Answer:
It returns the angle whose cosine is a given number.
Step-by-step explanation:
For every trigonometry function, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. (On some calculators the arccos button may be labeled arccos, or sometimes cos-1.) So the inverse of cos is arccos etc. When we see "arccos x", we understand it as "the angle whose cosine is x"
cos30 = 0.866 Means: The cosine of 30 degrees is 0.866
arccos 0.866 = 30 Means: The angle whose cosine is 0.866 is 30 degrees.
Use arccos when you know the cosine of an angle and want to know the actual angle.
Mary want to buy a bookcae to hold all of her 138 book. Bookcae A ha 4 helve and can hold 35 book on each helf. Bookcae B ha 5 helve and can hold 26 book on each helf. Which bookcae hould he buy?Bookcae A or bookcae B?
Answer:
Bookcase A
Step-by-step explanation:
Bookcase A
1 half = 35 book
4 half = 140 books
So, bookcase A can hold 140 books
Bookcase B
1 half = 26 books
5 half = 130 books
So, bookcase B can hold 130 books
So, Mary should buy bookcase A
Answer:
Bookcase A is the answer
Step-by-step explanation:
Mary has 138 books
Bookcase A = 4 shelves holds 35 books per shelf
= 4 * 35=140
Bookcase B = 5 shelves holds 26 books per shelf
= 5 * 26=130
He should buy Bookcase A, it has enough space for his books
A population P is growing at the rate of 9% each year and the initial population is P0. Find, as a multiple of P0, the rate of change of population at time t=T when the population has doubled from its initial time?
(Explain why, thank you!
The solution is Option B.
The rate of change of population at time t = T when the population has doubled from its initial time is P' = 2P₀ ln ( 1.09 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The formula for the population at time t is
P ( t ) = P₀ ( 1 + 9/100 )^t
P ( t ) = P₀ ( 1 + 0.09 )^t
P ( t ) = P₀ ( 1.09 )^t
Now , when population is doubled from the initial population ,
P ( t ) = 2P₀
Substituting the values in the equation , we get
2P₀ = P₀ ( 1.09 )^t
Taking logarithm on both sides of the equation , we get
log ( 2 ) = t x log ( 1.09 )
Divide by log ( 1.09 ) on both sides of the equation , we get
t = log ( 2 ) / log ( 1.09 )
To find the rate of change , take the derivative
P'( t ) = P₀ ( 1.09 )^t ln ( 1.09 )
Now , we find P'(log(2)/log(1.09))
So , the equation will be
P′ ( log( 2 ) / log( 1.09 ) ) = 2P₀ln( 1.09 )
Hence , the equation will be A = 2P₀ln( 1.09 )
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What is the median of 1 to 99?
The median of 1 to 99 is 50.
The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.
Median= 99+1/2 = 100/2 = 50th term, which in this case is 50.
Thus, the median of 1 to 99 is 50.
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Write an equation for nth 45, 30, 15, 0 sequences and series
Answer:
a_n = -15 (n - 4) (for all terms given)
Step-by-step explanation:
a_n = -15 (n - 4) (for all terms given)
45, 30, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, ...
To search for the nth sequence, replace n with the desired term.
what is simplify 4^-4
Answer:
1/256
Step-by-step explanation:
-4 times -4 times -4 times -4 = 256
A negative exponent means it's a fraction!
So, the answer is 1/256
answer :
1/256
steps:
negative exponent means it's a fraction
4^-4 =
1/4^4 :
4^4 =
4 * 4 * 4 * 4 =
256
again negative exponent means it's a fraction so
1/256
What are the factors of X² 11x 42?
Therefore , the solution to the problem is factors of the given equation comes out be (x-14)(x+3).
Describe the equation.By joining two expressions with the equivalent sign, a mathematical statement known as an equation is produced. The equation 3x - 5 = 17 is an illustration. By solving this equation, we can determine that the value of the variable x is 4.
Here,
In the given question the equation is given as [tex]x^{2}[/tex]-11x-42.
Given polynomial : [tex]x^{2}[/tex]-11x-42
Thus we factorise the given equation
First:
=> [tex]x^{2}[/tex]-14x+3x-42
Second:
=> x(x-14)+3(x-14)
=> (x-14)(x+3)
thus factors comes out to be
(x-14) and (x+3)
Therefore , the solution to the problem is factors of the given equation comes out be (x-14)(x+3).
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What is AAS and AES?
Answer:
⭐ AAS = Angle-Angle-Side
⭐ I don't know what AES is.
