one possible solution is to sell 60 tacos and 60 burritos. To graph these inequalities, we can start by graphing the boundary lines for each inequality, which are obtained by replacing the inequality signs with equal signs.
Let x be the number of tacos sold and y be the number of burritos sold. Then we can write the following system of inequalities:
x + y ≤ 120 (since Benjamin only has enough supplies to make 120 tacos or burritos)
3.75x + 8.25y ≥ 660 (since Benjamin must sell at least $660 worth of tacos and burritos each day)
To graph these inequalities, we can start by graphing the boundary lines for each inequality, which are obtained by replacing the inequality signs with equal signs.
For the first inequality, we have:
x + y = 120
This is the equation of a straight line passing through the points (0, 120) and (120, 0). We can graph this line by plotting these two points and connecting them with a straight line.
For the second inequality, we have:
3.75x + 8.25y = 660
This is the equation of a straight line in slope-intercept form, y = (-3.75/8.25)x + 80. We can graph this line by plotting the y-intercept (0, 80) and using the slope (-3.75/8.25) to find additional points on the line.
Next, we need to shade the feasible region, which is the region that satisfies both inequalities. This is the region below the line x + y = 120 and above the line 3.75x + 8.25y = 660.
One possible solution is the point where these two lines intersect, which we can find by solving the system of equations:
x + y = 120
3.75x + 8.25y = 660
Solving for x and y, we get:
x = 60
y = 60
Therefore, one possible solution is to sell 60 tacos and 60 burritos.
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Use substitution to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]4x+y=14\\y=8+2x[/tex]
Answer:
x = 1 , y = 10
Step-by-step explanation:
Given : y = 8 + 2x
by substitution,
4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1
y = 8 + 2x
y = 8 + 2(1)
y= 10
Proof :
if x = 1,
4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14
if y = 10 and x = 1
4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14
For both equations, LHS = RHS
Therefore Proved.
hope it helps!
PLEASE HELP!! I ONLY NEED HELP WITH THE LAST PART (ASKING AVERAGE SPEED)
Answer:
429
Step-by-step explanation:
The expression (1 - 2x)4 can be written in the form 1 + px + qx^(2) - 32x^(3) + 16x^(4) By using the binomial expansion, or otherwise, find the values of the integers p and q.
Using the binomial expansion theorem, the values of integers p and q are -8 and 24, respectively
Expanding an expression using the binomial theoremFrom the question, we are to use the binomial expansion to expand the given expression and determine the values of p and q.
We can expand (1 - 2x)^4 using the binomial theorem as follows:
(1 - 2x)^4 = 1^4 - 4(1^3)(2x) + 6(1^2)(2x)^2 - 4(1)(2x)^3 + (2x)^4
= 1 - 8x + 24x^2 - 32x^3 + 16x^4
Now, we will compare this expression to the given expression
Comparing the expression to the given expression, 1 + px + qx^2 - 32x^3 + 16x^4
We see that:
p = -8
q = 24
Hence, the values p and q are -8 and 24, respectively.
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-8x253.96 pls help if you can because i'm stuck on this problem, so please help if you can.
You spend a $5 per turn on a fair game to win $15 for each winYou lose the first round but win the next two rounds. What was the net payoff ?
If you spend a $5 per turn on a fair game to win $15 for each win and you lose the first round but win the next two rounds, then the net payoff is $15
Since you spend $5 per turn and play three rounds, your total cost is $5 x 3 = $15.
If you win a game, you receive $15, so winning two games will give you $15 x 2 = $30.
However, since you lost the first round, you only won two out of three rounds. Therefore, your net payoff is:
= $30 - $15
Subtract the numbers
= $15
Therefore, your net payoff is $15
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What is the advantage
of a two-way relative frequency table for
showing relationships between sets of
paired data?
A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.
A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.
The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:
Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.
Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.
Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.
In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.
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b. If there are 440 towers, how many customers does the company have? Write a proportion you can use to solve. Choose the correct proportion.
Answer:
What's your question
Step-by-step explanation:
How many customers in each tower
Isabel left her home at 11. 30 A. M. She took 45 minutes to jog to the park.
After exercising for 1 hour 55 minutes, she jogged home. She reached home at 3 P. M.
How long did she take to jog home? Explain how you got to this answer
Answer: 1 hour 50 minutes
Step-by-step explanation: it took her 2 hours to get home
she left home at 11:30 am it took her 45 minutes to jog to the park by the time she got to the park it was 12:15 pm she exercised for 1 hour and 55 minutes by the time she was done her work out it is 1:10 if she finished at 3 pm it took her 1 hour 50 minutes to get home
What will be the coordinates of point G after
a 90° counterclockwise rotation about the
origin?
