The value of the expression [tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex] is [tex]cot(A)+\frac{A}{sin^{2}A}[/tex].
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine derivatives, continuity, and integrals.
Mathematical expressions consist of at least two variables or numbers, at least one arithmetic operation, and a statement. It's possible to divide, multiply, add, or subtract with this mathematical operation.
Consider the expression,
[tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex]
Adding and subtracting Acot(A) and A common in the numerator,
[tex]\lim_{x \to A} \frac{xcot(A)-Acot(A)+Acot(A)-Acot(x)}{x-A}[/tex]
Taking cot(A) common,
[tex]\lim_{x \to A} \frac{cot(A)(x-A)+A(cot(A)-cot(x))}{x-A}[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A(cot(A)-cot(x)}{x-A}[/tex]
Now, using the identity:
cot x = cos x / sin x
[tex]\lim_{x \to A} cot(A) + \frac{A(\frac{cos(A)}{sin(A)} -\frac{cos(x)}{sin(x)}) }{x-A}[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{cos(A)sin(x)-cos(x)sin(A) }{sin(A)sin(x)})[/tex]
By using the identity, sin ( a - b ) = sin(a)cos(b) - sin(b)cos(a)
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=\lim_{x \to A} cot(A) +\lim_{x \to A} \frac{sin(x-A)}{(x-A)}\frac{A}{sin^{2}A}[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=cot(A)+1 \cdot \frac{A}{sin^{2}A}[/tex]
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operation of 12 less than x
Allison is saving money to buy a video game system. in the first week her savings were $8 less than 2/5 the price of the system. in the second week, she saved 50 cents more than 1/2 the price of the system. she was still $37 short. find the price of the system.
Hence , the price of the system $295 .
The linear equations in one variable is associate degree equation that is expressed within the sort of ax+b = zero, wherever a and b square measure 2 integers, and x may be a variable and has just one resolution. as an example, 2x+3=8 may be a equation having one variable in it.Let the price of the system be "x" .
It is given that in the first week her savings were $8 less than 2/5 the price of the system which can be represented by equation
First week savings = (2/5)x -8
It is also given that in the second week, she saved 50 cents more than 1/2 the price of the system which can be represented by equation
Second week savings = (1/2)x +0.5
savings + short = price of system
(2/5)x -8 + (1/2)x +0.5 + 37 = x
(2/5)x + (1/2)x + 29.5 = x
4x + 5x/ 10 + 29.5 = x
9x/10+ 29.5 = x
0.9x + 29.5 = x
29.5 = x - 0.9x
29.5 = 0.1x
$ 295 = x
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ever since renata moved to her new home, she's been keeping track of the height of the tree outside her window. the variable hhh models the height of the tree (in centimeters), ttt years since renata moved in. h
The tree was 210 cm tall.
Let 'h(t) ' models the height of the tree in centimeters and 't' denotes the number of years since Renata moved in.
Given, h(t) = 210 + 33t
This is a linear function in 't'.
This function says that in each year the tree grows 33 cm tall.
We need to find the height of the tree when Renata moved in.
When Renata moved in, the number of years, t = 0
Applying this into h(t) , we get,
h(t) = 210 + 33 x 0 = 210 cm
Therefore the tree was 210 cm tall when Renata moved in.
The question was incomplete. Find the complete question here:
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. h(t) models the height of the tree (in centimeters), t years since Renata moved in. h(t)=210+33t
How tall was the tree when Renata moved in?
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FIND THE LCM OF EACH SET OF NUMBERS USING THE PRIME FACTORIZATION METHOD.
(BEST ANSWER = BRAINLIEST)
1. {12,15}
2. {16,24}
3. {18,27}
4. {20,28}
5. {36,54}
6. {9,12,24}
7. {15, 20, 45}
8. {6,8,12}
9. {4,6,9}
10. {8,9,12}
The LCM of the set of numbers are:
1. {12,15} = 60
2. {16,24} = 48
3. {18,27} = 54
4. {20,28} = 140
5. {36,54} = 108
6. {9,12,24} = 72
7. {15, 20, 45} = 180
8. {6,8,12} = 24
9. {4,6,9} = 36
10. {8,9,12} = 72
What is the LCM?The least common multiple of two or more numbers is the least multiple that is common to two or more numbers. A multiple of a number is the product of an integer and that number. For example, the multiples of 6 are 12 and 18.
