An integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
What is integral?This is the value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.
Integral is a term derived form the word integration. Integration in calculus is the opposite of differentiation
Integration is used to get the whole by combining combine slices or smaller portions.
Finding areas, volumes, central points, and many other important things may be done with integration. However, it is simplest to begin by calculating the distance between a function and the x-axis.
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What is the odd integers from 1 to 100?
99
Step-by-step explanation:There are a total of 50 odd numbers between 1 to 100.
1 is the smallest, odd number:
The sum of all the odd numbers from 1 to 100 is 2500.
The average or mean of all odd numbers 1 to 100 is 50.
Soultion:
[tex]\boxed{ 3 + 2 = 5, 5 + 2 = 7, 7 + 2 = 9}[/tex]
The last number in the chart of odd numbers 1 to 100 given below is 99, as, if we add 2 to 99, we will get 101 which is greater than 100. So, 99 is the last odd number in the list of odd numbers from 1 to 100.
Therefore, the odd integers from 1 to 100 is 99
A picture is given below of all the odd numbers of 1 to 100:
How will you know if a function increases and decreases?
A function increases if the output value of function increases on increasing the input value and the function decreses if the output value of function decreases on increasing the input value
As we know a function is nothing but a relation between input values and output values where each input has exactly one output.
Consider a function y = f(x)
For a given function if the value of y increases on increasing the value of x, then the function is an increasing function
If the y-value decreases on increasing the value of x, then the function is a decreasing function.
Another method is that if we need to determine whether a function f(x) is increasing or decreasing at point 'a'.
If a function is differentiable on an open interval, we calculate the derivative of function f(x)
If the derivative f′(x) > 0 on an open interval, then function f(x) is increasing on that interval.
If the derivative f′(x) < 0 on an open interval, then function f(x) is decreasing on that interval.
Therefore, if the output value of function increases on increasing the input value then the function is an increasing function and if the output value of function decreases on increasing the input value then the function is an decreasing function.
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A number n is such that when divided by 3,7,11 or 13,the remainder is always one.Find the number n
Step-by-step explanation:
(3x7x11x13)+1=3004
n=3004
What is the equivalent of 2 by 7?
Answer:
in ratio 4:14
Step-by-step explanation:
When a prism and a pyramid have the same height and the same base the volume of the prism is greater than the pyramid?
Yes, the given statement is true the volume of the prism is greater than the volume of the pyramid when they have same base and same height.
As given in the question,
Formula required to calculate the volume of the pyramid and volume of the prism is given by :
Volume of a pyramid = (1/3) × (base area )× ( height )
Volume of a prism = (Base area) × (height)
When the base and height of the pyramid is same as that of the base and height of the prism then
Volume of the pyramid = ( 1/3) × ( Base area × height )
⇒Volume of the pyramid = ( 1/3) × ( Volume of the prism )
⇒Volume of the prism = 3 × ( Volume of the pyramid )
⇒Volume of the prism > Volume of the pyramid
Therefore, the volume of the prism is greater than the volume of pyramid is a true statement.
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How do you find the discontinuity point of a function?
discontinuity point of a function is a point at which the function is not continuous. There are three types of discontinuities: removable, jump, and essential.
A removable discontinuity is a point at which the function is not defined, but the limit of the function as x approaches the discontinuity point from both sides is equal to a finite value.
A jump discontinuity is a point at which the function is defined, but the limit of the function as x approaches the discontinuity point from both sides is not equal.
An essential discontinuity is a point at which the function is not defined and the limit of the function as x approaches the discontinuity point from both sides is infinite or does not exist.
To find the discontinuity points of a function, you can:
Plot the function on a graph and look for any breaks or gaps in the graph.
Use the algebraic definition of continuity to determine whether the function is continuous at a given point.
Use the limit definition of continuity to determine whether the function is continuous at a given point.
Use a computer algebra system (CAS) to find the discontinuity points of a function.
