The system for which at least one solution exists is 3(a - 5x) < 1 + x and 2 - x/2 > 3 + 5(x - a), where x lies between (3a - 1)/16 and (5a - 1)/7.
we need to find the system for which at least one solution exists.
Let's solve these inequalities one by one:
1.3(a - 5x) < 1 + x3a - 15x < 1 + x16x
< 3a - 1x < (3a - 1)/16(3a - 1)/16 > x
This inequality has a solution as x can take any value greater than
(3a - 1)/16.2.2 - x/2 > 3 + 5(x - a)2 - x/2 >
3 + 5x - 5a-x/2 - 5x > -5a + 1-7x > -5a + 1x < (5a - 1)/7
This inequality has a solution as x can take any value less than (5a - 1)/7.
Now, we need to find a common solution for both inequalities:
(5a - 1)/7 > x > (3a - 1)/16So, x
lies between (3a - 1)/16 and (5a - 1)/7.
Hence, the system for which at least one solution exists is
3(a - 5x) < 1 + x and 2 - x/2 > 3 + 5(x - a), where x lies between (3a - 1)/16 and (5a - 1)/7.
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❗️❗️❗️HELP❗️❗️❗️what is the probability that the spinner lands on either A or D?
O
2
Answer:
Step-by-step explanation:
Answer:
1 third
Step-by-step explanation:
6 divided by 2 is 3
one third is the answer hence forth
also 2 are valid and 4 are not out of 6 so one third of them are valid
Use the image to answer the question.Identify the legs in AXYZ.
Answer
option C
Explanation:
Given the right angled triangle XYZ
The legs are Length YZ and Length ZX
Therefore, the legs are YZ AND ZX
The sum of 18 + 45 is a multiple of which sum?
Answer: multiple of sum 2+5
Step-by-step explanation:
18/9=2
45/9=5
2+5=7
18+45=63
63/7=9
2+5
To solve the equation 5a + 3 = 18 in the fewest steps possible you would what
Answer:
Proofs attached to answer
Step-by-step explanation:
proofs attached to answer
\(\huge\text{Hey there!}\)
\(\mathtt{5a + 3 = 18}\\\\\textsf{SUBTRACT 3 to BOTH SIDES}\\\\\mathtt{5a + 3 - 3 = 18 - 3}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{5a = 18 - 3}\\\\\mathtt{5a = 15}\\\\\textsf{DIVIDE 5 to BOTH SIDES}\\\\\mathtt{\dfrac{5a}{5} = \dfrac{15}{5}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{a = \dfrac{15}{5}}\\\\\mathtt{a = 3}\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{a = 3}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
The Sugar Sweet Company delivers sugar to its customers. Let C be the total cost to transport the sugar (in dollars). Let S be the amount of sugar transported (in tons). The company can transport up to 30 tons of sugar. Suppose that =C+120S+3500 gives C as a function of S.
Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
1. What is domain? (amount of sugar transported (in tons), cost to transport sugar (in dollars)
2 .What is range? (amount of sugar transported (in tons), cost to transport sugar (in dollars)
3. What is set of values of domain?
4. What is set of values of range?
The potential input and output values of a function are its domain and range respectively as ( 3500 , ∞)
It is specified as follows
the region
This is a list of the function's potential S values
Due to the fact that S refers to a physical quantity, it cannot be less than 0. (i.e. tons of sugar)
Any number greater than zero may be used as S's value.
Thus, the following is the function's domain:
The variety
This represents the function's potential C values.
It is specified as follows:
When S = 0
C = 120 x 0 + 3500 = 3500
The preceding implies that:
C must be more than 3500.
Any number higher than 3500 can be used as the value of C.
Thus, the function's range is as follows: (3500 , ∞ )
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Suppose you take out a loan for 180 days in the amount of $13,500 at 11% ordinary interest. After 50 days, you make a partial payment of $1,000. What is the final amount due on the loan? (Round to the nearest cent)
The final amount due on the loan after the partial payment is approximately $13,070.41 (rounded to the nearest cent).
