calculate the temperature of the Carbon (iv )
Oxide
The temperature of the Carbon (IV) Oxide surrounding the thermometer is approximately -46.83 °C (226.32 K).
What is the temperature of the Carbon (IV) Oxide?We can use Charles's Law and Boyle's Law to relate the pressure of the gas in the thermometer to the temperature of the surrounding Carbon (IV) Oxide. Since the volume of the gas in the thermometer is constant, we can assume that the pressure is directly proportional to the absolute temperature.
Therefore, we can use the following equation:
P₁/T₁ = P₂/T₂
where;
P₁ and T₁ are the pressure and temperature at the first measurement (0 °C), and P₂ and T₂ are the pressure and temperature at the second measurement (100 °C).Solving for T₂, we get:
T₂ = (P₂/P₁) * T₁
T₂ = (105.2/82) * 273.15 K
T₂ = 348.85 K
Similarly, we can use the pressure at the third measurement (68.4 cm) and the temperature we just calculated (348.85 K) to find the temperature of the surrounding Carbon (IV) Oxide using the same equation:
T₃ = (P₃/P₁) * T₁
T₃ = (68.4/82) * 273.15 K
T₃ = 226.32 K
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Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
Answer:
8.50667 or approximately 8.51 feet per second
Step-by-step explanation:
The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.
Determine whether each sequence is arithmetic, geometric, or neither.
(4, -20, 100, 500, ...}
{1, 2, 3, 4, ...}
{-18, 11, 4, 3, ...}
{-3, -27, 243, -2187, ...}
{1, 8, 27, 64, ...}
{-9, -33, -57, -81, ...}
Step-by-step explanation:
1) geometric
2) arithmetic
3) neither
4) geometric
5) neither
6) arithmetic
you can this by usin their formulas or
you see if it has common difference which is for arithmetic sequence or you find the common ratio which is geometric sequence.
What is the value of x?
x+42°
x = [
O
X
X-21°
Answer:
x=63
Step-by-step explanation:
------------------
(B) 5 (C) 6 (D) 9 What is the solution set for the absolute value equation |2x-4|=20?
The solution set for the absolute value equation |2x-4|=20 is {-14, 14}.
Absolute Value EquationAn absolute value equation is one that contains an absolute value expression, such as ||x| - 1| = 2.
These types of equations are solved by breaking them down into two separate equations and solving each one separately:
one with the original absolute value expression and a positive value for the other side, and the other with the negated absolute value expression and a negative value for the other side.
The steps to solving an absolute value equation are as follows:
1. Write the equation in the form |expression| = value, where expression is the absolute value expression and value is the constant on the right-hand side.
2. Separate the equation into two equations: expression = value and expression = -value.
3. Solve each equation for the variable.
4. Check the solution(s) to ensure that they satisfy the original equation.
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For the given polynomial P(x) and the gven c, use the remain P(x)=x^(3)+5x^(2)-6x+6;3
The given polynomial is P(x) = x^3 + 5x^2 - 6x + 6. The given c is 3. To use the Remainder Theorem, we must divide P(x) by (x - c). The result of this division will be a quotient and a remainder. The remainder is the value of the polynomial when x = c, so in this case when x = 3, the remainder is 45.
This is because when x = 3, P(x) = 45. Therefore, according to the Remainder Theorem, the remainder when we divide P(x) by (x - 3) is 45. This means that when we divide P(x) by (x - 3), the remainder is 45. Thus, the Remainder Theorem can be used to determine the remainder when we divide a polynomial P(x) by (x - c), where c is some given constant.
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What is the solution of the inequality: b+1>-8
Answer: The answer would be b<-9 for the nonsimplified version though.
Step-by-step explanation:
b+1>-8
first, -1 from each side.
then you will have -9>b
But you are going to divide by a negative number, so you are going to flip the inequality.
( b>-9 )
I remember learning this is like 7th grade haha. Let me know if you have any questions
Arrange these in descending order
0. 68
0. 5
0. 345
0. 99
Solve the following rational equation: If no solution exists then state that. Show complete work. y/y−2y+ 4/y-3 = 4/ y2−5y+6
The answer: no real solutions to this equation
To solve the equation, we need to find a common denominator for all of the fractions on the left side of the equation. The common denominator will be (y-2)(y-3), so we will multiply each fraction by the appropriate factor to get the common denominator.