Step-by-step explanation:
AAS is a triangle congruence statement you use to say that 2 triangles are congruent ≅ (the same).
Here's how to determine if 2 triangles are congruent by AAS:
One of their corresponding side lengths is congruentOne of their corresponding angles is congruentAnother one of their corresponding angles is congruentOne of the corresponding, congruent angles is in between another corresponding, congruent angle and a corresponding, congruent side lengthCongruent side lengths and congruent angles are often denoted by tick marks.
⭐ Example:
Hiro painted his room. After 3 33 hours of painting at a rate of 8 88 square meters per hour, he had 28 2828 square meters left to paint. Let y yy represent the area (in square meters) left to paint after x xx hours.
The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.
The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.
Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.
Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.
We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:
28 = A₀ - 8 x 3
28 = A₀ - 24
A₀ = 52
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The complete question:
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?
solve | x + 4 | = -6
Answer:
Option D. No solution
Step-by-step explanation:
There is no value of x that makes the equation be true since an absolute value can never be negative.
No solution
Answer:
OptionD)
Step-by-step explanation:
[tex]x + 4 = -6\\x=-6-4\\x=-10\\[/tex]
Since there is no options with -10 only
The correct answer is OptionD)
the w10×15 cantilevered beam is made of a-36 steel and is subjected to the loading shown
For a w10×15 cantilevered beam of A - 36 steel subjected to loading as in the attached image, slope at B is 0.0042rad and displacement at B is 0.034ft.
For w10×15, moment of inertia I = 68.9in⁴ and for A - 36 steel, Young's modulus E = 29e3 ksi
Slope at B
θB = P₂x³/ (2EI) + P₁l³/ (2EI)
θB = (5 × 6³ + 9 × 12³)/ (2 × 29 × 10³ × 68.9)
θB = 0.0042rad
Displacement at B
yB = P₂x³(3l - x)/ (6EI) + P₁l³(3l - l)/ (6EI)
yB = ( 5 × 6³ × (3 × 12 - 6) + 9 × 12³ × 2 × 12)/ (6 × 29 × 10³ × 68.9)
yB = 0.034ft
--The question is incomplete, answering to the question below--
"The W10×15 cantilevered beam is made of A - 36 steel and is subjected to the loading shown.
1. Determine the displacement at B, if P1 = 9kip and P2 = 5kip
2. Determine the slope at B, if P1 = 9kip and P2 = 5kip"
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What is the range of this absolute value function? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line rises through (negative 10, negative 3), (negative 7, 0) to (0, 7), and then it falls through (7, 0), and (10, negative 3). A. -∞ < y ≤ 0 B. 0 ≤ y < ∞ C. -∞ < y ≤ 7 D. -∞ < y < ∞
The range is an absolute value functions is
B. 0 ≤ y < ∞What are absolute value functions?A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function.
Remember that a number's distance from 0 on the number line represents its absolute value.
A number can never have a negative absolute value. hence the negative values will never be in the range
This makes the range to start possibly from zero, from the graph explained 0 is among the values that are in the range
Considering that absolute values are non zero and option B is the only option that does not have a negative value. This is the best option
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Answer:
The range is an absolute value functions is
B. 0 ≤ y < ∞
Step-by-step explanation:
A right triangle has side lengths of 15 in, 12 in, and 9 in. it is dilated by a scale factor and has new side lengths on 5 in, 4in, and 3 in. what was the scale factor?
Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.
For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 35°, and a = 10. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = CA / sin B
The measure of the third angle is given as,
∠A + ∠B + ∠C = 180°
35° + 90° + ∠C = 180°
∠C = 55°
Then the measure of the side c (AB) is calculated as,
AB / sin C = BC / sin A
c / sin 55° = 10 / sin 90°
c = 8.2
Then the measure of the side b (AB) is calculated as,
AC / sin B = BC / sin A
b / sin 35° = 10 / sin 90°
b = 5.7
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How do you write more than 50?
More than 50 in mathematical expression is written as >50.
Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.
The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].
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Does 2 equal square root?
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
How to define square root ?The outcome of multiplying a number by itself produces the original number, which is the square root of that number. Squares and square roots are a few of examples of exponents. Try to visualize nine. Furthermore, this can be written as 3x3.
Here,
A quadratic function is one where an equation has two roots.
A quadratic function's two roots are equal if D=0.
D (discriminant) = 0 such that b24ac = 0 is needed in order for the roots of a polynomial function to be equal.
As a result, if an equation has two roots, a quadratic function is what it is.
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Which equation has an X intercept of 5 and a Y intercept of 10?