To calculate the final amount due on the loan, we need to consider the principal amount, the interest accrued, and the partial payment made.
Given information:
Principal amount: $13,500
Interest rate: 11% (per year)
Loan period: 180 days
Partial payment: $1,000
Partial payment date: 50 days
First, let's calculate the interest accrued on the loan from the loan start date to the partial payment date:
Interest accrued = Principal amount * Interest rate * (Number of days / 365)
Interest accrued = $13,500 * 11% * (50 / 365)
Interest accrued ≈ $201.37
Next, let's calculate the remaining principal balance after the partial payment:
Remaining principal balance = Principal amount - Partial payment
Remaining principal balance = $13,500 - $1,000
Remaining principal balance = $12,500
Now, let's calculate the interest accrued on the remaining principal balance for the remaining loan period (180 - 50 days):
Interest accrued = Remaining principal balance * Interest rate * (Number of days / 365)
Interest accrued = $12,500 * 11% * (130 / 365)
Interest accrued ≈ $570.41
Finally, we can calculate the final amount due on the loan by adding the remaining principal balance and the interest accrued:
Final amount due = Remaining principal balance + Interest accrued
Final amount due = $12,500 + $570.41
Final amount due ≈ $13,070.41
Therefore, the final amount due on the loan after the partial payment is approximately $13,070.41 (rounded to the nearest cent).
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6 ft
3 ft
6 ft
15 ft
Find the area of the figure above.
Answer:
15ft
Step-by-step explanation:
if you mean the area that is blank
(Tell me if i'm wrong)
Answer:
the answer would be 90 because the big triangle is 72 and the rectangle is 18
Module 3 DBA: What key features can be identified from graphs of polynomials of higher-
degrees and explain how the key features can be used sketch the graph of the polynomial
function? Remember to include how solutions are represented.
to be honest i dont remember srry
Answer:
Polynomials are algebraic expressions that contain more than two terms. AN example would be: f(x) = x^3 + x^2 + x +1. This equation contains three terms, with the 3rd degree as its highest term. It also means that the graph passed three x-intercepts. This depends in the highest degree. So, the first thing you do is plot the intercepts because for sure, the graph will pass there.
Step-by-step explanation:
solve the following:
2(x + 3) = x - 4
4(5x - 2) = 2(9x + 3)
Step-by-step Solution(s):
Solving for 2(x + 3) = x - 4.
2(x + 3) = x - 4=> 2x + 6 = x - 4=> 2x - x = -6 - 4=> x = -10Solving for 4(5x - 2) = 2(9x + 3)
4(5x - 2) = 2(9x + 3)=> 20x - 8 = 18x + 6=> 20x - 18x = 8 + 6=> 2x = 14=> x = 7Hoped this helped!
The surface of a cylinder is represented \(A = 2\pi r^{2} + 2\pi rh\), where r is the radius of the cylinder and h is its height. Factor the right side of the formula.
Therefore, the factored form of the right side of the formula is 2πr(r + h).
What is cylinder?A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that connects the base's circumference to a parallel circle at the other end of the shape. It is a type of prism with circular bases. The two circular bases of the cylinder are parallel and congruent, meaning that they have the same size and shape. The curved surface of the cylinder is composed of all the points that are equidistant from both bases. The cylinder is a common shape in real-life objects, such as cans, pipes, and drinking glasses. Its volume and surface area formulas are frequently used in geometry and applied mathematics.
Here,
Starting with the given formula:
A = 2πr² + 2πrh
We can factor out a common factor of 2πr:
A = 2πr(r + h)
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find two integers whose product is 136 such that one of the integers is seven less than three times the other integer
The two integers whose product is 136 are 17 and 8.
