lim x cot A - A cot x/x-A
x→A
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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p and q are both prime numbers with p < q.
They are each less than 18
Give an example where p + q is odd but not prime.
The value of p is 2 and q is either 7 or 13 and their sum is either 9 or 15.
It is given that the value of p and q is a prime number, and p<q.
But it is also given that the value of both should be less than 18 as well as a prime number.
Therefore the value of both should be 2, 3, 5, 7, 11, 13, and 17.
And it is also given that p<q.
Now we have to find the value of p + q which is odd but not a prime number.
To have a sum as an odd number one number should be even and as it is given that p<q, therefore p=2, and q = 3, 5, 7, 11, 13, 17.
So
p + q = 2 + 5 = 7, which is odd but it is prime
Now again, q = 7
p + q = 2 + 7 = 9 , which is odd as well as not prime.
Again take q = 11
p + q = 2 + 11 = 13, which is odd but prime
Now take q = 13
p + q = 2 + 13 = 15, which is odd as well as not prime.
Now take q = 17
p + q = 2 + 17 = 19, which is odd and prime.
Therefore we have p =2 and q = 7 or 13 and sum p + q =9 or 15 which is odd but not prime.
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7. 2x+1> 3 and 3x - 4 ≤ 17
Solve each compound inequality and graph the solution set
Answer:
2x+1>3
2x>4
x=2
3x-4≤17
3x≤21
x=7
A ramp with a constant incline is made to connect to a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?
The rate of change/slope of the ramp’s incline is found to be 3.
What is meant by rate of change or slope?A line's slope is defined as the change in y coordinate in relation to a change in x coordinate.
The net change in y coordinates is Δy, while it is x in Δx coordinates.As a result, the y coordinate shift in relation to the x coordinate shift could be written as,m = Δy/Δx
where, m is the slope
And, tan θ = Δy/Δx
Such an tan θ is also known as the line's slope.
The slope of a line could be determined by calculating using only two straight line points. The slope of line formula could then be used with two point coordinates.
Now, in response to the question;
To link a driveway to a front door, a ramp with a constant incline is built.
The ramp's height y₁ is 12 inches at a point 4 feet from of the driveway x₁.
The height y₂ of the ramp is 18 inches at a point 6 feet from of the driveway x₂.
The incline of the ramp's rate of change is given by:
Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)
The values given in the question;
(x₁, y₁) = (4, 12) and,
(x₂, y₂) = (6, 18)
Put the values in the formula of the slope;
Slope = m = (18 - 12)/(6 - 4)
m = 6/2
m = 3
Therefore the rate of change also called as ramp’s incline is calculated as 3.
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a travel agent is interested in the average price of a hotel room during the summer in a resort community. the agent randomly selects 18 hotels from the community and determines the price of a regular room with a king size bed. the average price of the room for the sample was $135 with a standard deviation of $25. assume the prices are normally distributed. construct an interval to estimate the true average price of a regular room with a king size bed in the resort community with 99% confidence. around the endpoints to two decimal places, if necessary.
The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 )
critical value at 0.01 significance level with 17 df = 2.898
x = mean;
99% confidence interval for μ is
(x - t * S) /√n < μ <( x + t * S) /√n;
(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;
14.74< μ< 48.89;
99% CI is ( 14.74, 48.89 ) ;
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can anybody help me ?
Answer:
Step-by-step explanation:
A and C
a rectangular garden is fenced on alls ides with 256 feet fencing. the garden is 8 feet longer than it is wide
The length and width of the rectangular garden is estimated as-
Length = 68 ft width= 60 ftHow to calculate perimeter of the rectangle?A rectangle's perimeter is the total length and distance of its border across all sides. The perimeter of a rectangular box is a linear measurement that is expressed in meters, feet, cm, or yards. Let us first examine the two primary characteristics of a rectangle.
A rectangle's four angles are all 90°.A rectangle's opposite sides are of equal length.The perimeter of the rectangle is given as-
Perimeter = 2(length + width)
perimeter= 256
Let the width of the rectangle be x.
Length is 8 feet longer than width, Thus,
length = x+8
Substitute the values in the formula of perimeter;
256 = 2( x+ 8+ x)
256 = 2( 2x + 8)
128= 2x + 8
120= 2x
x=60
Thus, width = 60 ft.
Length = 60 + 8 = 68 ft.
Therefore, the length and width of the rectangular garden is estimated.
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The complete question is -
A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8feet longer than it is wide. Find the length and width of the garden.
Number 6 please help!
Answer:
118 .........................
Answer all these questions, and I will give you brainly + 50 Points.
Answer:
Step-by-step explanation: Hello! My name is Madison and I will being helping you how to go about doing these problems! First things first.
1) 50,000 divided by 12 would be 4166.6 repeating.
2)
{(7x+y=14),(-2-y=6):}
Answer:12/8y
Step-by-step explanation:
i took the test
2/3x + 1/3x = x
Simplified
Answer: x=1
Step-by-step explanation:
Answer:
IMS (Infinitely Many Solutions)
Step-by-step explanation:
1. Combine like terms (2/3x + 1/3x) Equation: 1x = x
2. 1x is just x, so the final equation is x = x. When you get an answer like this, it means there are infinitely many solutions.
