Limits are the rate of change of a function and also used in many other concepts such as continuity, differentiability and many other concepts in calculus.
In calculus, limits are used to study the behavior of a function as the input, or independent variable, approaches a specific value. The limit of a function at a particular point, say x = a, is defined as the value that the function approaches as the independent variable x gets arbitrarily close to a, but not necessarily equal to it.
The notation for a limit is usually represented as:
lim x->a f(x) = L
Which means as x approaches a, f(x) approaches L.
Properties of limits include:
1) The limit of a constant is equal to the constant.
2) The limit of a sum, difference, or product of functions is equal to the sum, difference, or product of their limits, respectively.
3) The limit of a function at a point is unique, if it exists.
Limits are an essential concept in calculus as they are used to define the derivative, which is the rate of change of a function and also used in many other concepts such as continuity, differentiability and many other concepts in calculus.
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Question 4 of 6 What larger conclusion can you reach by stringing together the sentences given below? If Henry goes to the library, he reads a book. D If Henry reads a book, he becomes smarter. 0 If Henry becomes smarter, he becomes happier. • If Henry becomes happier, the world is a better place. D A. If the world is a better place, Henry becomes smarter. B. If Henry goes to the library, the world is a better place. C. If the world is a better place, Henry goes to the library. D. If Henry goes to the library, he looks for books on tape. ← PREVIOUS
The conclusion we can reach is D. If Henry goes to the library, he looks for books on tape.
What is mathematical induction?
An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, If Henry goes to the library, he reads a book.
If Henry reads a book, he becomes smarter.
If Henry becomes smarter, he becomes happier.
If Henry becomes happier, the world is a better place.
Now, The only statement that is valid is If Henry goes to the library, he looks for books on tape.
As reading books only by henry won't make the world a better place.
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What are the side lengths of a 45 45 90 triangle are in the ratio 1 1 2?.
The ratios in a 45-45-90 triangle are as follows: 1 : 1 : 2 for angles (45 degrees: 45° : 90°); and. 1 : 1 : 2 on the sides (a: a : a√2).
The 45-45-90 triangle is what?In addition, the 45-45-90 triangle is an isosceles triangle, which indicates that each of its legs is the same length.
In a triangle, the trigonometric ratio Tan Theta is the same as opposite or adjacent.
A 45-45-90 triangle has side lengths that are 1: 1: .
As a result, tan45 has a value of 1.
How long are the sides of a 45-degree, 90-degree triangle?According to the 45 45 90 triangle theorem, special right triangles with sides whose lengths are in a special ratio of 1: 1 : 2 1:1:sqrt2 1:1:2, two angles of 45 degrees, and one right angle of 90 degrees.
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Give me the answer, please
3x° - 3° = 2x° + 13°
They are vertically opposite angle...
3x° - 2x° = 13° + 3°
1x = 16°
x = 16°
hence...the value of x is 16°
The perimeter of the figure is 90 centimeters. Solve for x.
x =
Answer:
32
Step-by-step explanation:
22+22+7+7+x=90
44 + 14 + x = 90
58 + x = 90
x = 90 - 58
x = 32
Solve for b.
29b = 290
Answer: 10
Hope this helps :)
Step-by-step explanation:
29b = 290
/29 /29
b = 10
Answer:
b = 10
Step-by-step explanation:
29b = 290
----- ------
29 29
b = 10
PLS HELP what is the slope
Y=_x +_
Answer:
it's a little blurry but i think the slope is 2/3 and the y-intercept is -2
Step-by-step explanation:
Answer in the simplest radical form if necessary (NO DECIMALS!). Copy and paste this symbol if needed: √
The value of x from the given triangle is 20 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given figure,
In ΔABT,
AB²=AT²+BT²
AB²=100+25
AB²=125
AB=√125
In ΔANT,
AN²=AT²+TN²
AN²=100+x²
AN=√100+x²
In ΔABN,
BN²=AB²+AN²
(5+x)²=125+100+x²
25+10x+x²=125+100+x²
10x=200
x=20 units
Therefore, the value of x from the given triangle is 20 units.
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What i the eaiet way to combine a imilar file that are all located in the ame folder?