[tex]y/y -2y+ 4/y-3 = 4/ y2-5y+6[/tex]
[tex]y(y-3)/(y-2)(y-3) - 2y(y-2)/(y-2)(y-3) + 4(y-2)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]
Now we can combine the fractions on the left side of the equation:
[tex](y2-3y-2y2+4y+4y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]
Simplifying the numerator on the left side gives us:
[tex](-y2+5y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]
Now we can cross-multiply and simplify:
[tex](-y2+5y-8) = 4[/tex]
[tex]-y2+5y-12 = 0[/tex]
To solve this equation, we can use the quadratic formula:
[tex]y=\left(-5\pm \sqrt{52-4\left(-1\right)\left(-12\right)}\right)[/tex]
[tex]y=\left(-5\pm \sqrt{25-48}\right)[/tex]
[tex]y=\left(-5\pm \sqrt{-23}\right)[/tex]
Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is no solution.
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▪ (n³ - 11n² +21n-24)÷(n-9)
The result obtained from the long division of the polynomial is n² + 2n - 1 + 3/(n - 9).
What is the result of the long division?
The quotient of the polynomial is obtained by applying long division method as shown below.
n² + 2n - 1
________________________
n - 9 √ (n³ - 11n² + 21n - 24)
(n³ - 9n²)
____________
-2n² + 21n
-2n² + 18n
__________
3n - 24
3n - 27
______
3
Therefore, the quotient is n² + 2n - 1 and the remainder is 3.
n³ - 11n² + 21n - 24 = (n - 9)(n² + 2n - 1) + 3.
So when we divide the polynomial using long division method we would obtain the following result.
(n³ - 11n² + 21n - 24) ÷ (n - 9) = n² + 2n - 1 + 3/(n - 9)
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Find the quotient of this long division; (n³ - 11n² +21n-24)÷(n-9)
Line f has a slope of -2 and line g has a slope of -8/4. What relationship do the lines have, based on their slopes?
A.) The lines intersect.
B.)The lines intersect to form right angles.
C.)The lines are parallel.
D.)No relationship can be determined.
The lines are parallel , based on their. So the C option is correct.
What is slope formula?
The formula to find the slope between 2 coordinates of a line is given by;
m = (y₂ - y₁)/(x₂ - x₁)
Line f has a slope of -2 and line g has a slope of -8/4. To determine the relationship between the lines based on their slopes, we can compare their slopes.
If two lines have the same slope, they are parallel. If two lines have slopes that are negative reciprocals of each other, they are perpendicular (and intersect to form right angles). Otherwise, the lines are neither parallel nor perpendicular and will intersect at some point.
The slope of line g can be simplified to -2, which is the same as the slope of line f. Therefore, the lines f and g have the same slope and are parallel (option C).
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PLEASE HELP ME IM TIMED
Answer:
12
Step-by-step explanation:
g(-4)=2(-4)^2+4(-4)-8
g(-4)=8
f(8)=2(8)-4
f(8)=12
the sum of two numbers is 149 and the difference is 31.
Answer:
The two numbers are 90 and 59
Step-by-step explanation:
Let's call the two numbers x and y.
From the problem statement, we know that:
x + y = 149 (the sum of two numbers is 149)
x - y = 31 (the difference of the two numbers is 31)
To solve for x and y, we can use the method of elimination. Adding the two equations together eliminates the y term:
(x + y) + (x - y) = 149 + 31
2x = 180
x = 90
Substituting x = 90 into one of the original equations, we can solve for y:
x + y = 149
90 + y = 149
y = 59
Therefore, the two numbers are 90 and 59.
Use the table below to calculate the average percent change in population in California from 2000-2009.
If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
1.3567% is the average percent change in population in California from 2000-2009.
What is population?The term "population" is frequently used to describe the total number of people living in a particular location. To estimate the number of the residents within a certain territory, governments conduct censuses.
Population is referred to a group of people who share some established characteristics, such as region, race, culture, nationality, or religion, in sociology or population geography. The social science of demography involves the statistical analysis of populations.
average percent change in population =1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9
= 1.3567%
Therefore, 1.3567% is the average percent change in population in California from 2000-2009.
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Identify and explain any restrictions on the variablex in the expression √6x-2
The restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.
The restrictions on the variablex in the expression √6x-2 are determined by the fact that the square root of a negative number is not a real number. Therefore, the expression under the square root must be greater than or equal to zero. This gives us the following inequality:
6x-2 ≥ 0
Solving for x, we get:
6x ≥ 2
x ≥ 2/6
x ≥ 1/3
So the restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.
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Find the area of the regular figure below: 19 ft A)1725.9 ft2 B)1784.5 ft2 C)1812.3 ft2 D)1875.8 ft2 E)1904.1 ft2
To get the total area of the figure: 6 x 705 = 1725.9 ft².
What is area?
Area is a measure of the size of a two-dimensional surface, such as a region of land or a space in a building. It is typically measured in square units, such as square feet or square meters. Area can also be calculated for three-dimensional objects, such as a cube or other solid shape. Area is an important concept in mathematics and is used to measure the size of many different shapes.