Let x be one of the integers. Then, the other integer is 3x - 7. The product of the two integers is given by:
x * (3x - 7) = 136
Expanding and solving for x, we get:
x^2 - 7x + 136 = 0
Using the quadratic formula, we can find the two solutions for x:
x = (-(-7) ± √(\((-7)^2\) - 4 * 1 * 136)) / (2 * 1)
x = (7 ± √(49 + 544)) / 2
x = (7 ± √593) / 2
Since x must be an integer, we round down the decimal to the nearest integer to get:
x = 8 or x = 9
Since x represents one of the integers, the other integer is 3x - 7, so:
3x - 7 = 3 * 8 - 7 = 17
Therefore, the two integers are 8 and 17, and their product is 136.
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The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
Number line from negative 10 to positive 10 in increments of 1 is shown. In between the whole numbers, there should be a tick mark. Only the whole numbers are labeled. A point labeled R is placed halfway between the 3rd and 4th tick marks to the left of 0.
Answer: - 2.5
Step-by-step explanation:
The point R is - 2.5,
The numbers on the number line are arranged sequentially and in regular increment of 1 with only the integer numbers being displayed and ticked. The point R sits directly in between - 3 and - 2. Therefore, to accurately obtain the position of the blue dot, we take the average of both positions binding the blue dot. That is - 3 and - 2
Average = ( - 3 + - 2) / 2
Average = - 5 / 2 = - 2.5
Answer: yea it it - 2.5 i just did that test and got it right <3
Step-by-step explanation:
List the elements of each of the following sample spaces: (a) the set of integers between 1 and 50 divisible by 8. (b) the set S = {x | x^2+4x-5=0}. (c) the set of outcomes when a coin is tossed until a tail or three heads appear. (d) the set S= (x | 2x-420 and x <1).
The set S contains only one element, which is:
S = {210}
(a) The set of integers between 1 and 50 that are divisible by 8:
{8, 16, 24, 32, 40, 48}
(b) The set S = {x | x^2+4x-5=0} can be found by solving the quadratic equation:
x^2 + 4x - 5 = 0
Using the quadratic formula, we get:
x = (-4 ± sqrt(4^2 - 4(1)(-5))) / 2(1)
x = (-4 ± sqrt(36)) / 2
x = (-4 ± 6) / 2
So the two solutions are x = -5 and x = 1. Therefore, the set S is:
S = {-5, 1}
(c) The set of outcomes when a coin is tossed until a tail or three heads appear can be represented as a sequence of H's and T's. The sample space can be represented as:
{H, TH, HTH, HH, TTH, HTT, HHT, TTT}
where H represents a head, T represents a tail, and the sequence is read from left to right.
(d) The set S = (x | 2x-420 and x <1) can be rewritten as:
S = {x | 2x = 420 and x < 1}
Simplifying the first condition, we get:
2x = 420
x = 210
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The linear factors of the cubic are .
Answer:
(x-2)(x - 3)(x - 5)
(x - 2)(x-3)(x - 5)(x + 5)
(x + 2)(x + 3)(x + 5)
(x + 2)(x+3)(x - 5)
Answer:
first option
Step-by-step explanation:
(x-2)(x-3)(x-5)
16. Find the area of the sector.
The area of the sector with a central angle of 60 degree and radius of 8 units is approximately 33.5 sqaure units.
What is the area of the sector?A sector of a circle is simply part of a circle made up of an arc and two radii.
The area of a sector of a circle can be expressed as:
Area = (θ/360º) × πr²
Where θ is the sector angle in degrees, and r is the radius of the circle.
From the image:
Measure of central angle θ = 60 degrees
Radius r = 8 units
Plug these values into the above formula and solve for the area:
Area = (θ/360º) × πr²
Area = (60°/360°) × π × 8²
Area = 1/6 × π × 64
Area = 1/6 × π × 64
Area = 33.5 sqaure units.
Therefore, the area is approximately 33.5 sqaure units.
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pls help
Factor out the GCF
16x - 48
Answer:
16
Step-by-step explanation:
the greatest common factor of 16 and 48 is 16
Factors for 16: 1, 2, 4, 8, and 16.
Factors for 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
I need help I been asking for hours pls help
Answer:
419 ft
Step-by-step explanation:
1063 ft is about 324002.4 mm
324002.4/477 to get the scale ratio. Which is 679.25:1
I am halfway through the problem and notice I should have converted mm to ft and not the other way around. It gives the same answer it just takes an extra step.