O
US
If none of the stories can be represented, select "None of the above
(a) 9x = 99
Felipe finished reading his book in 9 days. Each
day, he read x pages. His book has 99 pages.
Felipe finished reading his book in x days. Each
day, he read 9 pages. His book has 99 pages.
A book is x pages long. Felipe read 9 pages. He
has 99 pages remaining.
A book has two parts. One part is x pages long.
The other part is 9 pages long. The book has 99
pages.
D None of the above
Check
(b) x + 5 = 25
0
Felipe uses 5 eggs to make a cake. He wants to
make x cakes. He needs 25 eggs.
A tray has x eggs. Another tray has 5 eggs.
Together, the two trays have 25 eggs.
Felipe had x eggs. Then his friend gave him 5
eggs. Felipe now has 25 eggs.
Felipe had x eggs in his refrigerator. Then he used
OS of them for his cake recipe. He now has 25
eggs left in the refrigerator.
None of the above
Answer:
Step-by-step explanation:
Amy and Myra each walked from their houses to the mall. Amy walked one
half a mile and Myra walked two-thirds of a mile. How far did the girls walk all
together?
Answer:
C
Step-by-step explanation:
just do 1/2+2/3
Common denominators
3/6+4/6=7/6=1+1/6
C
A stack of 9 cups measures 194 mm. Another stack of 22 of the same cups measures 272 mm.
1.) Find the height of one cup.
2.) How tall would a stack of n cups measure?
The result for the stack of cups are shown below;
The height of the one cup is found to be 6 mm,The height formed by the stack of n cups is 6n.What is defined as unitary method?The term unitary refers to a single or unique unit. As a result, the goal of this method is to determine values are related to a single unit.
The Unitary Method is the method in which we first find the value of one unit and then calculate the value of the necessary number of units.For example, if a car travels 44 kilometres on two litres of gasoline, we can employ the unitary method to calculate how far it will travel on one litre of gasoline.Now, as per the given question.
Part 1: The height of one cup;
The stack of 9 cups form the height 194 mm.
Similarly, the height of the 22 of the same cups measures 272 mm.
For the calculation of height of one cup;
Difference in the total height = 272 - 194 = 78.
Difference in the number of cups = 22 - 9 = 13.
Thus, the height of one cup = 78/13 = 6
The height of the one cup is found to be 6 mm.
Part 2: The height of n stack of cups;
The height of one cup is estimated as 6 mm.
There are total n number of cups.
Thus, the height of the n cups will be 6×n mm.
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3/2(8w-6)
can I get the answer in simplest form
Answer: 12w-9
Step-by-step explanation:
The lengths of the three sides of a triangle are consecutive integers. If the perimeter is 90 feet, find the value of the longest of the three side lengths
The value of the longest side of the triangle is 31 feet
The perimeter of the triangle is the sum of all its sides.
The formula for perimeter where a, b and c are the three sides of the triangle is given as:
Perimeter = a + b + c
It is given that the sides are consecutive integers and the perimeter is 90 feet, therefore
Let sides be x, x+1 and x+2
Perimeter = x + x+1 + x+2
90 = x + x+1 + x+2
90 = 3 + 3x
87 = 3x
x = 29 feet
The value of the longest side will be x+2, which will be 29+2 = 31 feet
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please help me answer this with solution
Answer:
Question 1:
[tex]{ \tt{f(x) = {x}^{2} - 10x + 25}}[/tex]
when f(x) is f(10), we substitute for x as 10; x = 10
[tex]{ \tt{f(10) = {10}^{2} - 10(10) + 25 }} \\ { \tt{f(10) = 100 - 100 + 25}} \\ { \boxed{ \tt{ \: f(10) = 25 \: }}}[/tex]
Question 2:
[tex]{ \tt{f(x) = \frac{2 {x}^{3} - 7 }{10} }} \\ [/tex]
when f(x) is f(-1), we substitute for x as -1; x = -1
[tex]{ \tt{f( - 1) = \frac{2 {( - 1)}^{3} - 7 }{10} }} \\ \\ { \tt{f( - 1) = \frac{ - 2 - 7}{10} }} \\ \\ { \boxed{ \tt{ \: f( - 1) = - \frac{9}{10} \: }}}[/tex]
WILL CHOOSE THE BRAINLIEST!
The measure of x, that is, the angle OBA is equal to 22.5°.
What is the measure of the missing angle in geometrical system?
Herein we find a geometric system formed by a circle, a diameter and a chord. In the image attached below we present all the possible angles of the geometric system, formed by two isosceles triangles.
According to Euclidean geometry, an isosceles triangle has two sides and two angles of equal length. Then, the sum of the internal angles of the triangle AOB is equal to:
m ∠ AOB + m ∠ OBA + m ∠ OAB = 180°
135° + 2 · m ∠ OBA = 180°
2 · m ∠ OBA = 45°
m ∠ OBA = 22.5°
By taking advantage of the properties of isosceles triangles, the measure of x, that is, the angle OBA is equal to 22.5°.