The easiest way to combine a similar file that are all located in the same folder are:
Using the command line.Using a script.Using a text editor.Using a file manager.Specify your file.Combine A Similar File
There are several ways to combine similar files that are located in the same folder, depending on the type of files and the operating system you are using. Some options include:
Using the command line: On Windows, you can use the "copy" command to combine all the files into one, while on Mac or Linux, you can use the "cat" command.Using a script: You can write a script in a language such as Python or JavaScript that reads all the files in a directory and concatenates their contents into a single file.Using a text editor: Some text editors, such as Sublime Text and Visual Studio Code, have a feature that allows you to combine multiple files into one.Using a file manager: Some file managers, such as Windows Explorer and Finder, have an option to select multiple files, right-click and select "combine" or "merge".Please specify your file type and the OS you are using for a more specific solution.Learn more about Combine a similar file here:
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a square and a rectangle have the same area. the length of the rectangle is 196x196 centimeters, and the width of the rectangle is 44 centimeters. what is the length, in centimeters, of a side of the square?
The length in centimeters of the side of the square is 8 cm.
What is the area of a rectangle and a square?The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y. Find the side of the square if the rectangle's length and width are 27 cm and 3 cm, respectively. Given, the area of a square equals the area of a rectangle. The first step is to calculate the rectangle's area using the specified length and width values.
The area of a rectangle and a square are -
A{R} = Length x Breadth
A{S} = Side x Side
Given is that a square and a rectangle have the same area. The length of the rectangle is 32 cm and the width of the rectangle is 2 cm.
It is given that -
A{R} = A{S}
Length x Breadth = Side x Side
32 x 2 = (Side)²
(Side)² = 64
Side = 8
Therefore, the length in centimeters of the side of the square is 8 cm.
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Two campers are traveling. One camper is 5 miles East and 4 miles north, represented by the
coordinates (5, 4). The other camper is 7 miles South and 3 miles East, represented by the
coordinates (3,-7). If each unit represents 1 mile, how far apart are the two hikers, to the
nearest mile?
The hikers are approximately
15 miles
from each other.
The two bikers are 11.18 miles apart from each other according o the coordinate plane.
What is coordinate plane?A surface with two dimensions made of two number lines is referred to as a coordinate plane. When the origin, the place where the X- and Y-axes intersect, is reached, it is produced. A coordinate grid's numbers are used to find points. For graphing points, lines, and many other things, a coordinate plane is helpful. It functions as a map and gives precise directions on how to get from one place to another.
Distance between two coordinates is given by
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here, (x₁, y₁) is (5, 4) and (x₂, y₂) is (3,-7)
Putting the values in formula
d = [tex]\sqrt{(3-5)^2+(-7-4)^2}[/tex]
d = [tex]5\sqrt{5}[/tex]
d = 11.18 miles
Thus, The two bikers are 11.18 miles apart from each other according o the coordinate plane.
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What angle is 360 degree?.
The angle 360 degree is called as complete angle.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
A form of angle that measures 360° is known as a full angle. When two lines meet at a point, an angle is created, and the angle is the width of the space created.
The angle generated in this case is referred to be the complete angle if, after one complete revolution, the final ray corresponds with the incident or initial ray. A round angle and a complete angle are the alternate names. The angle, which corresponds to the center of a circle, is 2 radians, or 360 degrees. A complete angle is made up of four right angles or two straight angles. The amount of rotation makes the angle different from a zero angle.
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Re-write the quadratic function below in Standard Form
y=-2(x-3)(x+4)
Answer:
[tex]\boxed{-2x^2 -2x +24\\}\\\\[/tex]
Step-by-step explanation:
The standard form of a quadratic function is:
[tex]y = ax^2 + bx + c\\[/tex]
where a, b and c are constants
[tex]\textrm{The given expression is $y=-2\left(x-3\right)\left(x+4\right)$}[/tex]
Expand the right side of this expression
[tex]-2\left(x-3\right)\left(x+4\right)[/tex]
First expand (x-3)(x+4) using the FOIL method:
[tex](x-3)(x+4)[/tex]
[tex]=x\cdot x+x\cdot \:4-3x-3\cdot \:4\\\\= x^2+x-12[/tex]
[tex]-2\left(x-3\right)\left(x+4\right)\\\\= -2(x^2+x-12)\\\\= \boxed{-2x^2 -2x +24\\}\\\\[/tex]
ANSWER
A craft store recieved the following amounts of colored beads in today's shipment. The beads are sold in bags that weigh 1/10 of a pound. How many full bags of pink beads can be made from today's shipment?