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A point where the function is not defined and the limit of the function as x approaches the discontinuity point from both sides is infinite or does not exist is referred to as an important discontinuity.
A function's discontinuity points can be located by:
Plot the function on a graph and check the graph for any splits or gaps.
To ascertain whether the function is continuous at a specific point, use the algebraic notion of continuity.
How many sides are equal in quadrilateral?
Therefore , for a regular polygon it must have four sides equal to be called as quadrilateral .
What is quadrilateral?A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. It is made up of four linked non-collinear points. The sum of the internal angles of quadrilaterals is always 360 degrees..
Here,
Each of them has four vertices.
Each side has four sides.
360 degrees is the sum of all interior angles.
Two diagonals are present.
There are regular and irregular quadrilaterals.
An ordinary quadrilateral must have four equal sides, four equal angles, and diagonals that cross one another.
Therefore , for a regular polygon it must have four sides equal to be called as quadrilateral .
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Lea wants to make two pillows for her new couch. She needs 314 square yards of fabric for the first pillow and 112 square yards of fabric for the second pillow. Lea wants to know how much fabric she will have to buy for both pillows. Which expression represents the total number of square yards of fabric she needs for both pillows?.
The equation for the total square yards of cloth she needs for both pillows is 314+112=426.
The total number of square yards of fabric Lea needs for both pillows is the sum of the fabric needed for the first pillow and the fabric needed for the second pillow. This can be represented by the expression:
314 square yards + 112 square yards = 426 square yards
Therefore, the expression that represents the total number of square yards of fabric Lea needs for both pillows is:
314 + 112 = 426
This expression would simplify to 426 square yards. This expression uses the addition operator (+) to add the two quantities of fabric that Lea needs for each pillow. The result is the total number of square yards of fabric that she needs for both pillows.
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The figure shows a loading dock and a side view of an attached ramp, whose run is 12 feet and whose rise is 39 inches. Alex is wondering whether a long rectangular box can be stored underneath the ramp, as suggested by the dotted lines. The box is 2 feet tall and 5 feet long. Answer Alex’s question.
The box with a length 5 feet, and height of 2 feet can be stored underneath the ramp.
How to illustrate the dimension?Dimensions are the measure of the length, width and height of a given object. Yes, a rectangular box of length 5 feet and height 2 feet can be stored underneath the ramp. The measure of the sides of a given object is referred to as its dimensions.
This can be with respect to its length, width, and height.It has been given that the height of the ramp is 39 inches. But,12 inches = 1 feetSo that,39 inches = x feet
make x the subject of the formula to have;
x = [tex]\frac{39}{12}[/tex] = 3.25 feet
x = 3.25 feet
Thus the dimensions of the ramp are ;length = 12 feetheight = 3.25 feet
Therefore, the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.
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Is a length of two sides of an isosceles triangle is 4 cm and 10 cm then the length of the third side?
The length of the third side of an isosceles triangle with sides 4 cm and 10 cm is 10 cm.
We know that in an isosceles triangle, two sides are equal.
One side of the triangle is 4 cm and the other is 10 cm.
Let us consider the third side to be 4 cm,
then 4 cm + 4cm = 8 cm and it is not greater than the third side 10 cm.
Hence, the third side cannot be 4 cm.
Then the third side can be 10 cm,
therefore, 4 cm + 10 cm = 14 cm > 10cm
and 10 cm + 10 cm = 20 cm > 10 cm.
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if f(x) = 2 cot x and g(x) = sin x/2 what is the slope of the line joining (0.f(0)) and (pi,g(pi))?
wow help
The slope of the line joining (0, f(0)) and (π, g(π)) is given as follows:
Undefined.
How to obtain the slope of a linear function?The slope of a linear function, given two points, is given as the division of the change in y by the change in x.
The numeric values for these functions are given as follows:
f(0) = 2 cot(0) = 2 cos(0)/sin(0) = undefined, as sin(0) = 0, and we cannot divide by 0.g(π) = sin (π/2) = 1. the sine of 90 degrees is of one on the trigonometric circle.Hence the points are given as follows:
(0, undefined) and (π, 1).