So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.
To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:
x' = -y
y' = x
This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).
If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.
Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:
x' = -y
y' = x
So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:
G' = (-y, x)
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what is 46x squared times 24x squard
Answer:
the answer to ur question is: 1218816
The following figure is made of 3 triangles and 1 rectangle.
4
2
B
Figure
Triangle A
Triangle B
Rectangle C
Triangle D
Whole figure
A
2
4
T
6
2C 2D
H
2
Find the area of each part of the figure and the whole figure.
Area (square units)
19
1
I
The areas of each part of the composite figure are;
Triangle A = 20 Square units
Triangle B = 2 Square units
Rectangle C = 4 Square units
Triangle D = 6 Square units
What is area?Area is a measurement of the two-dimensional surface of a shape or object. Area is often used when measuring the size of a plot of land or other physical space, such as a room or an outdoor area.
The area of each part of the figure can be found by adding the areas of the individual shapes that make up the figure. The area of a triangle can be found by using the formula A = 1/2bh, where b is the base and h is the height of the triangle. For a rectangle, the area is equal to the length multiplied by the width.
The composite figure's component parts' respective areas are;
20 Square Units = Triangle A
Triangle B = 2 units of the square
Square units = 4 for the rectangle C.
Triangle D = 6 units of the square
How can I calculate the composite figure's area?The formula for a triangle's area is straightforward;
A = 0.5 × base × height
Triangle A's area is;
Triangle A: (6 + 2 + 2) × 4 × 1/2
= ¹/₂ × 10 × 4
equals 20 square units
Triangle B's perimeter is;
Triangle A equals 1/2 × 2 × 2
equals 2 square units
Length × Width = Area of Rectangle C
= 2 × 2
equals 4 square units
Triangle D's area is;
Triangle D is equal to.5 × 6.
equals 6 square units
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Complete question -
Solve the equation by using the square root method:
9x^2 - 36x = 0
Answer:
Step-by-step explanation:
To solve the equation 9x^2 - 36x = 0 by using the square root method, we first need to rearrange the terms to get x^2 and x on one side:
9x^2 - 36x = 0
Factor out 9x from the left-hand side:
9x(x - 4) = 0
Now we have two factors: 9x = 0 and x - 4 = 0. Solving for x in each factor gives us:
9x = 0: x = 0
x - 4 = 0: x = 4
Therefore, the solutions to the equation are x = 0 and x = 4.
Answer:
x = 0, x = 4
Step-by-step explanation:
Unfortunately, the equation 9x^2 - 36x = 0 cannot be solved using the square root method directly. The square root method is used to solve quadratic equations of the form ax^2 + bx + c = 0 by isolating the x^2 term, taking the square root of both sides, and solving for x. However, in the given equation, there is no constant term (c = 0), and therefore, we need to use a different method to solve it.
As I mentioned earlier, we can factor the equation and use the zero product property to solve for x. This method involves finding two factors of the quadratic equation that multiply to give 0, setting each factor equal to 0, and solving for x. In this case, we can factor out x and obtain the factors x and (9x - 36), which multiply to give 0. By setting each factor equal to 0 and solving for x, we obtain the solutions x = 0 and x = 4.
To solve the equation 9x^2 - 36x = 0 using the factorization method:
Factor out x from the left-hand side of the equation to get:
x(9x - 36) = 0
Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for x:
x = 0 or 9x - 36 = 0
For the second equation, solve for x:
9x - 36 = 0
9x = 36
x = 4
Therefore, the solutions to the equation are x = 0 and x = 4.
Note that this method involves factoring the quadratic equation and then using the zero product property to obtain the solutions. It works for any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to zero.
A mixture of 50 liters of paint is 25% red tint, 30% yellow tint and 45% water.
5 liters of yellow tint are added to the original mixture.
The percent of yellow tint in the new mixture is ____?
Answer must be correct to 1 decimal place
From the given information provided, the percent of yellow tint in the new mixture is 36.4%.
The total amount of yellow tint in the original mixture is:
0.30 × 50 liters = 15 liters
When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:
15 + 5 = 20 liters
The total amount of new mixture is:
50 + 5 = 55 liters
To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:
(20/55) × 100 = 36.4%
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What is the remainder when \( f(x)=-6 x^{23}+x^{11}-x^{6}+2 x \) is divided by \( x+1 \) ? The remainder is
The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.
Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).
Here is the given polynomial,
()=−6^23+^11−^6+2
We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).
(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6
Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:
()=(−)()+()
where q(x) is the quotient of the division.
So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:
The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.
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The expression for the nth term of a sequence is 7(3 − n)
What are the first four terms of the sequence? Give your answers in
order.
