Answers
Using L'hopital we can see that the limit is equal to 1/22
How to solve the limit?Here we want to take the limit of x tending to zero for x/sin(22x)
Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:
y = x
y' = 1
And for:
y = sin(22x)
y' = 22*cos(22x)
Now taking the limit we will get:
\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)
That is the value of the limit.
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Related Questions
10 facts about Sudan in a
summary
Answers
Sudan is a member of the United Nations, the African Union, the Arab League, the Organisation of Islamic Cooperation and the Non-Aligned Movement, as well as an observer in the World Trade Organization. The National Assembly regulates the politics of Sudan. And the legal system in the country is based on Islamic law. The official name of Sudan is the Republic of the Sudan. The name sudan translates to the land of the blacks in Arabic. Sudan was once the largest and the most geographically diverse state in South Africa but it was split into two countries. Now it’s the 3rd
We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use the information to the right to help find the measure of angles 1 through 5
Answers
angle 1 = 180° - 115° (Linear Pair)
angle 1 = 65°
angle 2 = angle 1 = 65° ( Angles on the equal sides of an isosceles triangle )
angle 3 = 180° - (65° + 65°) (Angle Sum Property)
angle 3 = 180° - 130°
angle 3 = 50°
angle 4 = 180° - 65° (Linear Pair)
angle 4 = 115°
angle 5 = 115° (Vertically Opposite Angles)
What is the simplified ratio of female to male students in a class, if there are 18 boys and 9 girls?
Answers
There are 1 to 2 females to males
Work out the volume of the prism height of 12 4 and five
Answers
The calculated volume of the prism is 702 cubic cm
Finding the volume of the prismFrom the question, we have the following parameters that can be used in our computation
The trapezoidal prism (see attachment)
The formula of the volume of a trapezoidal prism is
Volume = Base area * Height
Where we have
Base area = 1/2 * (8 + 10) * 6
Evaluate the sum of 8 and 10
Base area = 1/2 * 18 * 6
Evaluate the products of 1/2, 18 and 6
Base area = 54
Also, we have
Height = 13
So, the volume is calculated as
volume = 13 * 54
Evaluate
volume = 702
Hence, the volume of the prism is 702 cubic cm
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A cylinder with a diameter of 8cm and height of 2m?
Answers
The volume of the cylinder with a diameter of 8cm and height of 2m is 100.48 cubic meters.
This question is incomplete, the complete question is:
Find the volumes of each of the following;
7) A cylinder with a diameter of 8cm and height of 2m?
What is the volume of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given that;
Diameter d = 8mRadius r = d/2 = 8m/2 = 4mHeight h = 2mVolume V = ?Plug the given values into the above formula and solve for V.
V = π × r² × h
V = 3.14 × ( 4m )² × 2m
V = 3.14 × 16m² × 2m
V = 100.48 m³
Therefore, the volume is 100.48 cubic meters.
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A pencil manufacturer makes a giant model pencil, 3m long. A real pencil is 18cm long and has a volume of 9cm(cube). Find the volume in m(cube) of the giant model.
NOTE: EXPLANATION IS REQUIRED.
Answers
Answer:
We always need an equation relating the given information to what is to be found. With this problem, we must assume that the giant model is proportional to the standard pencil.
3 m: 18 cm :: Vg:9 cm^3 where Vg is the volume of the giant pencil.
Before any calculations are performed all units must be the same.
The 3 m large pencil must be converted to cm. Each meter is 100 centimeters. Therefore: the proportion must be adjusted to:
300 cm : 18 cm :: Vg : 9 vm^3
300/18 = Vg/9 Now solve.
300 x 9 = 18 Vg By cross multiple
2700 = 18 Vg Divide both sides by 18
Vg = 2700/18 = 150 cm^3 = 0.00015 m^3
Conversion Factor: 1 cm^3 = 10^-6 m^3 Divide by 10^6.
Now Double Check
Step-by-step explanation:
Can all integers be rational??
Answers
Yes, all integers are rational numbers. If n is an integer, we can always write it as
n = n / 1
i.e. as a ratio of integers.
Answer:
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.
The equation of the red ellipse in the figure shown
Answers
ANSWER:
Larger circle:
\(x^2+y^2=81\)Smaller circle:
\(x^2+y^2=49\)STEP-BY-STEP EXPLANATION:
We have that the ellipse has the following equation:
\(\frac{x^{2}}{81}+\frac{y^{2}}{49}=1\)Where 81 is the length of the major axis and 49 is the length of the minor axis.