The undefined point means that there is a vertical asymptote at x = 0, meaning that the change in y is undefined, and thus the slope of the function is also undefined.
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What is an example of surface area?
Answer:
The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all 6 faces added together.
Step-by-step explanation:
For the following images write a triangle congruence statement
Answer:
no images are available here
Determine the x -intercepts of the quadratic y = x 2 + 2 x − 15 by factoring.
Answer:
x-intercepts: x=3, -5
Step-by-step explanation:
y = x^2 + 2x − 15
y = x^2 + 5x - 3x − 15 ==> 5*(-3)=-15 and 5+(-3) = 5-3=2
y = x^2 + 5x - 3x − 15
y = x(x+5) - 3(x+5)
y = (x-3)(x+5)
x-3=0 ==> x=3
x+5=0 ==> x=-5
x-intercepts: x=3, -5
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In Fig R5, PT is a tangent to a circle ABCT. Find ATC
What is the y-intercept of 2x y =- 3?
The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).
What is the y-intercept of the given equation?The slope-intercept formula is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation in the question
2x - y = -3
First, we solve form for y and reorder in slope intercept form.
2x - y = -3
Subtract 2x from both sides
2x - 2x- y = -3 - 2x
- y = -3 - 2x
Divide each term by -1
y = 3 + 2x
Reorder in slope intercept form
y = 2x + 3
To find the y-intercept, replace x with zero and solve for y
y = 2(0) + 3
y = 3
Therefore, the y-intercept is 3.
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gail was participating in a market research study, and she was given 20 pairs of brands of shampoo and asked to indicate which pair is most similar, which is second most similar, and so forth until all pairs were ranked. which type of indirect measurement technique used to assess gail's evaluative criteria does this represent? perceptual mapping conjoint analysis evaluative mapping regression analysis factor analysis
Perceptual mapping conjoint analysis evaluative mapping regression analysis factor analysis.
Perceptual mapping or market mapping is a diagrammatic technique used by asset marketers that attempts to visually display the perceptions of customers or potential customers.
The positioning of a brand is influenced by customer perceptions rather than by those of businesses. For example, a business may feel it sells upmarket products of high quality, but if customers view the products as low quality, it is their views which will influence sales.
Perceptual maps, also known as market maps, usually have two dimensions but can be multi-dimensional or use multiple colours to add an extra variable.
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How do you tell if the inverse of a function is a function?
The process by which we can tell that if the inverse of the function is also a function is the Horizontal Line Test .
The Inverse of the function is defined as a function, which can reverse into another function.
If the graph of the function does not pass the Horizontal Line Test, then the graphed function's inverse will not be a function; and
If all horizontal lines cross at most one spot on the original graph, then the inverse of the function will be a function.
Therefore , the horizontal line test is used to check whether the inverse is a function or not .
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help asap please :)
which of the following expressions is equal to -x^2-36?
A: (-x+6i)(x-6i)
B: (x+6i)(x-6i)
C: (-x-6i)(x+6i)
D: (-x-6i)(x-6i)
[tex] - x {}^{2} - 36 \\ - (x {}^{2} + 36) \\ - (x {}^{2} - (6i) {}^{2} ) \\ - (x - 6i)(x + 6i) \\ ( - x + 6i)(x + 6i) \: \: or \: \: (x - 6i)( - x - 6i)[/tex]
Answer: DAnswer:
D: (-x-6i)(x-6i)
Step-by-step explanation:
(-x-6i) (x-6i)
-x^2 +6ix -6ix -36
-x^2 -36
So, D is the correct
Miss Meg's salary increases by $450 to $1760. Find her percentage salary increase.
__________________________________________________________
Hello! In this question, we are trying to find the percentage increase in Miss Meg's salary.
__________________________________________________________
Explanation:
From the question, we were provided the following information:
Miss Meg's initial salary was $450Miss Meg's salary increased to $1760With this information, we will be able to find the percentage of increase in her salary.