C) 2x+y=10 is the line has an X intercept of 5 and Y intercept of 10
To find the eqaution of line whose X intercept and Y intercept is given we will use line intercept form of line
The equation of line with A units of X intercept and B units of
Y intersect is given by:
[tex]\frac{x}{A} + \frac{y}{B} =1[/tex] ----(i)
given that A= 5 (X intercept) and B= 10 (Y intercept)
so equation (i) reduces to
[tex]\frac{x}{5}+\frac{y}{10} =1[/tex]
so 2x + y = 1*10
so the equation of the line is 2x+y=10
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Complete question:
Which equation has an X intercept of 5 and a Y intercept of 10?
A) 3x+2y=10
B) 5x+7y=2
C) 2x+y=10
D) 11x+7y=9
What are examples of inverse relationships?
Examples of inverse relationships are : As the speed of the car increases the time taken to cover certain distance decreases and More buses on the road less space on the road.
inverse relationships
An inverse relationship, also known as a negative relationship, is a contrary correlation between two variables such that they move in opposite directions. For example, we have two variables X and Y. As X increases, Y decreases and as Y increases, X decreases .The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.
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How do you find the height of a pyramid when given the volume and area?
The height of pyramid when given the volume and area is estimated as; H = 3 * V / a²
Define the meaning of the term pyramid?A solid object having four flat, triangular sides that slope inward and come together to form a point at the top, as well as a flat, square base. A triangular-shaped pile of objects is sometimes known as a pyramid: By balancing on each other's shoulders, the acrobats created a pyramid.How is the height of the a square pyramid determined?
To find the base area, first square the base edge.Next, divide the base area by the known volume.Finally, divide the result by three to determine the height of the pyramid.H = 3 * V / A_b
In which,
H - height of pyramid;
V- volume of pyramid
A_b - base area of pyramid; A_b = a²,
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Giving 25 points!!!!!! PLEASE HELP
describe the correlation for this scatter plot
Answer: Strong Negative Correlation
Step-by-step explanation:
How many buses do you need for 500 people if each bus holds 40 people?
Answer:
13
Step-by-step explanation:
Divide 500 by 40 to find the amount of buses you need
500 ÷ 40 = 12.5
BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people
you'll need 13 buses
Answer:
13 buses
Step-by-step explanation:
12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.
How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation?
The equation of line in slope intercept form passing through (-5,-2) and parallel to y = -2x+1 is y = -2x -12 .
The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .
the required line is parallel to the line with equation ⇒ y = -2x+1 ,
on comparing it with slope intercept form of line ,
we get the slope(m) as "-2" .
the required line is passing through (-5,-2).
substituting the values , we get ;
-2 = (-2)(-5) + c ,
-2 = 10 + c ,
c = -10 -2
c = -12 .
So , the equation is ⇒ y = -2x -12 .
Therefore , the slope intercept form of the required line is y = -2x -12 .
The given question is incomplete , the complete question is
How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ? the point is (-5,-2); and is parallel to y = -2x + 1 .
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How do you read mean and SD?
The variability in your data collection is measured by the standard deviation. It reveals the average distance between each score and the mean.
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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What is the mean of 9 and 25?
Answer:
17
Step-by-step explanation:
(9+25)/2 = 34/2 = 17
when finding a mean, you have to add all the numbers and divide the sum by the number of values given.
The length of a
rectangle is 5 ft more than twice its width. The
area of the rectangle
is 33 ft^2. Find the dimensions of the rectangle.
The dimensions of the rectangle is length = 5ft and width = 3ft
Define System of equation
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Let,
x = length of rectangle
y = width of rectangle
Next, set up system of equation
We have given, the length of a rectangle is 5 ft more than twice its width.
x = 2y + 5 --------(a)
Next, The area of the rectangle is 33 ft²
xy = 33 ----------(b)
x = 33/y
substitute the value of x in eq(a)
x = 2y + 5
33/y = 2y + 5
33 = 2y² + 5y
2y² + 5y - 33 = 0
Factor it,
2y² + 11y - 6y - 33 = 0
y( 2y + 11) - 3( 2y + 11) = 0
(y - 3) (2y + 11) = 0
Split the values,
y - 3 = 0 and 2y + 11 = 0
y = 3 and y = -11/2 (ignore this as width cannot be -ve)
Substitute y = 3 in eq(b)
x * 3 = 33
x = 11
So, we get
length = 11 ft and width = 3 ft
Hence, the dimensions of the rectangle is length = 5ft and width = 3ft
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What is the difference between ≥ and ≤?