The correct answer is A) 1725.9 ft². To find the area of the regular figure, calculate the area of one of the triangles, and then multiply this by 6 (the number of triangles in the figure). The area of a triangle is A = ½bh, where b is the base and h is the height. The base of the triangle is 19 ft and the height is 12.5 ft. Therefore, A = ½(19) (12.5) = 117.5 ft². Multiply this by 6 to get 6 x 117.5 = 705 ft. Finally, multiply this by the number of triangles in the figure, which is 6, to get the total area of the figure: 6 x 705 = 1725.9 ft².
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College Algebra -3.1Modeling with Quadratics Angry Birss: * Cire cact aniwns. Hhe enty the fusctien to obraln yoar answerc. - Show all nocensary cakiadsina. - Wine your ancurers is complrte aeatrnces 1. Whor is the s-inerreept and nhat does a repreiert? 2. What is the ponatire eimerreps and whas doest throsetinaly tepereset? socirt?
The x-intercept is (-3,0) and the y-intercept is (0,9).
The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.
The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.
1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.
To find the x-intercept, set the function equal to 0 and solve for x:
0 = x^2 + 6x + 9
0 = (x+3)(x+3)
x = -3
To find the y-intercept, set x equal to 0 and solve for y:
y = 0^2 + 6(0) + 9
y = 9
Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).
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If f(v)=8v^(4)+34v^(3)-26v^(2)+21v+11, use synthetic division to find f(-5) Submit
By applying synthetic division concept, it can be concluded that if f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11, then, f(-5) = 6.
Synthetic division is a shorthand way of dividing polynomials where we can divide the coefficients of the polynomial by omitting variables and exponents. As a result, we get the coefficient of the quotient and the remainder.
Polynomial remainder theorem states that the value of p in argument b is equal to the remainder of the polynomial division p(x) / (x - b). Specifically, p(x) is divided by x - b with a remainder of zero if, and only if, b is a root of p.
We have the following polynomial:
f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11
To find f(-5) using synthetic division, we will divide the polynomial f(v) by (z + 5). The steps are as follows:
1. Put the coefficients in a row and multiply the outside coefficient by the divisor: 8(-5)= -40.
2. Add the inside coefficient to the product from the previous step: -40 + 34 = -6.
3. Multiply the result from the previous step by the divisor: -6(-5) = 30.
4. Add the next coefficient to the product from the previous step: 30 - 26 = 4.
5. Multiply the result from the previous step by the divisor: 4(-5) = -20.
6. Add the next coefficient to the product from the previous step: -20 + 21 = 1.
7. Multiply the result from the previous step by the divisor: 1(-5) = -5.
8. Add the last coefficient to the product from the previous step: -5 + 11 = 6.
The final result of the synthetic division is 6, so the answer to the question is f(-5) = 6.
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A certain map shows two roads. Road A is 1 1/5 miles long but is 1 1/2 inches long on the map. What is the unit rate for inches per mile on this map? If road B is 12 miles long, how long is road B on the map?
The unit rate for inches per mile is 0.8 inches.
The length of road B is 9.6 inches on map.
What is Unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.
Road in inches = 1 1/5 = 6/5 inches
Road in miles = 1 1/2 miles =
Inches per mile = 6/5 / (3/2)
= 6/5 x 2/3
= 4/5
= 0.8 inches
If the road B is 12 miles long, on the map it would be;
= 0.8 x 12
= 9.6 inches
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Which statement below is TRUE about section b of the drive?
Group of answer choices
The time driven stayed the same
The distance driven stayed the same
The distance was increasing
The distance was decreasing
Answer: Im pretty sure its B
Step-by-step explanation:
18
What can you conclude about data from its equation, y = 3x - 7? Select all that apply.
A- y causes a.
B- The data are correlated.
C- The data are not correlated.
D- You cannot determine if there is causation between x and y.
The linear equation y = 3x - 7 has a data that is correlated because it has a linear relationship and we cannot determine if there's a causation between x and y
What does the linear equation represent?A. y causes a. is not applicable in this case, as there is no variable named "a" in the equation.
B. The equation y = 3x - 7 represents a linear relationship between two variables, x and y. As the equation has a slope of 3, it indicates that as the value of x increases by 1, the value of y increases by 3. Therefore, the data are correlated positively.
C. This is incorrect. As mentioned in B, the equation represents a linear relationship between two variables, x and y, which are positively correlated.