188*679.25=127699mm for one side.
Convert that back to ft and you get 418.959 which would just be 419 ft
Answer:
419 ft
Step-by-step explanation:
convert ft to mm: 1063 ft ≈ 324002.4 mm (I just used g00gle)
324002.4/477 ≈ 679.25, the real Eiffel tower is ≈ 679.25 times larger
188 x 679.25 = 127699 mm
convert mm to ft: 127699 mm ≈ 418.96 ft ≈ 419 ft
The Spanish club sold hot pretzels as a fundraiser. The pretzels normally sold for $2.00, but near the end of the sale the price was reduced by 25%. What was the new price for a hot pretzel?
who ever complete this gets brainlist and i WILL remember to give you
Answer:
1. 6
2. There will be two middle numbers. 18 and 4. Add them
(18+4)=22
Now divide by 2
(22/2)
Ans. 11
3. There will be two middle numbers. 50 and 30. Add them
(50+30)=70
Now divide by 2
(70/2)
Ans. 35
4. 26
5. 76
6. There will be two middle numbers. 11 and 10. Add them
(11+10)=21
Now divide by 2
(21/2)
Ans. 10.5
7. There will be two middle numbers. 5 and 1. Add them
(5+1)=6
Now divide by 2
(6/2)
Ans. 3
8. There will be two middle numbers. 2 and 4. Add them
(2+4)=6
Now divide by 2
(6/2)
Ans. 3
║
((7, 15, 12, 9, 7))
Mean: =50/5 Ans. 10
Mode: = (7, 7, 9, 12, 15) Ans. 7
Median: Ans. 12
((10, 8, 4, 5, 8, 5, 7))
Mean: =47/7 Ans. 6.71
Mode: = (4 , 5 , 5 , 7 , 8 , 8 , 10) Ans. 5 and 8
Median: (5+8) =13/2 Ans. 6.5
((4 , 8 , 11, 11, 12, 12, 12, 12,)
Mean: 82/8 Ans. 10.25
Mode: Ans. 12
Median= (11+12)= 23/2 Ans. 11.5
((7, 5, 11, 7, 12, 8, 6, 9, 7))
Mean: 72/9 Ans. 8
Mode: (5, 6, 7, 7, 7, 8, 9, 11, 12) Ans. 7
Median: Ans. 12
What is the greatest common factor of 54x^2 will give brainly
27 well if you're asking that then
(t/f) if 0 is an eigenvalue of a, then a is invertible.
The matrix cannot be inverted if any eigenvalue is 0, which also means that the determinant is zero. This suggests a linear dependence between the columns of A. As a result, A is not of full rank and is not invertible.
What does "linearly dependent" mean?
A set's ability to have at least one linear combination of its components equal to zero when the coefficients are taken from another provided set and at least one of those coefficients is not equal to zero.
This feature applies to matrices or vectors. adjective that depends on linearity.
What does it mean to be linearly dependent?
A group of non-zero vectors is said to be linearly dependent if at least one of them can be expressed as a linear combination of the others.
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in utah, if not directly involved in diving activity, motorized vessels and personal watercraft (pwcs) must remain what distance from diver down flags?
In Utah, if not directly involved in diving activity, motorized vessels and personal watercraft (PWCs) must remain 150 feet from the diver down flags.
The diver down flag is a banner that is used by vessels to indicate that divers are in the water. It is typically a red flag with a white diagonal stripe that is used to indicate the presence of divers in the water. The flag must be at least 12 x 12 inches in size and must be clearly visible from all directions. When the flag is raised, boaters are expected to keep a safe distance from the divers and to take extra precautions to ensure that they do not pose a hazard to the divers.The diver down flag should be used whenever there are divers in the water. This includes scuba divers, free divers, and anyone else who is swimming or diving underwater. The flag should be raised before the divers enter the water and should be lowered when they exit the water. In addition to the flag, divers are required to use other means of indicating their presence in the water, such as lights and audible signals, to ensure that boaters can see and hear them. Motorized vessels and personal watercraft (PWCs) must remain at least 150 feet from the diver-down flag. This means that they must keep a safe distance from the divers and take extra precautions to ensure that they do not pose a hazard to the divers. If a motorized vessel or PWC is directly involved in the diving activity, such as transporting divers to and from the dive site, they may operate closer to the flag, but they must still maintain a safe distance from the divers at all times.