The number of bags of pink beads that can be made from today's shipment is given as follows:
5 bags.
How to obtain the number of bags?The number of bags is obtained applying the proportions in the context of this problem.
We have that each bag weights 1/10 of a pound.
The shipment was of 4/7 pounds of pink beads, hence the total number of bags of pink beads that can be made from today's shipment is calculated as follows:
4/7/(1/10) = 4 x 10/7 = 40/7 = 5.
(rounded down, as the number of bags is a countable amount).
Missing InformationThe problem is given by the image presented at the end of the answer.
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Mitch's pool can hold 10,000 gallons of water. At noon, the pool is 80% full. Unfortunately, the pool has a leak, and it loses 120 gallons of water every hour. Mitch turns on a house at noon that fills the pool at a rate of 225 gallons per hour. He checks the water level in the pool every hour, starting at 1 PM. At what time does Mitch first see the pool overflowing?
Step-by-step explanation:
He starts at 8000 gallons when he adds 2000 gals it will overflow
120 gal go out each hour 225 gal goes in each hour net : 105 gal per hour IN
105 x = 2000 gal
x = 19.048 hours until overflow
1 pm + 19 .048 hours = 8.048 AM = ~~8 :03 AM Since he checks every hour, he will first see the overflow at 9:00 AM
NEED IT VERY URGENT PLEASE!!!!!!
at a right angle. Sidewalk B extends 500 feet on either side of the intersection with
Reason Four sidewalks form two right triangles. Sidewalk A and Sidewalk B intersec
Sidewalk A. Sidewalk C and Sidewalk D start at the ends of Sidewalk B and intersect
Sidewalk A at the same point. Do you have enough information to prove that the two
right triangles are congruent? Explain your reasoning.
A pair of right triangles are said to be congruent if the lengths of their respective sides and angles are the same.
Are two right angle triangles congruent?If the size and shape of two right triangles match, they are said to be congruent. Alternatively said, two right triangles are said to be congruent if the length of their respective sides and angles are equal. Fig. 1 shows that ABC = RPQ since A = R, C = Q, and B = P.
No, not every right triangle has a congruent angle. If the hypotenuse and the leg of one right-angled triangle match the hypotenuse and the corresponding leg of the other triangle, the two triangles are said to be congruent. This circumstance, known as RHS congruence of two triangles, only applies to right angled triangles. An isosceles triangle is one that possesses two congruent sides.
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how do i solve? im studying so please be detailed
Answer:
26. Scale Factor of A to B: [tex]\boxed{\dfrac{3}{4}}[/tex]
27. Scale factor of B to A: [tex]\boxed{\dfrac{4}{3}}[/tex]
Step-by-step explanation:
If two triangles are similar, the ratios of the side length to the corresponding side length of the other must be the same for all sides
The first challenge is to figure out which side of triangle A corresponds to which side of triangle B
If you flip triangle A counterclockwise by 90° the angles will be aligned with each other and it is easier to see the corresponding sides of A and B
We see that ....
side length 24 of A matches with side length 18 of B
side length 36 of A matches with side length 27 of B
side length 32 of A matches with side length 24 of B
B is of smaller size than A so the scale factor of A to B is less than 1
26.
Therefore the scale factor of A to B is
[tex]\dfrac{18}{24} = \dfrac{27}{36} =\dfrac{24}{32}\\\\\\\dfrac{18}{24}= \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 6}[/tex]
[tex]\dfrac{27}{36} = \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 9}\\\\\\\dfrac{24}{32} = \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 8}\\\\\\[/tex]
So the scale factor of Figure A to Figure B is [tex]\dfrac{3}{4}[/tex]
----------------------------------------------------------------------------------------------
27.
The scale factor of Figure B to Figure A is the reciprocal of
[tex]\dfrac{3}{4}[/tex]
Reciprocal of
[tex]\dfrac{3}{4} \; is \; \dfrac{4}{3}[/tex]
So scale factor of B to A is
[tex]\dfrac{4}{3}[/tex]
The ratio of girls to boys in the school play is 5:2. There are 49 kids in the school play.How many are boys?