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Make x the subject of the formula
√a=x−b^2/2c
Answer:
x = [tex]\sqrt{a}[/tex] + [tex]\frac{b^2}{2c}[/tex]
Step-by-step explanation:
[tex]\sqrt{a}[/tex] = x - [tex]\frac{b^2}{2c}[/tex] ( add [tex]\frac{b^2}{2c}[/tex] to both sides )
[tex]\sqrt{a}[/tex] + [tex]\frac{b^2}{2c}[/tex] = x
Examine the following graph of y=−3x+7.
Match each x-coordinate with the corresponding y-coordinate.
x-coordinate=2
x-coordinate=5
x-coordinate=3
x-coordinate=0
-----------------------------------
Answer choices to match with the X coordinates
Y coordinate = -2
Y coordinate = -8
Y coordinate = 7
Y coordinate = 1
Answer:
y = -3(2)+7
y= -6+7
y= 1
(2,1)
y=-3(5)+7
y= -15+7
y= -8
(5,-8)
y= -3(3)+7
y=-9+7
y=-2
(3,-2)
y=-3(0)+7
y=0+7
y=7
0,7)
Step-by-step explanation:
substitute the values of x in the equation
What is an undefined term?
Answer : Undefined terms are those terms that don’t require a formal definition. The four terms are point line plane and set
Step-by-step explanation:
I need help with this!
Answer:
-0.5
Step-by-step explanation:
[tex]\frac{f}{g} =\frac{f(n)}{g(n)} = \frac{4n}{n^2-3n}[/tex]
[tex]\frac{4(-5)}{(-5)^2-3(-5)} =\frac{-20}{40} =\frac{-1}{2}[/tex]
A stand in a supermarket can hold 157.5 kg. How many 1.25 kg bags of potatoes will it hold?
Answer:
If a stand can hold 157.5kg
x stand can hold 1.25kg
1=
Answer:
126 bags.
Step-by-step explanation:
157.5 / 1.25
= 126.
Name the segment in the scaled copy that corresponds to segment AD
Segment PS in the scaled copy corresponds to segment AD in polygon ABCD in polygon PQRS. They are similar in appearance and appear in the same location.
What is a polygon?A polygon is a two-dimensional flat shape with straight, fully closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
Polygon is derived from the Greek word "polugonos." It has evolved into the term "polygon" over time. The term "polygon" means "many" and "gon" means "angled." This is due to the fact that a polygon has numerous angles and corners within its shape.
The Greeks may have been the first to recognize polygons, as there are numerous examples of them recognizing polygons such as the pentagram in their ancient art and writings.
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I need help ASAPPPPPPPPP
Answer:
C) 3/8 < 1/2 good luck
Step-by-step explanation:
brainliest please
The temperature at 3:00 p.m. was 7F. By 9.00 p.m. the temperature had dropped by 12 degrees. What was the temperature at 9.00 p.m.?
Answer: The answer is -5
Step-by-step explanation: According to the question it stated that the temperature was 7 degrees at 3pm and by 9pm it dropped 12 degrees so from my answer it would -5 degrees
V
What is the measure of the angle shown?
Answer:
The arrow indicates that the angle terminates in the second quadrant, meaning that its more than 270 deg
Find the surface area of a cylinder with a height of 8 inches and base diameyer of 6 inches i need help badly
The surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
How to find the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches?The given parameters are
Height, h = 8 inches
Diameter, d = 6 inches
The radius is calculated as
r = d/2
So, we have
r = 6/2
r = 3
The surface area of a cylinder is calculated as
S = 2πr(r + h)
So, we have
S = 2 * 3.14 * 3 * (3 + 8)
Evaluate
S = 207.24
Hence, the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
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marilyn is going on a class outing to an amusement park. she has $40 to spend. the admission price is $20. she plans to buy a sandwich for $5. a cup of lemonade costs $3.00. write an inequality to show how many cups of lemonade, c, she can buy.
The inequality for the number of cups of lemonade she can buy is :
0 < c < 5.
Marilyn has $40 to spend in the amusement park.
Admission price = $20
So money left = 40 - 20 = $20
Now she plans to buy a sandwich for $5.
So the money left now will be = 20 - 5 = $15
Price of a cup of lemonade = $3
Marilyn can buy at most $15/3 = 5 cups of lemonade.
She can either choose to not buy a cup of lemonade or can buy at most 5 cups of lemonade.
So the inequality for the number of cups of lemonade she can buy will be
0 < c < 5 , where 'c' denotes the number of cups of lemonade.
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a cell phone carrier charges a monthly fee of $20 and also charges customers $0.05 per text message. the function c(t) = 0.05t +20 represents the cost, c, per month based on t text messages in a month. which best describes the domain of the function?
The best description of the domain of the function is t >= 0
How to determine which best describes the domain of the function?The equation of the function is given as
C(t) = 0.05t + 20
The above equation is a linear function, and the variable t represent the number of text messages in a month
The number of text messages in a month cannot be negative
This means that
t >= 0
Hence, the best description of the domain of the function is t >= 0
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