Prime factors of 12 = 2 x 2 x 3
Prime factors of 15 = 3 x 5
LCM = 2 x 2 x 3 x 5 = 60
Prime factors of 16 = 2 x 2 x 2 x 2
Prime factors of 24 = 2 x 2 x 2 x 3
LCM = 2 x 2 x 2 x 2 x 3 = 48
Prime factors of 18 = 2 x 3 x 3
Prime factors of 27 = 3 x 3 x 3
LCM = 2 x 3 x 3 x 3 = 54
Prime factors of 20 = 2 x 2 x 5
Prime factors of 28 = 2 x 2 x 7
LCM = 2 x 2 x 5 x 7 = 140
Prime factors of 36 =2 x 2 x 3 x 3
Prime factors of 54 = 2 x 3 x 3 x 3
LCM = 2 x 2 x3 x 3 x3 = 108
Prime factors of 9 = 3 x 3
Prime factors of 12 = 2 x 2 x 3
Prime factors of 24 = 2 x 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 x 3 = 72
Prime factors of 15 = 3 x 5
Prime factors of 20 = 2 x 2 x 5
Prime factors of 45 = 3 x 3 x 5
LCM = 2 x 2 x 3 x 3 x 5 = 180
Prime factors of 6 = 2 x 3
Prime factors of 8= 2 x 2 x 2
Prime factors of 12= 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 = 24
Prime factors of 4 = 2 x 2
Prime factors of 6= 2 x 3
Prime factors of 9= 3 x 3
LCM = 2 x 2 x 3 x 3 = 36
Prime factors of 8 = 2 x 2 x 2
Prime factors of 9= 3 x 3
Prime factors of 12 = 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 x 3 = 72
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Please help!! State which property of equality justifies the statement:
If 7x=28, then x=4.
The property of equality justifies the given statement is Transitive property of equality.
Given,
The statement:
If, 7x = 28,
then, x = 4
We have to find the property of equality that justifies this statement:
The transitive property of equality formula is given as follows:
If y = z and x = y, x must be z. Where items belong to the same category as x, y, and z. For instance, if a line segment's measurement is represented by "x," then its measurement should also be represented by "y" and "z."
The property of equality that justifies this statement If, 7x = 28,
then, x = 4 is transitive property of equality.
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what is 2.3,3.3% and 2/3 in oder greatest to least.
2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.
What is descending order?Arrangement in a series that begins with the greatest or largest and ends with the least or smallest.
Now the given numbers are,
2.3,3.3% and 2/3
Converting them into decimals we get,
2.3 = 2.300
3.3% = 0.033
2/3 = 0.667
Arranging them from greatest to least we obtain,
0.033 > 0.667 > 2.3
Thus, the given numbers from greatest to least are,
3.3% > 2/3 > 2.3
Hence, 2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.
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Suppose A is (-2,4) and M is (3,1) and M is the Midpoint of AB, find the coordinates of AB
(x+5/2) + (x-3/3) = 3 1/6
Answer:
Step-by-step explanation:
x=2
Solve for a.
ab + c = d
Shawn stated that 5x + 2 is equal to 7x . Is Shawn's claim, correct? EXPLAIN.
Need answer asap
"Shawn stated that 5x+2 is equal 7x" its is an incorrect statement, because we can only add like terms.
Given,
The statement
5x+2 is equal to 7x
Here 5x and 2 are not like terms. So we can't add them together.
So the given statement is incorrect
5x+2 is not equal to 7x
Hence, "Shawn stated that 5x+2 is equal 7x" it is an incorrect statement, because we can only add like terms.
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Please Help Important!!!!!!