The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).
What is Inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way. By comparing the sizes of two numbers on the number line, it is most frequently utilized. Different types of inequalities are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
A is not equal to b in either situation. These relationships are referred to as stringent inequalities, which means that an is strictly less than or strictly bigger than b. Equivalence is not included.
There are two kinds of inequality relations that are not strict, in contrast to strict inequalities:
When something is written with an an or b, it signifies that.
A is smaller than or equal to b when a notation like a ≤ b is used (or, equivalently, at most b, or not greater than b).
A greater or equal value for a indicates that b is greater than it (or, equivalently, at least b, or not less than b).
The symbol for "greater than" that is divided in half by a slash, "not," can also be used to express the connection not greater than. The same applies to and not less than and a b.
Hence, The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).
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It signifies that the supplied variable or number must have a value that is larger than or equal to the specified limit. It is the opposite of less than or equal to.
What is Greater and Lower than equal to function ?The phrase "more than or equal to" denotes that the variable is either greater than or equal to a specific value. When a quantity is bigger than another, the phrase "more than" is used to indicate this. Two quantities are said to be equal when the phrase "is equal to" is used. It is possible for the quantity or amount value limit to be equal to or larger than the stated limit when these phrases are combined to form the new term Greater Than Or Equal To.
The phrase "less than or equal to" denotes that a variable is either less than or equal to another quantity, number, or variable. Other ways to say "less than or equal to" include at most, no more than, a maximum of, and not surpassing.
Inequalities like less than or equal to and greater than or equal to are represented in a different way on a number line. To denote these, we use the closed circle to mark the limit value and point the arrow towards the given condition of inequality.
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What are the 4 methods of solving linear equations?
Systems of linear equations in two variables can be solved in one of four ways: by graphing; by the substitution approach; or by the elimination method and by matrix approach.
Define linear equation.A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." Because a straight line emerges when we attempt to display the graph of the provided linear function, a linear equation is known as linear.
Given,
The four methods of solving linear equations are:
The Substitution Method
The Graphing Method.
The Addition Method, also known as the Linear Combination Method, and the Elimination Method.
The Matrix Approach
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Why is 2 root 2 equal to root 2?
Therefore , the given expression of this problem of square root
2√2 not equal to √2.
What is square root?The value that results from multiplying the square root of an integer by itself is the number.
Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.
Here,
In this case, the mathematical symbol for Root 2 is 2.
Root 2 then multiplied by Root 2.
√2 + √2 = 2√2
If we take the estimated value of 2 = 1.4142
Then
=> 2√2 = 1.4142 x 2
=> 2.8284 (approximately)
Please take note that 2 is an irrational number.
Alternatively, root2* root 2
√2 * √2 = 2
Because 2 is just the square root of 2,
Therefore,
what happens when root 2 + root 2 and root2 root 2 are different
2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)
Therefore , the given expression of this problem of square root
2√2 not equal to √2.'
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What does it mean when numbers are closed?
Whole numbers are closed under addition and multiplication. If we add and multiply any two whole numbers, the result will be a whole number.
What are Whole numbers ?
The numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Whereas Integer: A counting number, zero, or the negative.
If we add any two whole numbers, the result will be a whole number. For example, 2 + 4 = 6 and 6 is a whole number.
Therefore, whole numbers are closed under addition.
If we multiply any two whole numbers, the result will be a whole number. For example, 2 × 4 = 8 and 8 is a whole number.
Therefore, whole numbers are closed under multiplication.
Also , Whole numbers are not closed under Subtraction and division.
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Consider a computer that uses 5 bits to represent positive and negative integers, using 1 bit for the sign and 4 bits for the actual value. Which of the following operations would result in integer overflow?
7+1
12 + 3
6 + 9
8×2
2×4
1+15
The operation 1+15 would result in integer overflow, because the result of this operation (16) cannot be represented with 4 bits.
What is integer overflow ?Integer overflow occurs when an arithmetic operation on two integers produces a result that is too large to be represented within the allocated number of bits. In the case of the computer described, integer overflow would occur if the result of an operation had a value that is too large to be represented with 4 bits.In this case, the operations 7+1, 12+3, 6+9, 82, and 24 would not result in integer overflow, because the results of these operations (8, 15, 15, 16, and 8, respectively) can be represented with 4 bits. However, the operation 1+15 would result in integer overflow, because the result of this operation (16) cannot be represented with 4 bits.To learn more about arithmetic operation refer :
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Is i squared negative 1 or 1?
The value of "i" squared results in:
(-1) = i²
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
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