D. This is correct. Although the equation represents a linear relationship between x and y, it does not imply causation. It is possible that x causes y, y causes x, or some other variable or variables may be influencing both x and y. Therefore, we cannot determine if there is causation between x and y based on the equation y = 3x - 7 alone
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The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0. (a) Derive the distribution of Y (b) Evaluate E(Y)
(a) The distribution of Y is P(Y = y) = (12^y * e^-12)/y!
(b) E(Y) = 12.
The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0.
(a) The distribution of Y ~ Poisson(12) is given by:
P(Y = y) = (12^y * e^-12)/y!
(b) The expected value of a Poisson distribution is simply the mean, which in this case is 12. Therefore, E(Y) = 12.
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n Exercises 5-6, find the coordinates of the segmen PQ. Calculate the distance from the midpoint to the ori in. 5. P=(2,3,1),Q=(0,5,7) 6. P=(1,0,3),Q=(3,2,5) 7. Let A=(−1,0,−3) and E=(3,6,3). Find points B,C, and D on the line segment AE such that d(A,B)=d(B,C)=d(C,D)=d(D,E)= 41d(A,E)
C= (1.17,9.93,−32.25
D= (3.33,14.9,−47).
For Exercise 5, the coordinates of the segment PQ are P = (2,3,1) and Q = (0,5,7). To calculate the distance from the midpoint to the origin, use the midpoint formula: M = [(P + Q) / 2].
In this case, M = [(2,3,1) + (0,5,7)] / 2 = (1,4,4).
Then calculate the distance from the midpoint to the origin by using the distance formula: d = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2], where (x1, y1, z1) is the midpoint coordinates and (x2, y2, z2) is the origin coordinates. In this case, d = √[(1-0)2 + (4-0)2 + (4-0)2] = √17.
For Exercise 6, the coordinates of the segment PQ are P = (1,0,3) and Q = (3,2,5). To calculate the distance from the midpoint to the origin, use the midpoint formula: M = [(P + Q) / 2]. In this case, M = [(1,0,3) + (3,2,5)] / 2 = (2,1,4). Then calculate the distance from the midpoint to the origin by using the distance formula: d = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2], where (x1, y1, z1) is the midpoint coordinates and (x2, y2, z2) is the origin coordinates. In this case, d = √[(2-0)2 + (1-0)2 + (4-0)2] = √21.
For Exercise 7, let A = (−1,0,−3) and E = (3,6,3). To find points B, C, and D on the line segment AE such that d(A,B)=d(B,C)=d(C,D)=d(D,E)= 41d(A,E), first calculate the distance between A and E using the distance formula: d(A,E) = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2], where (x1, y1, z1) is the coordinates of A and (x2, y2, z2) is the coordinates of E. In this case, d(A,E) = √[(3-(-1))2 + (6-0)2 + (3-(-3))2] = √122.
To find the coordinates of points B, C, and D, use the following formula: B = A + (d(A,B)/d(A,E))(E-A), where d(A,B) is the distance from A to B, d(A,E) is the distance from A to E, A is the coordinates of A, and E-A is the vector pointing from A to E. Using this formula, the coordinates of B can be calculated as B = (−1,0,−3) + (41/122)((3,6,3) - (−1,0,−3)) = (−1,4.97,−17.5). Similarly, the coordinates of C and D can be calculated as C = (−1,4.97,−17.5) + (41/122)((3,6,3) - (−1,4.97,−17.5)) = (1.17,9.93,−32.25) and D = (1.17,9.93,−32.25) + (41/122)((3,6,3) - (1.17,9.93,−32.25)) = (3.33,14.9,−47).
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5. (3 marks) Determine the area of the parallelogram formed by the following vectors:
u = (1,2,2) , v = (4.4.0)
The area of the parallelogram formed by the vectors u and v is 12.
The area of a parallelogram formed by two vectors u and v can be determined by finding the cross product of the two vectors and then taking the magnitude of the resulting vector.
First, we need to find the cross product of u and v:
u × v = [(2)(0) - (2)(4), (2)(4) - (1)(0), (1)(4) - (2)(4)] = [-8, 8, -4]
Next, we need to find the magnitude of the resulting vector:
|u × v| = √((-8)² + (8)² + (-4)²) = √(64 + 64 + 16) = √144 = 12
Therefore, the area of the parallelogram formed by the vectors u and v is 12.
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FIND THE GREATEST COMON FACTOR AND THE LEAST COMON MULTIPLE FOR 12,18,24
Answer: LCM is 72. GCF is 6.
QUICK
HELP ME PLS
I NEED ERGENT HELP
Answer:
Step-by-step explanation:
For any cube the total edge length is equal to 12n, with n being the length of an edge side. Knowing this:
Cube A - Total edge length = 12(3) or 36
Cube B - 12(5) or 60
Cube C - 12(9.5) or 114
If any cube has edge length s, the total edge length is 12s
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