Seeing that substituting the value x ≤ -2, did not yield a result that is correct with the equation x5 +7 > x3 we can say that Sam's conjecture is incorrect
Given data
x ≤ -2
x5 +7 > x3
How to test Sam's conjectureSam's conjecture is tested by substituting the value x ≤ -2 into the equation x5 +7 > x3. If the result is in accordance with the equation then Sam's conjecture is correct, however if the result is not in accordance with the equation the Sam's conjecture is incorrect.
The substitution will give
( -2 )^5 + 7 > ( -2 )^3
-32 + 7 > -8
-25 > -8 (since -25 is less than -8, Sam's conjecture is incorrect )
Seeing that substituting the value x ≤ -2, did not yield a result that is correct we can say that Sam's conjecture is incorrect
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201.96+38.7+0.84
Eh this question I been on it for like 3 hours
I need help
Answer:
241.5
Step-by-step explanation:
201.96+38.7+0.84
5/6=1/3+d
omg help mee
Answer:
[tex]d=1/2[/tex]
How to solve:
Group.Find d.Step-by-step explanation:
[tex]\frac{5}{6}=\frac{1}{3}+d\\\frac{1}{3}+d=\frac{5}{6}[/tex]
Group
[tex]\frac{1}{3}+d=\frac{5}{6}\\\frac{1}{3}+d-\frac{1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1}{3}+\frac{-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{0}{3}=\frac{5}{6}-\frac{1}{3}\\d+0=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}+\frac{-1\cdot 2}{3\cdot 2}\\d=\frac{5}{6}+\frac{-1\cdot 2}{6}\\d=\frac{5}{6}+\frac{-2}{6}\\d=\frac{5-2}{6}\\d=\frac{3}{6}\\d=\frac{1\cdot 3}{2\cdot 3}\\d=\frac{1}{2}[/tex]
Hope it helps.
use the accompanying statcrunch session to obtain a simple random sample of 5 high schools in the city of chicago.
Using sampling concepts, one sample of 5 high schools in the city of Chicago is given by:
Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.
What is the missing information?The problem is incomplete, but researching it on a search engine, it gives us a list of 15 high schools in Chicago, and asks us to take a sample of 5.
What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.Hence, from the concepts of sample and populations, the sample of 5 means that we have to select 5 schools from the 15 listed, hence they are:
Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.
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you are about to buy a calculator for $10, and the sales-person tells you that the model you want to buy is on sale for $5 at the store’s other branch, which is a 20 minute drive away.
Answer:
The question is incompleye. Do elaborate?
find the rise and the run
Answer:
down below
Step-by-step explanation:
The picture is a little blurry so the graph is hard to read. But I believe the answer is 7/8. The rose would be counting up or down the y axis and the run is counting forward or backward on the x axis.
Hope this helps! :)
Answer:
rise = 7, run = 8
slope = rise/run = 7/8
See attached picture for graph in case you have to plot
Step-by-step explanation:
Take two distinguishable points, (x1, y1) and (x2, y2) on the graph. Find the difference in their y values= y2 - y1. This will be the rise
Find the corresponding difference in the x values, x2 - x1. This will be the run
Divide the y difference by the x difference and you get rise/run which is the slope of the line
Two clear points are (x1 = 0, y1= -7) and (x2=8, y2=0)
(y2 - y1)/(x2 - x1)
= (0 - (-7)/(8 - 0))
= (0+7/(8 - 0) ==> 2 negatives make a positive
= 7/8 and that is rise/run
Rise = 7, run = 8
Picture shows rise and run if you want to graph it
An electrically neutral atom of beryllium has four protons. Which statement is true? There are four protons in the nucleus. There is a charge of −4 on an atom of beryllium. There are four neutrons in the nucleus. There is a charge of +4 on an atom of beryllium.
The right answer is that there are four electrons.
What is an atomic number?The charge number of an atomic nucleus is the chemical element's atomic number, also known as the nuclear charge number.
For conventional nuclei, this is comparable to the proton number, or the number of protons found in the nucleus of each atom of that element.
Equal numbers of protons and electrons make up a neutral atom. This figure establishes the atom's atomic number.
The fourth element on the periodic table is beryllium.
Number of protons in Be-atom = 4
Number of electrons in Be-atom = 4
Therefore, it is true that there are four electrons.