__________________________________________________________
Solve:
To find Miss Meg's percentage salary increase, let us first calculate the difference between her new and initial salary.
$1760 - $450 = $1310
We now know that Miss Meg's salary increased by $1310
Using this information, we can then get her salary increase amount and divide it by her original salary.
$1310 ÷ $450 = 2.9111
Multiply 2.911 by 100 to get the decimal into percentage form to show us the percentage salary increase.
2.911 × 100 = 291.11%
This means that Miss Meg's percentage salary increase was 291.11%
__________________________________________________________
Answer:
[tex]\boxed{291.11\%}[/tex]
__________________________________________________________
What is the equation of the line in point slope form containing the point (2, -7) and the slope of 4?
The required equation of the line is y = 4x - 15
The slope-intercept form of a line:
The slope-intercept form of a line is given by
y = mx + cWhere m = slope and c = y-intercept
Given slope of line m = 4 and the point is (2, -7)
As we know
The slope-intercept form is, y = mx + c --- (1)
From the given data, m = 4
Substitute m = 4 in (1)
=> y = 4x + c ---- (2)
Here (2) will pass through (2, -7)
(2) => - 7 = 4(2) + c
=> - 7 = 8 + c
=> c = - 8 - 7
=> c = - 15
=> (2) => y = 4x - 15
Therefore,
The required equation of the line is y = 4x - 15
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Which is an expression?
A. 4+3<9
B. 2 x 6
C. 2 + 5 = 5 + 2
D. 1 = 3 - 2
Answer:
B. 2 x 6
Step-by-step explanation:
The expression doesn't have an equal sign, so C and D is wrong.
So, the correct answer is B
B is correct answer.
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GEOMETRY HELP PLEASE!
Do rigid transformations result in congruent figures?
Numbers that undergo rigid transformations are congruent. Congruent can always require precise changes even if you could conceive of them as forms that "appear exactly the same."
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
∠X = ∠Q
And, also
XY = PQ
XZ = RQ
Therefore,
ΔXYZ ≅ ΔPQR
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37. Rajiv gets pocket money from his farther everyday. Out of pocket money, he saves ₹ 2.75 on 1st day and on each
succeeding day he increases his saving by 25 paise
(i) On which day he saves 7.75?
(ii) Find the difference between the amount saved by Rajiv on 25th day and 14th day.
(iii) Find the sum of amount saved on first 10 days.
Step-by-step explanation:
first we come up with a formulae:
Amount of money saved = 2.25+0.25x,
where x is the number of days
Answer:
1. 7.75 = 2.25 + 0.25(x)
7.75 - 2.25/ 0.25 = x
x = 20
2. 2.25+0.25(25) - 2.25 +0.25(14)
= 9.75
3. 2.25 + 0.25(10)
= 4.75
I hope i explained it well...
( i ) 21st day he saves 7.75
(ii) the difference between the amount saved by Rajiv on the 25th day and the 14th day is 2.75 rupees.
(iii) the sum of the amount saved in the first 10 days is 5 rupees.
Solution: (i) given: on each succeeding day he increases his saving by 25 paise.
2.75 rupees he saves on the first day
so = 2.75 +(0.25×20)
= 2.75+5
= 7.75 rupees
(ii) amount saved by Rajiv on the 25th day is:
= 2.75+(0.25×24)
= 2.75 + 6
= 8.75
amount saved by Rajiv on the 14th day is :
=2.75+(0.25×13)
=2.75+3.25
=6
therefore the difference between Rajiv' saving on the 25th day and the 14th day is : = 8.75-6
= 2.75
(iii) the sum of the amount saved in the first 10 days is :
= 2.75+(0.25 ×9)
= 2.75+2.25
= 5
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What is the multiplicity of 0?
The multiplicity of 0 is the number of times that 0 appears as a root of a polynomial equation.
