a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.
c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
What is a function?
A function is a mathematical relationship between two variables, often denoted as "f(x)" or "y = f(x)". A function assigns a unique output to each input within its domain. In other words, for every value of x, there is a corresponding value of y, and each value of x can only correspond to one value of y.
a. To find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0, we need to find the Taylor series of f(t) centered at 0. The general term of a Taylor series is given by:
f(t)^(n) / n! * (t-0)^n
The Taylor series of f(t) = 3/(1+t^2) centered at 0 is:
f(t) = 3 - 3t^2 + 3/3t^4 - 3/5t^6 + ...
The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b. To find the first four nonzero terms and the general term for the power series expansion of g(x) = ∫f(t)dt about x=0, we need to integrate the Taylor series of f(t) term by term.
g(x) = ∫f(t)dt = (3t - 3/3t^3 + 3/5t^5 - ...) from 0 to x
g(x) = 3x - 3/3x^3 + 3/5x^5 - ...
The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7
c. The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence for g(x), we can use the ratio test.
The ratio test states that if the limit of |a(n+1)x^(n+1)|/|a(n)x^n| as n approaches infinity is less than 1, the series converges for all x.
|3/7x^7|/(|3/5x^5|) = |x^2|/(|3/5|) < 1 when |x| < sqrt(5/3)
So, the interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
Hence,
a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.
c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
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A physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.
How many puffs will the patient take daily?
The puffs that the patient will take daily include:
1 puff every 4 hours for 24hrs = 6
1 puff every 6 hours for 24hrs =4
2 puffs every 4 hours for 24hrs =12
2 puffs every 6 hours for 24 hrs =8
How to calculate the number of puffs?From the information, a physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.
In this case, it should be noted that puff every 4 hours for 24hrs will be 6 times. Also, 1 puff every 6 hours for 24hrs will be 4 times.
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On a line segment, U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3, what is TU?
The value of TU is 117.
What is a line segment?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Here, we have
Given: U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3.
We have to find the value of TU.
TV = TU + UV
20x − 3 = 11x − 15 + 10x
20x − 3 = 21x - 15
-3 + 15 = 21x - 20x
12 = x
Now, we have TU = 11x − 15.
We put the value of x on TU and we get
TU = 11x − 15
TU = 11(12) - 15
TU = 132 - 15
TU = 117
Hence, the value of TU is 117.
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Luisa has four boxes of chocolate bars there are 10 chocolate bars in each pack in each chocolate bar has eight pieces find two equivalent expressions that could be used to find the total number of chocolate pieces Luisa has
The two equivalent expressions that could be used to find the total number of chocolate pieces that Luisa has are given as follows:
(4 x 10) x 8.4 x (10 x 8).How to obtain the number of chocolate pieces that Luisa has?To obtain the number of pieces that Luisa has, we must consider that:
She has four boxes.Each box is composed by 10 bars.Each bar is composed by 8 pieces.Hence the multiplication operation giving the number of pieces is given as follows:
4 x 10 x 8.
The associative property of multiplication states that the order in which 3 or more terms are multiplied does not change the product, hence the equivalent expressions are given as follows:
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A text message plan costs $6 per month plus $0.43 per text. Find the monthly cost for x text messages The monthly cost of x messages is dollars.
The monthly cost of x messages is 0.43x + 6 dollars.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given
Cost of message plan for one month = $6
cost for each text = $0.43
The monthly cost is calculated by adding the price of the message plan for one month to the cost of each text message multiplied by the number of messages sent in a month.
Total number of messages sent in a month = x
monthly cost for x text messages = (0.43 * x) + 6
Monthly cost for x text messages = 0.43x + 6 dollars
Hence the cost is 0.43x + 6 dollars.
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The mean for baking pie is 65 minutes with a standard deviation of 12 minutes. The mean for sautéing carrots is 13 minutes with a standard deviation of 2 minutes. What is the mean time required to bake a pie and then sauté carrots?
A regular hexagon is composited of 6 equilateral Triangles.