Answer:
14 boys
Step-by-step explanation:
We know
The ratio of girls to boys is 5:2, which means for every 7 kids, there are 5 girls and 2 boys
So, 49 kids there are
2 x 7 = 14 boys
So, there are 14 boys
A rectangle’s length is 8 more than it’s width. Express its perimeter in terms of its width.
Answer:
length= 8x
width= x
perimeter of a rectangle= 2L+2W
=2(8x) + 2(x)
=16x + 2x
perimeter=18x
In 1940, a coat cost $25.00. Thirty years later, the price increased by 310%. How much more did a coat sell for thirty years later?
Please answer and explain the answer I will mark brainlisest
Answer:
70.80
Step-by-step explanation:
40.00 increased by 77% is 70.80. The increase is 30.80.
hamid has gained weight
he now weighs 88kg which is 10% higher than his normal weight
what is hamids normal weight
Answer:
Let's say Hamid's normal weight is x.
88kg = 110%x
88kg=11/10x
Divide by 11 on each side
8kg=1/10x
Multiply by 10 on each side
80kg=x
Hamid's normal weight is 80kg
Carton A contain 6. 789 L of juice and Carton B contain 6. 235 L of juice. Which carton contain more juice and approximately how much more?
Carton A has more juice than Carton B, by approximately 0.554 Litres (L).
Carton A: 6.789 L
Carton B: 6.235 L
Difference between Carton A and Carton B:
6.789 L - 6.235 L = 0.554 L
Carton A contains 6.789 Litres (L) of juice, while Carton B contains 6.235 L of juice. To calculate the difference between the two cartons, we subtract the amount of juice in Carton B from the amount of juice in Carton A. We do this by subtracting 6.235 L from 6.789 L, which gives us 0.554 L. This means that Carton A contains more juice than Carton B, by approximately 0.554 L. This difference may seem small, but it can still make a significant difference in the amount of juice one carton can provide compared to the other.
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Help
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20.) Margaret, Justin and Leigh are babysitting for the neighbor's children during the summer. Each week they make a total of $72.00, and they split the money evenly. At the end of 4 weeks, how much money did Justin make? **Show your work! a) $130.00 b) $144.00 c) $72.00 d) $96.00
Using multiplication, Correct option is B, Justin earned $144 in 4 weeks.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.
What components make up multiplication?The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product. Let's examine a few various forms of multiplication sentences and discover how to finish them.
As per the question,
Each week they make a total of $72.00,
Money earned in 4 weeks = 72 × 4 = $288
They split in equal halves,
⇒ $288 / 2 = $144
∴ Justin earned $144 in 4 weeks.
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what is 2 divided by 3/7 PLS HELP MEEEEEEEEEEEEEEEEEE
Answer:
2 / 3/7
2/1 x 3/7
Cross Multiply
14/3
The mass
a cube, M (kg),
is proportional to the cube of
the length of its edge,
L (m).
The mass
the cube is 40
kg when the length of its
edge is 35 cm.
Work out M (to 2 DP) when L
=
0.6 m
Thanks
The mass when L = 0.6 is given as follows:
M = 68.57 kg.
How to obtain the mass of the cube?The mass of the cube is modeled according to a proportional relationship, as follows:
M = kL.
In which k is the constant of proportionality.
The mass the cube is 40 kg when the length of its edge is 35 cm = 0.35 m, hence the constant is obtained as follows:
0.35k = 40
k = 40/0.35
k = 114.28.
Hence the mass when L is of 0.6 m is given as follows:
M = 114.28 x 0.6
M = 68.57 kg.
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A baeball team ha won 25 game and lot 12 game. If the baeball team' rate continue through a 148 game eaon then how many game will they have won
They will win 100 games if the team rate continues through a 148-game season.
We will solve our question with the help of the Multiplication rule.
As per the question, the baseball team has won 25 games and lost 12 games. This will give us a total of 25+12= 37 games.
It is given that if the baseball team rate continues through a 148-game season which is 37*4 = 148 games.
So, we should multiply our initial won matches by 4 to get the final won matches as per the given condition, we will get:
25*4 = 100 matches.
We can also find the answer by:
You would multiply 25 by 148 divided by 37 to determine the number of games won if you were comparing the 25 of the 37 games won to the total of 148 games played.