In other words, it is the number of times that 0 is a solution to the equation. For example, the equation x^2 - 4x + 4 has two solutions, 0 and 4. The multiplicity of 0 is therefore 2, since 0 is a repeated solution.
If a polynomial equation has only one 0 as a solution, the multiplicity of 0 is 1. In some cases, a polynomial equation may have no 0s as a solution, in which case the multiplicity of 0 is 0.
In general, the multiplicity of a number is the number of times it appears as a solution to a polynomial equation. For example, the equation x^2 - 2x + 8 has two solutions, 2 and 4. The multiplicity of 2 is 1, since 2 appears only once as a solution, while the multiplicity of 4 is 2, since 4 appears twice as a solution.
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Match each radius to the exact area of the circle with the radius
Areas of Circles are for [tex]490.873m^2[/tex] radius 12.5m, [tex]706.858m^2[/tex] for radius 15m, [tex]1256.637m^2[/tex] for radius 20m.
What is area of a circle?The region encircled by a circle with radius r is known as πr² in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.
This formula, which was first discovered by Archimedes, can be derived by considering the circle as the boundary of a series of regular polygons. A regular polygon's area is equal to half its perimeter times the distance from its center to its sides. The equivalent formula, [tex]A=\frac{1}{2} *2\pi r*r[/tex] states that the area is equal to half the perimeter times the radius.
The limit for a circle is held by [tex]\pi r^{2}[/tex].
Calculation:Given;
1) r=12.5m
[tex]A=\pi r^2=\pi (12.5)^2=490.873m^2[/tex]
2) r=15m;
[tex]A=\pi r^2=\pi (15)^2=706.858m^2[/tex]
3) r=20m;
[tex]A=\pi r^2=\pi (20)^2=1256.637m^2[/tex]
Areas of Circles are for [tex]490.873m^2[/tex] radius 12.5m, [tex]706.858m^2[/tex] for radius 15m, [tex]1256.637m^2[/tex] for radius 20m.
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XYZW is a parallelogram with diagonals XZ and YW that intersect at point A. If XA=3x, ZA=5x-4, and YW = 10x, find the value of x and the length of Wa
Answer:
Step-by-step explanation:
AW=10
Step-by-step explanation:
In a parallelogram opposite sides are congruent meaning XA and AZ are congruent. YA and AW are congruent. So...
Solving for XA and AZ
XA=AZ
3m=5m-4
-2m=-4
m=2
If YW=10m then 10 x 2 = 20
20 divided by 2 = 10
What is the value of k if 1 2 is a root of the equation x2 kx 5 4 0?
The value of k in the quadratic equation is k = 2
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + kx - 5/4 = 0 be equation (1)
Now , on simplifying the equation , we get
If 1/2 is the root of given equation, then it will satisfy it.
So , when x = 1/2
( 1/2 )² + k ( 1/2 ) - 5/4 = 0
( 1/4 ) + k/2 - 5/4 = 0
k/2 - 1 = 0
Adding 1 on both sides of the equation , we get
k/2 = 1
Multiply by 2 on both sides of the equation , we get
k = 2
Therefore , the value of k is 2
Hence , the value of k in the equation is 2
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when milo went to register for classes at the last minute, the only classes left to take were seven math courses, five computer science courses, three statistics courses, and four science courses. he shut his eyes and picked one at random. find the probability that milo selected either a science course or a math course. express your answer as a reduced fraction. (the probability that milo will ever graduate using this strategy is an interesting question, too.)
The probability that Milo selected either a science course or a math course is 7/19 (or 0.3684210526).
Using this strategy, Milo has a 36.84% chance of selecting either a science or math course. This strategy is highly risky and unreliable, as there is no guarantee that Milo will select a course he is interested in or capable of taking. Additionally, Milo has a 63.16% chance of selecting a course he may not be interested in or able to take. There is no assurance that Milo will succeed with this strategy, and it could put him at a disadvantage in his academic career. As such, it is not recommended that Milo use this strategy to register for classes.
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