X is 6.7cm.
What is the vertical height of the hexagon?
X
According to the question of equilateral triangles, 6.7√3 cm is the vertical height of the hexagon.
What is equilateral triangles?An equilateral triangle is a triangle with all three sides having the same length and all three angles measuring 60 degrees. It is one of the three basic shapes in geometry and is considered to be the most symmetrical triangle. The sides of an equilateral triangle are always congruent, meaning all three sides have the same length. The sides of an equilateral triangle are also always perpendicular, meaning all three angles are equal to 60 degrees. The area of an equilateral triangle can be calculated using the formula A = (1/2)bh, where b is the length of the base and h is the length of the height.
The vertical height of the hexagon can be calculated using the Pythagorean Theorem. The length of each side of the equilateral triangle is x/2 and the height of the triangle is x√3/2.
The total vertical height of the hexagon is therefore 6 x x√3/2, which is equal to 6.7√3 cm.
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The 3-4-5 right triangle is a commonly used right triangle. Use the inverse sine function to determine the measure of the angle opposite the side of length 3.
The measure of the angle opposite the side of length 3 is approximately 53.13 degrees.
To find the measure of the angle opposite the side of length 3, we need to use the inverse sine function. The inverse sine function can be written as sin^−1(x). We can use the Pythagorean Theorem to calculate the side length of the triangle, which is 3^2 + 4^2 = 5^2. Therefore, we can use the inverse sine function to calculate the measure of the angle opposite the side of length 3. To do this, we will take the ratio of the side of length 3 to the hypotenuse, which is 3/5. We can then plug this value into the inverse sine function, which gives us sin^−1(3/5). Calculating this value gives us approximately 53.13 degrees, which is the measure of the angle opposite the side of length 3.
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The Summerfield Opera House sold 22,200 tickets this year, but it has been experiencing a 6% drop in sales from one year to the next. If this trend continues, then how many tickets will the opera house sell 2 years from now?
Answer: 20,009
Step-by-step explanation:
pk you you have to divide it by 100 sk its 1% then multiply it by 12 sibce its two years
19,616 Answer:
Step-by-step explanation: you divide
What’s the difference between 13/4 and 1/2
Answer:
11\4
Step-by-step explanation:
the lcm of 4 and 2 is 4. divide 4 by each denominator. your answer multiplied by the numerator. then you find the difference between the two numbers
the questions for quiz 2 will include all 6 trig functions with angles on the unit circle in the interval [0, 2pi], given in radians or degrees.
Trigonometry is the study of relationships between angles and sides of a triangle.
The six trigonometric functions—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)—are used to describe the relationships between the angles and sides of any triangle.
The unit circle is a circle of radius one centered at the origin of a Cartesian coordinate system. When we determine the coordinates of points on the unit circle, we are using the six trigonometric functions. The unit circle is used to find the values of the trigonometric functions for angles of measures 0°, 30°, 45°, 60°, and 90°.
In the interval [0, 2π], we can use the unit circle to calculate the trigonometric functions of the angles in both degrees and radians. For example, sin 0° = 0, cos 0° = 1, tan 0° = 0, csc 0° = undefined, sec 0° = 1, cot 0° = undefined. The corresponding values in radians are sin 0 = 0, cos 0 = 1, tan 0 = 0, csc 0 = undefined, sec 0 = 1, cot 0 = undefined.
By using the unit circle, we can find the value of all six trigonometric functions for any angle in the interval [0, 2π], given in degrees or radians. We can also use the unit circle to find the trigonometric functions for any angle in any interval.
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Which coordinates are solutions to the equation? Select ALL that apply.
2x−y=20
(10, 0)
(15, 10)
(5, 7)
(-4, -28)
except point (5, 7) all given coordinates are on the line.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
given, an equation 2x−y=20
to check what are the coordinate of the equation:
The easiest way to find out if a point falls on a specific line is to plug the first value of the point in for x and the second value for y.
Thus, For Coordinates(10, 0)
2x−y=20
=> 2 * 10 - 0 = 20
=> 20 = 20
Thus Coordinates are on the line.
