The limit is normally defined as
[tex]lim _{x- > c} f(x) = L[/tex]
It is read as “the limit of f of x, as x approaches c equals L”.
In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behaviour at a certain time. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly defined.
Limits in maths are unique real numbers. Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as
[tex]lim _{x- > c} f(x) = L[/tex]
It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows the limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. The right and left-hand limits still exist even though the limit is not specified in this situation.
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In 1970 a dress cost $40.00. Ten years later, the price increased by 77%. How much more did it sell for ten years later?
please help 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.
Answer:
$70.80
Step-by-step explanation:
The dress was $40 to add the 77% increase, you would multiply 40 x .77= 30.80, then you would add the 30.80 to the original 40, giving you a total of $70.80
When the standard deviation is 4 The variance is equal to?.
The standard deviation is 4 The variance is equal to 16.
In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.
Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.
The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.
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The formula to determine the period of one
swing of a simple pendulum is
L
T = 2√, where L is the length of the
string and g is the acceleration due to
gravity. Solve the formula to solve for g in
terms of T, T and L.
Answer:
To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:
First, we divide both sides by 2π:
T/2π = √(L/g)
Then, we square both sides:
(T/2π)² = (L/g)
Then, we multiply both sides by g^2 :
(T^2/4π^2) = L
Finally, we divide both sides by L:
(T^2/4π^2 * L) = g
So the formula for g in terms of T, L is g = (T^2/4π^2 * L)
Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.
R^2-59R-82r^2+60 is equivalent to
Answer: 83r^2 - 59 + 60
Step-by-step explanation:
R^2 - 59R - 82r^2 + 60
= 83r^2 - 59 + 60
One atom i ×110−8 centimeter in length. How many atom could be laid end-to-end on a metertick (which i 100 cm in length)? Leave the anwer in cientific notation. Round to two decimal place, if neceary
The number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms.
A meter is equivalent to 100 centimeters (cm), and an atom is about 10^-8 centimeters in length. So, when we divide the length of a meter stick (100 cm) by the length of one atom (10^-8 cm).
we are essentially dividing 100 by a decimal number on the order of 0.00000001.
This is the same as multiplying 100 by a number on the order of 100,000,000. In other words, we are multiplying 100 by 10^8.
So, 100 cm / (1*10^-8 cm) = 10^8 atoms
This means that the number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms which is a very big number, this is why we use scientific notation to represent it.
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Solve the quadratic equation by completing the square. 2+x=6x^2 Completing the square gives us: (x- Answer )^2 = Answer Enter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth. x=Answer and x=Answer
Answer:
6xˆ2 - x - 2 = 0
D = 1 + 1*2*6*4=49=7ˆ2;
using formula of discriminant you get
x1= -1/2
x2= 2/3
answer = x1, x2
A teacher gave his students the four graphs below. Which graph represents a geometric sequence?
Graph A
Graph B
Graph C
Graph D
Answer:
I believe the answer is Graph A
What is the axis of symmetry of the quadratic function y x 3 ² 2?.
The axis of symmetry is the line x=3.
As y is a linear term and x is quadratic, this means we’re dealing with either an ‘n-shaped’ parabola or a ‘u-shaped’ parabola.
As the coefficients of x² and y have the same sign they’re both positive, which means we have a ‘u-shaped’ parabola.
One can express a parabola in the vertex form, y=a(x−p)²+q, which tells us that the vertex is the point (p,q) and the axis of symmetry is the line x=p.
So, let’s apply this format to your parabola.
y=(x−3)²=(x−3)²+0
From this, it’s clear that:
The vertex is the point (3,0)
The axis of symmetry is the line x=3
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Write down in terms of n, an expression for the nth term
of the following sequences:
b) 9 11 13 15 17
9 11 13 15 17
first term (a) = 9
diffrence (d) = 11-9 = 13-11 = 2
we know
a + (n-1)d
9+(n-1)2
9+2n-2
7+2n
2n + 7
2n + 7 is the sequences of 9 11 13 15 17 for nth term
Kweku and kofi are brothers they are both 35 years Kofi's age is two thirds kweku's age find their age
Kweku age is 21 years and his brother kofi is 14 years
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Lets call Kweku's age as (x)
Sofi's age will be 2/3x
If both are 35 then the equation is as follow:
x + 2/3x = 35
Clearing the variable we have:
(3x+2x) /3 = 35
5x = 35*3
5x = 105
x = 105/5
x = 21
Kweku's age is 21 years
Sofi's age is 2/3x = 2/3*21 = 14 years
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If the mode for 6 numbers is 100 and the mean and median are the same what are the 6 numbers?
Solve for x. Figures are not necessarily drawn to scale.
The required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
In the figure, Similar triangles is shown,
Applying the property of proportional sides in the triangles
30/18 = 20/x
x = 18 / 30 × 20
x = 12
Thus, the required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.