Answer:
14, 7, 0, -7.
Step-by-step explanation:
To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.
The expression for the nth term of the sequence is 7(3 - n).
Let's find the value of the first term (n = 1):
T₁ = 7(3 - 1) = 7(2) = 14
The first term of the sequence is 14.
Now, let's find the value of the second term (n = 2):
T₂ = 7(3 - 2) = 7(1) = 7
The second term of the sequence is 7.
Next, let's find the value of the third term (n = 3):
T₃ = 7(3 - 3) = 7(0) = 0
The third term of the sequence is 0.
Finally, let's find the value of the fourth term (n = 4):
T₄ = 7(3 - 4) = 7(-1) = -7
The fourth term of the sequence is -7.
Therefore, the first four terms of the sequence are:
To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.
The expression for the nth term of the sequence is 7(3 - n).
Let's find the value of the first term (n = 1):
T₁ = 7(3 - 1) = 7(2) = 14
The first term of the sequence is 14.
Now, let's find the value of the second term (n = 2):
T₂ = 7(3 - 2) = 7(1) = 7
The second term of the sequence is 7.
Next, let's find the value of the third term (n = 3):
T₃ = 7(3 - 3) = 7(0) = 0
The third term of the sequence is 0.
Finally, let's find the value of the fourth term (n = 4):
T₄ = 7(3 - 4) = 7(-1) = -7
The fourth term of the sequence is -7.
Therefore, the first four terms of the sequence are:
14, 7, 0, -7.
The cost price of an article when 22% profit is made after selling it for 's'
The cost price of the article when a profit of 22% is made after selling it for a certain price 's' can be calculated using the formula c = 0.78 * s.
Let's assume the cost price of the article is 'c'. Then, the profit made on selling the article is:
Profit = Selling price - Cost price
Since a profit of 22% was made on the selling price 's', we can express the selling price as:
Selling price = Cost price + Profit
= Cost price + 0.22 * Selling price
Rearranging this equation, we get:
0.78 * Selling price = Cost price
Substituting the given selling price 's' into this equation, we get:
0.78 * s = c
Therefore, the cost price of the article is 0.78 times the selling price. If we know the selling price 's', we can calculate the cost price 'c' using this formula. For example, if the selling price of the article is $100, then the cost price would be:
c = 0.78 * s
= 0.78 * $100
= $78
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There are 2 boys and 2 girls working on an art project. They are sharing 10 ounces of paint equally. How much paint should each child get?
Answer:
2 ounces per person
Step-by-step explanation:
Find the area of the triangle. Round your answer to one decimal place. B=115∘,C=29∘,a=52
The area of the triangle is 715.7 square units, rounded off to one decimal place.
The given triangle's side lengths and the angles are a = 52, B = 115°, and C = 29°. The area of the triangle can be determined by applying the formula:A = (1/2) a² sin B sin C, where a is the length of the side opposite to angle A.The area of the triangle is (rounding off to one decimal place)Therefore, the area of the triangle is 715.7 square units, rounded off to one decimal place.
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4 - 3x = 16
How do you solve this.... I somehow got -4 but I don't think that is right.
Answer:
yes you are right
Step-by-step explanation:
move 4 to other side so its -3x=12
divide 12 by -3
x=-4
Sal stands a candle up inside a paper bag, opened at the top. The candle and bag are both in the shape of right rectangular prisms. The dimensions, in inches, are given.
Length Width Height
Bag 2 4 8
Candle 1 2 3
Sal wants to put sand inside the bag surrounding the base of the candle. He wants the sand to be between 12 and 34 inches deep. How much sand, in cubic inches, should Sal put inside the bag? Select your answers from the drop-down lists
Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.
Base area of the bag = 4 × 2 = 8 in²
Base area of the candle = 2 × 1 = 2 in²
therefore, we know that base area to be filled with sand:
= 8 - 2 = 6 in²
now, height of sand is known to be between 1/2 and 3/4 inches,
therefore, we can make out that the volume of land is between 6 × 1/2 in³ and 6 × 3/4 in³
3 in³ and 4.5 in ³
therefore, amount of sand is between 3 cubic inches and 4.5 cubic inches, with this we know that Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.
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Determine the eccentricity for r=5/2+1sin theta
0. 5
5
2
1
Determine the equation of the directrix of r=26. 4/4+4. 4 cos theta
X=-6
Y=6
X=6
The eccentricity for r=5/2+1sin theta and the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6
To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:
r = 5/2 + 1sin(θ)
r = 5/2 + 1y/r
r^2 = (5/2)r + y
x^2 + y^2 = (5/2)r + y
x^2 + y^2 = (5/2)√(x^2 + y^2) + y
x^2 - (5/2)√(x^2 + y^2) + y^2 = 0
We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:
e = √(1 - b^2/a^2)
Plugging in our values, we get:
e = √(1 - 1/(5/2))
e = √(3/5)
e ≈ 0.5
Therefore, the answer is (A) 0.5.