Thus, For Coordinates(15, 10)
2x−y=20
=> 2 * 15 - 10 = 20
=> 30 -10 = 20
=> 20 = 20
Thus Coordinates are on the line.
Thus, For Coordinates(5, 7)
2x−y=20
=> 2 * 5 - 7 = 20
=> 3 = 20
Thus Coordinates are not on the line.
Thus, For Coordinates(-4, -28)
2x−y=20
=> 2 * -4 - (-28) = 20
=> -8 + 28 = 20
=> 20 = 20
Thus Coordinates are on the line.
Therefore, except point (5, 7) all given coordinates are on the line.
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List the values of x at which f has a local minimum. Select the correct
choice below and fill in any answer boxes within your choice.
The correct choice is b. There are no local maxima. The intervals where the function is increasing. Since the square of any real integer is always positive, the function 3x² will always be growing right since it will never be less than 6 right.
What is mean by local maxima? Local maxima refers to the highest point on a graph in a particular neighborhood. It is the highest value of a function in a region of its domain, which lies immediately before and after a lower value. It is a point where the slope of the graph is zero, or the point at which the graph changes direction from increasing to decreasing. Local maxima can be used to identify regions of increased activity or intensity in a graph, or they can be used to determine the rate of change of a function over a range of values. Local maxima are also known as local peaks or local extrema.To learn more about local maxima refer to:
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Kory pays 1/3 of his income in tax. He then spend 4/5 of what remains after tax, and places the rest into a savings account. What fraction of his income does he put into his saving account?
Answer:
2/5 of income put into savings
Step-by-step explanation:
Let Kory's income be X
1/3 of his income goes to taxes so taxes are X/3
Remaining is (1- 2/3) of income = (2/3 ) X
He spends 4/5 of this remaining amount
So balance after expenditure = (1- 4/5) = 1/5 of the remaining income and this amount is put into savings
Fraction of income in savings = 1/5 x 2/3 X = (2/15)X
So fraction put into savings account is 1/5 of total income
If you find it confusing to work with fractions such as these, I suggest an alternate approach which may make it easier to understand
Pick an amount for total income. Since the denominators are 3 and 5, choose an amount which is divisible by both 3 and 5 or in other words divisible by 15
Let's choose 300, a convenient number
Tax Paid = 1/3 x 300 = 100
Income after tax = 300 - 100 = 200
which is same as 2/3 x 300
Spending = 4/5 x 200 = 160
Balance in savings = 200 - 160 = 40 same as 1/5 x 200
So amount in savings as a fraction of income = 40/300 = 2/15
use method of reduction of order to find a second solution of the given equation; t^(2)y''+2ty'-2y=0, t>0
if y_1(t)=t , (given hint): set y_2= v(t)t
The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.
The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.
y_2(t) = t^2v'(t) + 2t v(t) - y_1(t)
Substituting y_1(t) and y_2(t) in the given equation, we get
t^2v''(t) + 2tv'(t) - 2v(t) = 0
This is a first order linear differential equation and can be solved as
v'(t) = -2v(t)/t
Integrating both sides, we get
v(t) = c/t^2
Therefore, the second solution of the given equation is
y_2(t) = c/t
The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.
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It’s Election Day for a club. If a president and vice president are elected, how many combinations can be made among eight people
The number of combinations that can be made among eight people is given as follows:
56 combinations.
How to obtain the number of combinations?As there are different roles, the order is important, hence the permutation formula is used to solve this question.
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
For this problem, two people are selected from a set of 8, hence the number of combinations is given as follows:
P(8,2) = 8!/6! = 8 x 7 = 56 combinations.
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12*8=
13*90=
show your work
Answer:
96 and 270
Step-by-step explanation:
12×8=96
90
×13
180
+90
270
Jacob received a deck of cards for his birthday. The length, width, and height of the card box are shown below.
A measurement of a cards box bottom as 2 and half in, side as 3 and half in, and width as 2 by 3 in.
What is the volume of the card box?