These values also represent the radius squared of the circles.
For the larger circle the major axis would be 81, therefore the radius squared would also be 81.
The equation of a circle has the following form:
\(x^2+y^2=r^2\)Therefore, the larger circle equation would be:
\(x^2+y^2=81\)For the smaller circle the minor axis would be 49, therefore the radius squared would also be 49.
Therefore, the smaller circle equation would be:
\(x^2+y^2=49\)PLEASE HELP ME
A new clothing company prints the same t-shirt in different colors. The ratio of the number of red t-shirts to the number of blue t-shirts was 8:5. After reviewing their sales for the first three months, the company determined that blue t-shirts were more popular and changed the printing ratio to 4:9. If they initially printed 75 blue t-shirts, how many red t-shirts are now being printed?
Answers
Answer:
480
Step-by-step explanation:
Solve the following equation algebraically: x^2 = 50 a. 7.07 b. -5.87, 5.87 c. -7.07, 7.07 d. -25, 25
Answers
Answer:
C
Step-by-step explanation:
The square root of 50 is 7.07
The value of x for the expression x² = 50 is
-7.01 and 7.01.
Options A and C 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,
x² = 50
x = √50
x = ±7.01
Thus,
The value of x is -7.01 and 7.01.
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A dolphin is at the surface of the ocean.What is the dolphin’s elevation?
Answers
Answer:
0
Step-by-step explanation:
surface of ocean = sea level = elevation of zero
The dolphin is at the surface of the ocean, that is at sea leave, and therefore it is at zero elevation
Given the points P (3, 5) and Q (-5, 7) on the cartesian plane such that R (x, y) is
the midpoint of PQ, find the equation of the line that passes through R and
perpendicular
to PQ.
Answers
Answer:
-22=22
Step-by-step explanation:
3,5-5,7=
-22/22
The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.
The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.
The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.
So, the coordinates of the midpoint R are (-1/2, 6).
Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:
(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)
Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:
(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))
Simplifying the equation:
(y - 6) = (2 / -8) \(\times\)(x + 1/2)
(y - 6) = -1/4 \(\times\)(x + 1/2)
4(y - 6) = -x - 1/2
Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
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in coin changing problem, show that the greedy strategy fails for the denominations 25, 20, 10, 5, and 1 cents. (hint: prove that we cannot construct the solution by making decisions to choose each item to add to the solution optimally, and never reversing decisions already made
Answers
In coin changing problem, the greedy strategy fails for the denominations 25, 20, 10, 5, and 1 cents.
The greedy algorithm for the coin change problem (pay a certain amount with the fewest number of coins feasible) is effective. It always chooses the coin with the largest denomination that does not exceed the remaining sum, and it consistently determines the right answer for certain coin sets.
But for certain set of denominations, it fails. For example take a sum of 44 cents then by greedy algorithm, first taking the highest denominations one 25 cent is taken and now 19 is remaining. So now one 10 cent is taken, and 9 is remaining. Now, one 5 cent is taken and four 1 cent is taken. So total we get 7 coins.
Now let us deviate from greedy algorithm and take two 20 cents, now 4 is remaining. So now four 1 cent is taken, this sums up only 6 coins. So this is a much optimal solution than the one obtained by greedy algorithm.
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That’s the Answer in the right order
Answers
Answer:
3rd one
Step-by-step explanation:
i hope have a great day
Can someone help me out?
Answers
Answer:
I think the answer might be 58 sorry if i'm wrong
Step-by-step explanation:
There are 175 glasses ellen need to wash she washes 68% of the glasses . How many glasses does Ellen have left to wash
Answers
Answer:
175-119= 56
Step-by-step explanation:
because 68%of 175 = 119
so she has washed 119 and 56 are left
The graph of the line y= 3 is a line that has which of the following characteristics?
Answers
Answer:
21
Step-by-step explanation:
A table has an area of 12 li and a perimeter of 16 ft. What are the dimensions of
O
O
2 ft by 6 ft
2 ft by 8 ft
4 ft by 3 ft
4 ft by 4 ft
O
Answers
Your answer would be i'm pretty sure 2ft by 6 ft or 4ft by 3ft I am not positively sure but if I did my maths right then they should be our answer(s) not sure...still.