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What is the completely factored form of 12xy 9x 8y?.
Given that the polynomial is 12xy - 9x - 8y + 6, we must determine its fully factored form.
There are two variables in the given polynomial.
12xy - 9x - 8y - 6 = 3x(4y - 3) Now, 12xy - 9x - 8y - 6 = 3x(4y - 3) - 2(4y - 3) = (3x - 2)(4y - 3) The polynomial's fully factored form is (3x - 2)(4y - 3)
(3x - 2)(4y - 3) is the fully factored form of 12xy - 9x - 8y + 6.
One approach to factoring expressions is factoring by grouping. If the expression can be broken down into its component parts, this approach is helpful. On the other hand, we can employ additional strategies.
A polynomial is an expression made up of variables, constants, and exponents that are added, subtracted, multiplied, and divided using mathematical operations (no division by a variable).
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Full Question = What is the completely factored form of 12xy - 9x - 8y + 6?
The price at Yogurt World is $2.56 for 8 ounces. How much-frozen yogurt could you get for $3.52? ____Ounces
Answer: 11
Step-by-step explanation: (8/2.56) x 3.52 = 11 ounces
In gym cla tudent were aked to form ix equal group. If there were 18 tudent in each group, then how many total tudent were there?
If there were 18 students in each group and they were asked to form six equal groups, then there would be a total of 108 students.
i.e. (18 students x 6 groups = 108 students)
When a group of students are asked to form a certain number of equal groups, the total number of students can be determined by multiplying the number of students in each group by the number of groups.
In this case, the students were asked to form six equal groups and there were 18 students in each group.
To find the total number of students, we simply multiply 18 by 6.
18 x 6 = 108Therefore, there were 108 students in total.
This is because when you have x number of groups and y number of students in each group, the total number of students is xy.
In this case x=6 and y=18, so the total number of students is 6*18 = 108.
Question:
"In gym class, students were asked to form ix equal group. If there were 18 students in each group, then how many total students were there?"
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Part A: Write the polynomial function with zero { -2, 0, 3√2 }
Part B: Write the polynomial function with zero { -1, 3, 2i }
The polynomial function with zeroes at -2, 0, and 3√2 is (x+2)(x-0)(x-3√2) = [tex](x+2)*(x-3\sqrt{2}) = x^3 - 3x\sqrt{2x} - 2x^2.[/tex]
The polynomial function with zeroes at -1, 3, and 2i is (x+1)(x-3)(x-2i) = [tex](x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]
A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is the degree of the polynomial and the a_i are constants. To find a polynomial function with zeroes at -2, 0, and 3√2, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+2)(x-0)(x-3\sqrt{2}) = (x+2)x(x-3√2) = x^3 - 3x\sqrt{2x} - 2x^2[/tex].
In this case, we can see that x = -2, x = 0, x = 3√2 are the zeroes, so we know that (x+2), x and (x-3√2) are the factors of the polynomial.
Similarly, to find a polynomial function with zeroes at -1, 3, and 2i, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+1)(x-3)(x-2i) = (x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]
In this case, we can see that x = -1, x = 3, x = 2i are the zeroes, so we know that [tex](x+1), (x-3), (x^2+4)[/tex]are the factors of the polynomial.
It is worth noting that (x-2i) is a zero of the polynomial, so (x-2i)(x+2i) = [tex]x^2[/tex]+4 is a factor of the polynomial and it is included in the polynomial..
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What is the degree of the polynomial 3x2y3 4xy x6 y5?.
The degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.
A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.
To find the degree of a polynomial, you can do the following:
→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.
→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.
Given,
p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵
Here,
Degree of polynomial is 6
As, 6 is highest of all the exponent given in p(x)
Hence, the degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.
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What is the nature of roots of 2x² 4x +3?.
D) The quadratic equation's roots, 2x2 4x + 3 = 0, are imaginary in nature.
How may a quadratic problem be solved in four different ways?The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.
Given a quadratic equation, it is 2x 2 + 4x + 3= 0.
∴ a=2,b=4,c=3
As a result, the discriminant of this equation is given by D=b 2 4ac.
∴D=(4) \s2 \s −4(2)(3) (3)
∴D=16−24
∴D=−8<0
The equation's roots are therefore fictitious.
An easy quadratic equation is what?The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. An example of a quadratic equation is x2 + 2x + 1.