(148*25)/(25+12)
= 3700/37 = 100
Therefore if the baseball teams' rate continues through a 148-game season, then they will win 100 matches.
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How do you write and graph linear inequalities in two variables?.
Now, According to the question:
Linear inequalities are defined as a mathematical expression in which two expressions are compared using the inequality symbol. The expression can be an algebraic expression or numerical expression or a combination of both.
Graph Linear Inequalities in Two Variables:
Identify and graph the boundary line. If the inequality is ≤ or ≥, the boundary line is solid. Test a point that is not on the boundary line. (If not on the boundary line, (0,0) is usually a convenient test point.) Shade in one side of the boundary line.Learn more about Linear Inequalities at:
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Find the vertex, focus, directrix, and focal width of the parabola.
x2 = 28y
Vertex: (0, 0); Focus: (0, -7); Directrix: x = -7; Focal width: 112
Vertex: (0, 0); Focus: (7, 0); Directrix: x = 7; Focal width: 7
Vertex: (0, 0); Focus: (0, 7); Directrix: y = -7; Focal width: 28
Vertex: (0, 0); Focus: (7, 0); Directrix: y = 7; Focal width: 112
These are the vertex, focus, directrix, and focal width
Vertex: (0, 0), Focus: (0, 7), Directrix: y = -7, Focal width: 28
The vertex, focus, directrix, and focal width of the parabola described by the equation x^2 = 28y are:
Vertex: (0, 0)
Focus: (0, 7)
Directrix: y = -7
Focal width: 28
The vertex of a parabola is the midpoint of the directrix and the focus, which in this case is (0, 0). The focus is the point on the parabolic curve that is closest to the directrix, which in this case is (0, 7).
The directrix is the line along which the distance between the parabolic curve and its focus is minimized, which in this case is y = -7. The focal width is the distance between the focus and the directrix, which in this case is 28.
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You must show your work for each
Answer:
1. 8
2.3
Step-by-step explanation:
This for num 2
[tex] \sqrt{8} = \sqrt{2 \times 4} = 2 \sqrt{4} = 2[/tex]
6÷2=3
1.
To solve [tex]\sqrt[n]{16}=2[/tex], you need to turn the question around and ask what value of n makes [tex]2^n=16[/tex].
n = 4
2.
To simplify this, your teacher could mean two things, either "just simplify the radical" or "rationalize the denominator."
For the first option, [tex]\sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt{2}=2\cdot\sqrt{2}[/tex], so your overall expression becomes:
[tex]\dfrac{6}{2\cdot\sqrt{2}} = \dfrac{3}{\sqrt{2}}[/tex]
Now if your teacher also wants the denominator rationalized, then you keep going and multiply that by [tex]\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]:
[tex]\dfrac{3}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{3\sqrt{2}}{2}[/tex]
Calculator
Bookwork code: M56
X not allowed
a) What is the y-intercept of this line?
b) What is the gradient of this line?
Answer:
6 and 2
Step-by-step explanation:
(a)
the y- intercept is the point on the y- axis where the line crosses.
the line crosses at (0, 6 ) , then y- intercept = 6
(b)
the gradient m ( slope) of the line is calculated using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 6) ← 2 points on the line
m = [tex]\frac{6-0}{0-(-3)}[/tex] = [tex]\frac{6}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2
From the adjacent image we can identify the points of the graph.
From the points we can easily find y-intercept and gradient.
How can we identify the points.
Line where cut the x-axis and y-axis. Take that location as point.
For writing point observe the distance of x-axis and y-axis
Let say point A=(0,6) and point B=(-3,0)
For find y-intercept we must know gradient first
Gradient formula for two points m=[tex]\frac{y_{2} -y_{1 }}{x_{2} -x_{1 }}[/tex]
Submit Point A and Point B m=[tex]\frac{0 -6}{-3 -0\\}[/tex]
m=[tex]\frac{-6}{-3 \\}[/tex]
m=2
Therefore, Gradient of slope m=2
To find y-intercept, we must solve lin equation
Line equation y=mx+b
m = gradient and b=y-intercept
Submit m in line equation y=2x+b
Submit any one point in the line equation
Take pointA=(0,6)
6=2(0)+b
b=6-2
b=4
Therefore ,y-intercept equals to 4
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