The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer:
A. The y-intercept represents the number of mammals when they were originally counted.
B. The line y = 0 is an asymptote of the graph.
C. The y-intercept.is 75.
D. The y-intercept is 120.
E. The asymptote indicates that the number of mammals counted when the study began was 120.
F. The asymptote indicates that as years pass, the number of mammals will approach 0.
G. The line x = 0 is an asymptote of the graph.
Answers
The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;
A. The y-intercept represents the number of mammals when they were originally counted was 120
B. The line y = 0 is an asymptote of the graph
D. The y-intercept is 120
F. The asymptote indicates that as years pass, the number of mammals will approach 0
What is an asymptote of a graph?An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.
The points on the graph of the exponential function are;
(0, 120) and (55, 17)
The rate at which the population is decreasing = -3.5%
The output of the graph, y = The number of mammals x years after counting
The key features of the exponential function are;
The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct
The coordinates of the y-intercept is (0, 120)
The y-intercept is therefore the point y = 120
Therefore, option D is correct
The general form of the growth exponential function is presented as follows;
f(x) = a·bˣ + k
r = b - 1
b = 1 + r
Therefore;
b = 1 - 0.035 = 0.965
a = The first term = 120
Plugging in the known values from the graph, we get;
f(0) = 120 = a + k
120 = 120 + k
k = 120 - 120 = 0
k = 0 = The asymptote
Therefore, an asymptote is the line y = 0 option B is therefore correct
The number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity
Therefore as the years pass the number of mammals will approach 0, option F is correct
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What is the best description of originality?
nonobvious
special or interesting
convergent
having a low probability, unique
Answers
Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.
Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.
An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.
Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.
Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.
Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.
In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.
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A round pencil is sharpened to a cone shape at both ends.calculate the volume of the pencil if the two radius is 1.2 and heights are 8cm
Answers
Answer:
A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm
Calculate the volume using the value 22/7.
Step-by-step explanation:
6. If Jeremy has a batting average
of 0.5014
and Alex has a batting average of 0.50098
who has the better average?
Answers
the difference between two negative umers is always negative
Answers
Select all multiples of the number: 9
Answers
Answer:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90
Step-by-step explanation:
hi
Answer:
9,18,27,36,45,54,63,72,81,90
Step-by-step explanation:
Meg borrows $8650 to buy a car at 4.5% interest.
years?
How much interest will she pay after 5 years
Answers
The answer is 1922, but round and you might get your answer.
Answer:
Meg will pay $10,596.25
Step-by-step explanation:
A=Prt
A=(8650)(.045)(5)= 1946.25
8650+1946.25=10596.25
A=$10,596.25
A bakery sold a total of 500 cupcakes in a day, and 190 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?
Answers
Answer: 50/19
Step-by-step explanation:
I'm no math genius however I believe this is division.
500/190 gave me a fraction which is 50/19.
What is another way to write 54?
A. 5×5×5×5
B. 4×4×4×4×4
C. 4+4+4+4+4
D. 5+5+5+5
Answers
Answer:
None of the above
Step-by-step explanation
is this a trick question?
Option A is correct, 5×5×5×5 expression is another way to write the 5⁴
What is Expression?An expression is combination of variables, numbers and operators.
Let us find the other way to write the expression 5⁴.
Five to the power of four.
Five to the power of four is nothing but multiplying five four times.
5⁴ = 5×5×5×5
5×5×5×5 is another way to write the expression 5⁴
Hence, Option A is correct, 5×5×5×5 is another way to write the 5⁴
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write a fraction and a percent for the shaded portion of each one.
Answers
Answer:
Fractions:
a. 1/4
b. 1 and a half
c. 2/3
Percentages:
a. 25%
b. 50% unsure abt this one
c. 66.67%
Step-by-step explanation:
I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
Answer this with explanation please
Answers
The measure of angle MTU m∠MTU is 114 degree.
What is the measure of angle MTU?From the figure in the diagram:
Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.
m∠STU = 145°m∠STM = 31°m∠MTU = ?Since, angle STU composes or is the sum of angle STM and angle MTU.
To find angle MTU, simply subract angle STM from angle STU.
m∠STU = m∠STM + m∠MTU
Hence:
m∠MTU = m∠STU - m∠STM
Plug in the given values and simplify
m∠MTU = 145° - 31°
Subtract 31 from 145
m∠MTU = 114°
Therefore, angle MTU measure 114°.
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