To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:
r = 26.4/4 + 4.4cos(θ)
r = 6.6 + 4.4x/r
r^2 = 6.6r + 4.4x
x = (r^2 - 6.6r)/4.4
We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:
y = (1/4p)x^2
Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:
y = 1.65
However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:
x = 0
Therefore, the answer is (C) x = 6.
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PLEASE SHOW WORK!!!!!!!!!
Answer:
The answer is G
A group of Physicians must build an addition to their existing private clinic. They are considering three different sized additions; a small addition, a medium addition and a large addition. If the medical demand is high (there is a favorable market for the addition) they would realize a net profit of $100,000 with a large addition, a net profit of $40,000 with a medium addition and a net profit of $10,000 with a small addition. If the medical demand is low (there is an unfavorable market for the addition) they would realize a net loss of $40,000 with the large addition, a net loss of $10,000 with the medium addition and a net profit of $5,000 with the small addition. The Physicians were also able to assign the following utility preference values to each of the potential payoffs they could encounter. Utility of $100,000 is 1.0, U ($40,000) is 0.9, U ($10,000) is 0.6, U ($5,000) is 0.5, U ($-10,000) is 0.4, and U ($-40,000) is 0.0. The physicians also have a reliable forecast indicating a 40% probability of the high medical demand. Using expected monetary value theory, what should they do and what is the expected value of that decision? Using expected utility theory, what should they do and what is the expected utility of that decision?
Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).
What is probability, exactly?The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
The following formula can be used to determine each option's anticipated financial value:
=> EMV of big addition = (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.
=> EMV of the middle addition is
= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.
=> EMV of a minor addition = (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000
The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.
dividing each outcome's usefulness value by its likelihood, then adding the results:
=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.
=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.
Smaller EU = (0.4 * 0.5) + (0.6 * 0.6) = 0.58
The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.
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Do the three lines 5x - y = 7, x + 3y = 11, and 2x + 3y = 13 have a common point of intersection? If so, find it. if not, explain why not .
Answer:
429
Step-by-step explanation:
Which of the following rectangles has an area that can be represented by the algebraic expression 9x+9
?
Responses
Image with alt text:
Image with alt text:
Image with alt text:
Image with alt text:
Answer: we can't see the images
Step-by-step explanation:
Answer:
Step-by-step explanation:
be can not see the pictures sir do better ni***
Please help me with this needs to be done by today thanks
Answer:
cubic unit eg m³
Step-by-step explanation:
Raised to power 3
Answer:
Units cubed or unit^3
Explanation:
Volume= (base)(width)(height), therefore, this would be cubed. x^3
Area=(base)(height), therefore, this would be squared. x^2
Letter answer only answer only!
Answer: B
Step-by-step explanation:
help would be appreciated
Challenge A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 30% discount. Otherwise, you get a 25% discount. The table shows the results of 200 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? explain
Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.
Discount Number of customers Relative Frequency
10% 70 0.35
25% 99 0.495
30% 31 0.155
To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).
Relative frequency for 25% discount = 99/200 = 0.495
Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.
Step-by-step explanation:
Relative to the origin O, the position vectors of two points A and B are a and b respectively. b is a unit vector and the magnitude of a is twice that of b. The angle between a and b is 60°. Show that [a×[ob + (1-o)a] =√k, where k is a constant to be determined.
Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.
What is the proof that [a * [ob + (1 - o)a] = √kThe vector OB can be expressed as OB = b since b is a unit vector and O is the origin.
The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.
The angle between a and b is 60°, so we have:
|a| |b| cos 60° = a · b
2|b| · 1/2 = a · b
|b| = a · b
We can now express the vector [OB + (1 - O)A] as:
[OB + (1 - O)A] = b + (1 - O)2b
= (2 - O) b
The cross product of a and [OB + (1 - O)A] is:
a × [OB + (1 - O)A] = a × [(2 - O) b]
= (2 - O) (a × b)
The magnitude of the cross product is:
|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|
= |2 - O| |a| |b| sin 60°
= √3 |2 - O| |b| |a| / 2
= √3 |2 - O| |b|^2 |b| / 2
= √3 |2 - O| |b|^3 / 2
Substituting |b| = a · b, we get:
|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2
Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:
√k = √3 |2 - O| (a · b)^3 / 2
Squaring both sides, we get:
k = 3 (2 - O)^2 (a · b)^6 / 4
Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.
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