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find the percent of change when 25 meters change to 30 meters
Answer:
20 %
Step-by-step explanation:
There was a change from 25 m to 30 m. When we find percentage change of something, we first calculate the difference of final and initial value. Then divide it by initial value × 100.
Change:
= 30 m - 25 m
= 5 m
% change:
= 5 m / 25 m × 100
= 100 / 5
= 20 % (ans)
Michael makes a model to show the distances between the Sun and the planets.
Earth is 1.50 x 10¹¹ m from the Sun. The distance on the model is 30 cm. What is the ratio of the lengths of the model to the actual distance?
Step-by-step explanation:
do 1.50 times 10 and the multiple by 30 to get the answer
The ratio of the lengths of the model to the actual distance is approximately 2 x 10⁻¹³.
To find the ratio of the lengths of the model to the actual distance, we need to compare the lengths in the same unit. Let's convert the actual distance between the Sun and Earth from meters to centimeters, so both values are in centimeters.
1 meter = 100 centimeters
Actual distance from the Sun to Earth = 1.50 x 10¹¹ meters
Actual distance from the Sun to Earth in centimeters = 1.50 x 10¹¹ meters * 100 centimeters/meter
Actual distance from the Sun to Earth in centimeters = 1.50 x 10¹¹ meters * 100 centimeters/meter = 1.50 x 10¹³ centimeters
Now, we can compare the lengths:
Length on the model = 30 centimeters
Actual distance from the Sun to Earth = 1.50 x 10¹³ centimeters
The ratio of the lengths of the model to the actual distance is:
Ratio = Length on the model / Actual distance from the Sun to Earth
Ratio = 30 centimeters / (1.50 x 10¹³ centimeters)
To simplify this ratio, let's express the actual distance in scientific notation:
1.50 x 10¹³ = 15 x 10¹² = 1.5 x 10¹³
Now, the ratio becomes:
Ratio = 30 centimeters / (1.5 x 10¹³ centimeters)
Now, notice that both values are in the same unit (centimeters). We can proceed with the division:
Ratio ≈ 0.0000000000002
Therefore, the ratio of the lengths of the model to the actual distance is approximately 2 x 10⁻¹³. This means that every 1 centimeter on the model represents approximately 2 x 10⁻¹³ centimeters in actual distance between the Sun and Earth.
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Answer(with steps pls)
Answer:
b. No
Step-by-step explanation:
7/6 can be changed to an equivalent ratio(fraction) by multiplying by the same number on top and on the bottom.
example:
7/6 = 7×3 / 6×3
= 21/18
21/18 is equivalent to 7/6.
7 doesn't even go into 52 for one thing. But 6×8 is 48 so try 8.
7/6 = 7×8 / 6×8
= 56/48
56/48 is equivalent to 7/6, not 52/48
I will Mark Brainlist ...Find the length of p. Please Help its Math question i will Mark Brainlist !!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's use Trigonometric ratios to find p :
[tex]\qquad \sf \dashrightarrow \: \cos(60) = \cfrac{6}{p} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{2} = \dfrac{6}{p} [/tex]
[tex]\qquad \sf \dashrightarrow \: p = 6 \times 2[/tex]
[tex]\qquad \sf \dashrightarrow \: p = 12 \: \: units[/tex]
Maria wanted to bring back 5 million grains of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?
a
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg
b
Multiply 5 x (6.7 x 10^-7) = 33.5 x 10^-7 = 3.35 x 10^-6 kg
c
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + 7)) = 33.5 x 10^13 = 3.35 x 10^14 kg
d
Divide (5,000,000 / 6.7 x 10^-7) = (5 x 10^6) / (6.7 x 10^-7) = (5 / 6.7) x (10^(6 - 7)) = .74 x 10^-1 = 0.074 kg
PLEASE HELP
Answer:
3.35
Step-by-step explanation:
5,000,000*6.7 * 10^-7
= 5 * 10^6 * 6.7*10^-7
= 33.5 * 10^-1
= 3.35
The weight of 5 million grains of sand is 3.35 kg.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Weight of each grain of sand = 6.7 x [tex]10^{-7}[/tex] kg
Weight of 5 million grains of sand.