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a class of 20 students is divided into two groups of 10 and then each group is lined up in a particular order. how many ways are there to divide the class and line up the groups?
There are ²⁰С₁₀ × 10! × 10! ways to divide the class and line up the groups.
Number of students in the class = 20
Selection of group one = ²⁰С₁₀ ways
Selection of group two = 1 way
Number of ways to arrange 10 students in a group = 10!
So, Total number of ways = ²⁰С₁₀ × 10! × 10! ways.
Hence there are ²⁰С₁₀ × 10! × 10! ways to divide the class and line up the groups.
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decide whether inductive reasoning or deductive reasoning is used to reach the conclusion: "what goes up must come down. the ball went up. it will come down."
The statement ""what goes up must come down. the ball went up. it will come down." can be reached through a deductive reasoning.
What is a deductive reasoning?The mental process of forming deductive deductions is known as deductive reasoning. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if the premises cannot be true while the conclusion is false.
The primary distinction between inductive and deductive thinking is that inductive reasoning seeks to develop a hypothesis, whereas deductive reasoning seeks to test an existing theory. Inductive thinking proceeds from individual observations to broad generalizations, whereas deductive reasoning proceeds in the other direction.
In conclusion, the correct option based on the information is a deductive reasoning.
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Please answer each part in almost 500 words.
a. Suppose Jet Airways wants to ascertain the image it has in the minds of its patrons. Construct a seven-item and semantic differential scale to measure the perceived image of the airlines. Make sure that the seven under each format correspond to the same seven dimensions.
b) Find a technical and business report from your library or on the internet and examine the contents of the reports against what has been discussed in the chapter. What deviations did you find from the stated structure? What you think could have been the reason for this?
a) Part A: The perceived image of Jet Airways
Jet Airways is one of the well-known airlines in India. It is headquartered in Mumbai and operates both domestic and international flights. The perceived image of Jet Airways in the minds of its customers is important to the success of the airline. Perceived image refers to what the customers think about the airline, and this is important for customer loyalty and retention.
Constructing a seven-item and semantic differential scale to measure the perceived image of Jet Airways would be as follows:
1. Reliability: how reliable is Jet Airways on a scale of 1 to 7 (with 1 being extremely unreliable and 7 being extremely reliable)
2. Responsiveness: how responsive is Jet Airways to the needs of its customers on a scale of 1 to 7 (with 1 being extremely unresponsive and 7 being extremely responsive)
3. Empathy: how empathetic is Jet Airways to the concerns of its customers on a scale of 1 to 7 (with 1 being extremely unempathetic and 7 being extremely empathetic)
4. Assurance: how assured do you feel when you travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely unassured and 7 being extremely assured)
5. Tangibles: how do you rate the physical appearance of Jet Airways on a scale of 1 to 7 (with 1 being extremely poor and 7 being extremely good)
6. Price: how do you rate the price of Jet Airways on a scale of 1 to 7 (with 1 being extremely expensive and 7 being extremely affordable)
7. Convenience: how convenient is it to travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely inconvenient and 7 being extremely convenient)
The above semantic differential scale helps in measuring the perceived image of Jet Airways. The seven-item and semantic differential scale ensure that the seven under each format correspond to the same seven dimensions.
By answering each question, the customers can rate Jet Airways on various factors, and the airline can use this feedback to improve its service and overall image.
b) Part B:
Examination of a technical and business report
The structure of a technical and business report includes a title page, abstract, table of contents, introduction, main body, conclusion, and references. An examination of a technical and business report from the internet reveals some deviations from the stated structure. One of the significant deviations is the absence of the abstract section. The abstract provides a brief summary of the report, including the purpose, methodology, and findings. The report from the internet did not have an abstract section, and this deviation could be due to the report being a short summary of a more extensive study.