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Full Question = The nature of the roots of the quadratic equation 2x ^2 + 4x + 3= 0 are
A. Real & Distinct
B. Real & Equal
C. No Real Roots
D. Imaginary
Find the cp
Wooden shelf : sp = 6786, loss % = 13%
Answer:
cp=(SP * 100 ) / ( 100 – percentage loss)
6786*100/100-13
7800
The heat Q required to raise the temperature of water varies jointly as the mass m of the water and the amount of temperature change T, and Q = 20,930 joules(J) when m = 1kg and T = 5° C. To the nearest tenth of a kilogram, find m when Q = 8,349 J and T = 3°C. When Q = 8,349 J and T = 3°C, the mass of the water m is _ kg
To the nearest tenth of a kilogram, m = 0.6 kg.
What is ttemperature rate ?
With increase in temperature, the rate of the reaction and the rate constant increases. As a generalization, the rate of the reaction (and the rate constant) becomes almost double for every ten degree rise in temperature. This is also called temperature coefficient.
the heat Q required to raise the temperature of water varies jointly as the mass m of the water and the amount of temperature change T, and Q = 20,930 J when m = 1 kg and T = 5°C.
So, write an equation for Q as:
Q = k * m * T
where k is a constant of proportionality.
Substituting the known values, we can find k:
20930 = k * 1 * 5
k = 20930 / (1 * 5) = 4186
Now that we have k, use it to find m when Q = 8349 J and T = 3°C:
8349 = 4186 * m * 3
m = 8349 / (4186 * 3)
To the nearest tenth of a kilogram, m = 0.6 kg.
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The mass of the water m is 0.7 kg.
Since Q varies jointly as m and T, we know that Q = k * m * T where k is a constant of proportionality. Using the given information, we can find the value of k:
Q = 20,930 J when m = 1 kg and T = 5° C
k = Q / (m * T) = 20,930 / (1 * 5) = 4186
Now that we have found k, we can use it to find m when Q = 8,349 J and T = 3°C:
Q = k * m * T
8,349 = 4186 * m * 3
m = 8,349 / (4186 * 3) = 8,349 / 12,558
m = 0.67 kg
To the nearest tenth of a kilogram, m = 0.7 kg.
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Given that f(x)=x^2=11x+30 and g(x)=x-5, find f(-g)(x) and express the result as a polynomial in simplest form.
Hey there,
We have,
f(x) = x² + 11x + 30g(x) = x + 6
Now,
(f.g)(x) = f(g(x))
Substituting...
g(x) = x + 6f(g(x)) = f(x + 6)
Now,
f(x + 6)= (x + 6)² + 11(x + 6) + 30= x² + 12x + 36 + 11x + 66 + 30= x² + 23x + 132
So,The value is x² + 23x + 132
Sorry for the writing around the problem but I really need help ASAP!
Answer:
125
Step-by-step explanation:
5x + 20 + 3x - 8 = 180
8x + 12 = 180
8x = 168
x = 21
5(21) + 20
= 105 + 20
= 125
Your chool i putting on a production of Wet Side Story. Ticket cot $5 for tudent and $9 for non-tudent. On one night there were three time a many tudent a there were non-tudent. On thi night, they old $4,608 in ticket. How many tudent ticket were old? How many non-tudent ticket were old?
On that particular night, there were 144 student tickets and 432 non-student tickets sold.
Let x be the number of student tickets sold that night
y be the number of non-student tickets sold that night
On that night, there were three times as many student as there were non-students. Hence, we can write that as an algebraic expression such that
3x = y
If tickets cost $5 for students and $9 for non-students, and on that night, they sold $4,608 in tickets, then we can express that as
$5x + $9y = $4608
5x + 9y = 4608
Substitute the value of y from the first expression to the second and solve for x.
5x + 9y = 4608
5x + 9(3x) = 4608
5x + 27x = 4608
32x = 4608
x = 144
Plug in the value of x into the first expression and solve for y.
y = 3x
y = 3(144)
y = 432
Hence, the number of tickets sold on that night to students and non-students were 144 and 432, respectively.
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(X^2+y^2-1)^3=x^2y^3 Write the mapping notation to transform the parent function then describe the transformations made to the parent function.
The relation's graph can be seen in the graphic at the bottom, where it is clear that it is function.
How to determine if the relation is a function?The actual function can be specified using this "mapping" notation. Writing f:(x,y)x+y would allow us to define the above f(x, y). Real numbers are referred to as scalars to distinguish them from vectors. Each input is translated into a single output in a relation known as a function (input, output).
The horizontal axis is used for inputs, and the vertical axis is used for outputs. Here, we have the relationship shown below:
(-5,-1), (-4,1), (-3,3), (-1,5), (1,7) (1,7)
The figure below shows the graph of these points. Since there are no two points on the same vertical line, the relation is a function, as you can see.
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Is 52 a perfect square?.
No, the number 52 is not a perfect square. Because the square root of 52 is an irrational number.
An irrational number is a real number that cannot be expressed as a ratio of two integers, or in other words, as a fraction. Irrational numbers include numbers such as pi (π), the square root of 2, and the square root of 3, which are not terminating or repeating decimals. They cannot be written as a finite decimal or a fraction of integers. Irrational numbers have an infinite number of decimal places, which means they cannot be represented exactly as a decimal.