= 5,000,000 x 6.7 x [tex]10^{-7}[/tex] kg
= 5 x [tex]10^6[/tex] x 6.7 x [tex]10^{-7}[/tex]
= 33.5 x [tex]10^{-1}[/tex] kg
= = 3.35 kg
Thus,
The weight of the total grain of sand is 3.35 kg.
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Use the function: f(x)=√√2x-5 to answer the following:
a) f(7)
b) f(x + 1)
c) f(-x)
d) the domain of f(x).
Answer:
the answer is a because if you calculate it correctly that the answer I got
Bamboo the elephant weighed 235 lb at birth. Each month Bamboo has gained 180 lb.
If Bamboo now weighs 1495 lb, how old is she?
please help yall
Answer:7lb
Step-by-step explanation:
7x180=1260lb
1260+235=1495lb
Write each statement as a conditional.
a. A triangle with all angles congruent is equilateral.
b. Alberto can go to the movies if he washes the car.
Answer:
Step-by-step explanation:
Write each statement as a conditional.
a. A triangle with all angles congruent is equilateral.
b. Alberto can go to the movies if he washes the car.
a. If all angles of a triangle are congruent then the triangle is an equilateral triangle
b. If Alberto washes the car he can go to the movies
All members of a class of 27 students participated in at least one event on sports day. 20 students participated in individual events and 12 students took part in team events. how many students took part in both individual and team events?
5 students took part in both individual and team events.
What is data?Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.
Given:
Total students participated = 27
20 students participated in individual events
12 students took part in team events.
We have N(All students) = 27
N(individual) = 20
N(Team)= 12
So,
[tex]N_{\text{individual \; and \; team}} & = N_{\text{individual}} + N_{\text{team}} - N_{\text{All students}}[/tex]
=20+12-27
=32-27
=5
Hence, 5 students took part in both individual and team events.
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what is the solution to this problem? 2 | x+5 | =4
Answer:
x = -7
x = -3
Step-by-step explanation:
Given the following question:
[tex]2\left|x+5\right|=4[/tex]
To find the answer to this question we have to remember to apply the absolute value. The absolute value means we have to convert any negative within the lines into positive.
[tex]2\left|x+5\right|=4[/tex]
[tex]\frac{2\left|x+5\right|}{2}=\frac{4}{2}[/tex]
[tex]\left|x+5\right|=2[/tex]
Apply absolute value:
[tex]x+5=-2[/tex]
[tex]x+5=2[/tex]
Solve each equation:
[tex]x+5=-2[/tex]
[tex]5-5=0[/tex]
[tex]-2-5=-7[/tex]
[tex]x=-7[/tex]
[tex]x+5=2[/tex]
[tex]5-5=0[/tex]
[tex]2-5=-3[/tex]
[tex]x=-3[/tex]
Your answers are "x = -3 and x = -7."
Hope this helps.
Answer:
x = -3
x= -7
Step-by-step explanation:
l x + 5 l = 4/2
(x + 5) = 2 or - (x + 5) = 2
- (x + 5) - 5 = 2 - 5
x = -3
- x - 5 = 2
- x - 5 + 5 = 2 + 5
-x = 7
x = -7
Evaluate the expression for c =
10.
2c - 11 =
okay this is another question for you my good friend jdoe0001
The independent variable: lengths of the sides
The dependent variable: the perimeter of a square,
K(5) = 20.
What is the Dependent and Independent variable of a Function?The dependent variable of a function is the output of a function that changes as a result of any change in the independent variable, which is the input of the function.
The input (independent variable) determines the output (dependent variable) of a function.
Therefore, we can make the following deductions:
The independent variable, x, represents lengths of the sides, and the dependent variable is the perimeter of a square, because the perimeter of the square depends on the length of the side of the square.
The function that relates to the variables is: K(x) = 4x
So, K(5) = 4(5) = 20.
This means, if 5 is the length of one of the sides of the square, then 20 is the perimeter of the square.
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What
is the slope of the line that passes through the points (-4, 6) and (-4, 18)?
Write your answer in simplest form.