The deck of cards Jacob got has a volume of 6.833 cubic inches.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, Jacob received a deck of cards for his birthday. The length, width, and height of the card box are shown below.
Length = 3 1/2 = 7/2
Width = 2 1/2 = 5/2
Height = 2/3
From the general formula of volume:
volume = Length * width *Height
volume = 7/2 * 5/2 * 2/3
The volume of a pack of cards = 35/6 = 6.833
Therefore, the volume of the Deck of cards Jacob received is 6.833 cubic inches.
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Sove the inequality, I need the step by step for this please
|x +1|>-3
The solution for the inequality |x +1|>-3 is x > -4 or x < -4.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To solve the inequality |x + 1| > -3, we need to consider two cases:
x + 1 > -3: In this case, we can subtract 1 from both sides to get x > -4.
x + 1 < -3: In this case, we can subtract 1 from both sides to get x < -4. However, we also need to reverse the inequality symbol because we are multiplying or dividing by a negative number.
So the solution for the inequality is x > -4 or x < -4.
To get the final solution, we need to consider the combined solution from both cases:
x < -4 or x > -4
This represents as follows:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
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Karen divided 560.9 by 10³ and got
a quotient of 0.5609. Julio thinks the
quotient should be 5.609. Who is correct?
Explain your answer.
Karen divided 560.9 by 10³ and got a quotient of 0.5609 ,therefore he is right.
What do you mean by division?
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
What do you mean by quotient ?
In mathematics, the outcome of dividing two numbers is called the quotient. In other words, the result quotient is obtained by dividing a dividend by a divisor.
How to Divide a Long Number by Decimals?
Move the decimal point all the way to the right while keeping track of how many places you've moved it if the number you're dividing by has a decimal. Then, move the decimal point the same number of places to the right in the number you are dividing.Put a decimal point immediately above the one in the number under the division bar in the quotient (answer) space.Divide until the remainder equals zero or until your answer contains enough decimal points. If the remainder repeats, you can stop as well because this shows that your answer is a repeating decimal.Hence, Karen divided 560.9 by 10³ and got a quotient of 0.5609.
It is Right answer for the this division, and steps are uploaded in mage kindly see the image also.
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Savod Seiko wants to broaden her functional business knowledge. Which of the following activities should she engage in? Multiple Choice Wearing o blue hat attending a business conference reading a magazine article writing a reflection journal
Attending a business conference is the activity she should engage in.
Why conferences are important for businesses?A business conference is held for those employed by the same organisation or sector. They meet together to talk about potential business prospects and emerging trends. On a broader scale, a trade conference is held.Industry experts and solution providers can network, exchange contacts, and potentially start working together during conferences. With their technology, advice, or product, the event's exhibitors can assist you in solving your problems.For the networking possibilities, yes. One of the few opportunities you may have to network with trailblazing members of your field is at a conference. Even though some conferences are expensive and may seem like a waste of time, going can be a wise business decision.Learn more about Business conference refer to :
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Given: E is the midpoint of overline BD and overline AC perp overline BD .Prove : triangle BAE cong triangle DAE . Statement reason eis the midpoint of bd ac bd type of statement kote:- gd and ur cogmnents step given'
The ΔBAE is congruent to ΔDAE. ΔBAE and ΔDAE have three corresponding angles that are congruent, so they are congruent.
The Triangle Congruence Theorem states that if two triangles have three corresponding angles that are congruent, then the triangles are congruent.
This can be seen by looking at the angles BAE, BAE, and DAE. All three of these angles are equal, so they are congruent. Additionally, the side lengths of the triangles are the same, so the triangles are also congruent. The Triangle Congruence Theorem is an important tool for determining the congruence of two triangles.
It is used to compare the angles and side lengths of two triangles, and if the angles and side lengths are the same, then the triangles are congruent. When ΔBAE and ΔDAE have the same angles and side lengths, then it is clear that they are congruent.
According to question,
E is the midpoint of,
AC⊥ BD,
As given E is the midpoint of the line ,
So, BE = ED,
further, line AE = AE, because this is the common line between the two triangles.