They are also non-repeating and non-terminating decimals. Irrational numbers have many important properties and applications in mathematics, such as in geometry, where they are used to calculate the lengths of curves and the areas of circles. They also appear in trigonometry and calculus. Irrational numbers are also important in physics and engineering as well as other branches of science and technology. They are often used to express the precise measurements and calculations that are essential in these fields.vb
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How is FG calculated?.
To calculate the composition of two functions, "F" and "G", represented by the notation "FG", you first need to have a specific input value, usually represented as "x".The first step is to apply the function "G" to the input "x", resulting in G(x).
The next step is to take the output of the function G, which is G(x), and use it as the input for the function F.
The final step is to apply the function F to the output of G(x) resulting in F(G(x)), which is the composition of the two functions F and G.
In other words, you apply the function G to the input x, and then you apply the function F to the result of G(x). The final result is the function F(G(x)), which is the composition of the functions F and G.
It's important to note that the order of the functions in composition matters and can change the result of composition. The notation "FG)(x)" is different from "GF)(x)" which means that the order of the functions matter in composition.
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please help!!
<RQT is a straight angle. What are m<RQS and m<TQS?
angle RQS = 101 degrees
angle TQS = 79 degrees
===================================================
Explanation:
A straight angle has a measure of 180 degrees. It's another way of saying "straight line".
The two angles shown add to 180.
We'll use this fact to solve for x.
(angleRQS) + (angleTQS) = angle RQT
(9x+2) + (7x+2) = 180
16x+4 = 180
16x = 180-4
16x = 176
x = 176/16
x = 11
Use this x value to determine the angles we're after.
angle RQS = 9x+2 = 9*11+2 = 99+2 = 101 degreesangle TQS = 7x+2 = 7*11+2 = 77+2 = 79 degreesCheck:
(angleRQS) + (angleTQS) = 101+79 = 180 which confirms the answer is correct.
Maggie has 2/3 pounds of peanuts. She will put an equal amount of peanuts into 6 different containers. What amount of peanuts in each container?
The amount of peanuts Maggie puts in each container is 1/9 pounds per container.
What amount of peanuts in each container?Number of pounds of peanut Maggie has = 2/3 pounds
Number of containers = 6
Number of peanuts in each container = Number of pounds of peanut Maggie has / Number of containers
= 2/3 ÷ 6
multiply by the reciprocal of 6
= 2/3 × 1/6
= 2/18
= 1/9 pounds per container
Hence, there are 1/9 pounds of peanuts in each container if Maggie puts an equal amount.
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Find the Value of X in the Problem shown.
Answer:
X = 20
Step-by-step explanation:
The two quadrilaterals are similar to each other. So the ratio of each side of the larger quadrilateral to the corresponding side of the smaller quadrilateral must be the same.
Examining the two figures we see the side which has 68° and 128° pf the smaller quadrilateral has length 2
The corresponding side of the larger quadrilateral on the right is 6
So each side of the larger quadrilateral =6/2 = 3 times each side of the smaller one
Side which has length 10 pf the smaller quadrilateral corresponds to the side with length x+10 of the larger one. This ratio must also be 1:3
So
[tex]\dfrac{10 + x}{10}= 3\\\\[/tex]
Cross-multiplying we get
10 + x = 10 x 3
10 + x = 30
x = 30-10
x =20
ANSWER
You survey your class and 4 like vanilla ice cream
and 14 like chocolate ice cream. Write the ratio of
people who like vanilla to people who like chocolate ice
cream, then write the ratio in simplest form.
Answer: 2:7
Step-by-step explanation:
Vanilla icecream = 4
Chocolate icecream = 14
4:14=2:7
2X2=4
7X2=14
Step-by-step explanation:
a ratio is simply relating 2 (or more) groups and their sizes.
in our case here the ratio is
4/14 = 2/7
this is often written as
4:14 = 2:7
it means that for every 2 people liking (I assume "preferring") vanilla ice cream there are 7 people liking (preferring) chocolate ice cream.
FYI
in total, a ratio also tells us about the size of the sample for the observation or analysis. 4/14 tells us there are 18 (4+14) people in the survey. and the simplified form 2/7 tells us that we can split the whole survey group into units of 9 (2+7) people with the same behavior as the total group.
a ratio is a fraction (incl. all the calculation and comparison rules) with a special meaning.
so, don't mix the ratio up with e.g. the fractions of the different behaviors in the group :
4/18 = 2/9 of the whole group prefer vanilla.
14/18 = 7/9 of the whole group prefer chocolate.
the ratio is now the relative size relationship between both : 2/9 / 7/9 = 2/7