The report from the internet did not have a separate conclusion section. The conclusion is important as it summarizes the findings of the study and provides recommendations for further research. The report from the internet integrated the findings and recommendations into the main body of the report, and this deviation could be due to the length of the report.
Another deviation is the lack of a reference section. The reference section is essential as it provides the sources used in the study. The report from the internet did not have a reference section, and this deviation could be due to the type of report and the fact that it was not a formal research report.
In conclusion, technical and business reports should follow a specific structure to ensure that they are clear, concise, and easily understood. Deviations from the stated structure can affect the quality and accuracy of the report. The deviations in the report from the internet could be due to the length, type, and purpose of the report.
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when 40 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
Answer:
5
Step-by-step explanation:
Let x be that number.
(x^2) - 40 = 3x
x^2 - 40 = 3x
x*2-3x-40=0
(x-5)(x+8)=0
x=5
What is a correct expansion of (4x+1)(2x^2-2)
A. 4x*2x^2+4x*(-2)+1*2x^2+1*(-2)
B. 4x*2x^2+4x*(-2)+1*4x+1*(-2)
C. 4x*2x^2+4x*(1)+1*2x^2+1*(-2)
Answer: B. 4x*2x^2+4x*(-2)+1*4x+1*(-2)
Step-by-step explanation: Hope this help :D
Answer:
A. 4x * 2x^2 + 4x * (-2) + 1 * 2x^2 + 1 * (-2)
Step-by-step explanation:
We have the binomial (4x + 1)(2x^2 - 2) and are asked to see how it looks like expanded.
When solving binomials, we need to follow the FOIL method :
First - First number in first parenthesis multiplied by first number in second parenthesis
Outer - First number in first parenthesis multiplied by second number in second parenthesis
Inner - Second number in first parenthesis multiplied by first number in second parenthesis
Last - Second number in first parenthesis multiplied by second number in second parenthesis
If we follow the definitions given, we can find our correct answer and also see where all the other answers mess up at :
A. 4x*2x^2+4x*(-2)+1*2x^2+1*(-2)
This follows FOIL entirely from start to finish.
B. 4x*2x^2+4x*(-2)+1*4x+1*(-2)
This did not follow the Inner part of FOIL.
C. 4x*2x^2+4x*(1)+1*2x^2+1*(-2)
This did not follow the Outer part of FOIL.
Vertical angulation: Group of answer choices remains the same whether you are using the paralleling or the bisecting technique. is generally greater for images taken with the paralleling technique than it is for images taken with the bisecting technique. refers to the side-to-side plane. differs according to whether the paralleling or bisecting technique is being used.
Vertical angulation refers to the angle at which the x-ray beam is directed when taking dental radiographs. It is an important factor in obtaining clear and accurate images.
In both the paralleling and bisecting techniques, the group of answer choices remains the same. However, the vertical angulation is generally greater for images taken with the paralleling technique compared to the bisecting technique.
This is because the paralleling technique requires the x-ray beam to be directed more vertically in order to capture the entire tooth structure on the film. On the other hand, the bisecting technique involves angling the x-ray beam downward to intersect the imaginary bisector between the long axis of the tooth and the film.
Therefore, the vertical angulation differs depending on which technique is being used.
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Help me pls
What is the students error?
Answer:
first one;)
Step-by-step explanation:
Cuál es el valor principal de sin−1(1)?
The maximum value of the sine function is 1, the angle corresponding to sin^(-1)(1) is π/2 or 90 degrees.
The principal value of sin^(-1)(1) is π/2 or 90 degrees.
The function sin^(-1)(x), also known as arcsin(x) or inverse sine, represents the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is 1.
Since the sine function oscillates between -1 and 1, the angle corresponding to sin^(-1)(1) is the maximum value where the sine is equal to 1.
This occurs at π/2 or 90 degrees, making it the principal value for sin^(-1)(1).
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