Also, ∠BED =∠DEA =90°, as AC⊥ BD.
Therefore, the ΔBAE is congruent to ΔDAE.
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the sum of two consecutive integers is 65. find the two numbers
Answer:
x=32
x+1=33
Step-by-step explanation:
let the first consecutive integer be 'x'
let the second consecutive integer be 'x+1'
x+x+1=65
2x+1=65
2x=65-1
2x=64
x=64÷2
x=32
x+1=(32+1)
x+1=33
Which of the following are square properties? Choose ALL that apply.
Four right angles.
Exactly one pair of parallel sides.
Diagonals are perpendicular.
Diagonals are congruent.
Given the two rectangles below. Find the area of the shaded region.
Answer:
The area of the shaded region is 36.
Step-by-step explanation:
First, let's find the area of the rectangle as a whole, which will be 5*10 = 50. How did we get 50? The right side is 5 (from 2+3), and the top is 10 (3+7). Multiplying those numbers together will give you the area.
Now, the problem asks to find the shaded region. Let's solve for the area of the non-shaded region: (7*2) = 14.
Now, we can subtract the whole rectangle area minus the non-shaded region to find the shaded region:
50 - 14 = 36
A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?
I. 30
II. 35
III. 45
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
The answer is D. I and II only. The number of people who chose A as their favorite brand could be 30 or 35 since x is rounded to the nearest integer, which is 3. However, it cannot be 45 since 3 is the nearest integer.
1. x is rounded to the nearest integer, which is 3
2. If x is equal to 30, then the number of people who chose A as their favorite brand would be 30
3. If x is equal to 35, then the number of people who chose A as their favorite brand would be 35
4. If x is equal to 45, then the number of people who chose A as their favorite brand would be 45
5. Since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45
6. Therefore, the answer is D. I and II only.
1,150 respondents were asked to select their preferred brand among brands A, B, and C of laundry detergent. x% of those polled indicated that A was their preferred brand. The outcome is 3 if x is rounded to the nearest integer. This means that x could be 30, 35, or 45. However, since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45. Therefore, the answer is D. I and II only, meaning that the number of people who chose A as their favorite brand could be 30 or 35. This is because if x is equal to 30, then the number of people who chose A as their favorite brand would be 30 and if x is equal to 35, then the number of people who chose A as their favorite brand would be 35.
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Two lines are parallel when their slopes are the same
Two lines are perpendicular when the product of their slopes is -1
Two lines are intersect when their slopes are different
Let's define our slopes as m1 and m2, != means not equal
Solution:
1) m1 = m2 Parallel
2) m1*m2=-1 Perpendicular
3) m1*m2=-1 Perpendicular
4) m1=m2 Parallel
5) m1=m2 (-4 = -4) Parallel
6) m1 != m2 Neither
7) m1 != m2 Neither
8) m1*m2=-1 Perpendicular
A circular dartboard is divided into regions with various central angles. The probability of a dart randomly landing in a particular region is 1/6. What is the corresponding measure, in degrees, of the central angle of this section of the dartboard?
The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.
The probability of randomly landing in a particular region of a circular dartboard is 1/6. This means that each region of the dartboard is equivalent in size, and thus has the same central angle. Since the dartboard is circular, the total measure of the central angles must add up to 360 degrees. Therefore, the measure of the central angle of each section of the dartboard is 360 divided by 6, which is equal to 60 degrees.
The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6. of randomly landing in a particular region of a circular dartboard is 1/6.
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Open MINITAB file rateMP.mpj from your email. This data represents information on 700 instructors from the popular website ratemyprofessors.com. All instructors are sampled from the Foothill-De Anza Community College District. Here is a description of the data: College: Foothill or De Anza Smiley: Positive - Neutral Negative Photo: Instructor has a photo Hot: Instructor has a chili pepper Gender: Male or Female Dept: Academic Department (example - Mathematics) Division: Academic Division (example - PSME) Num: Number of Ratings for that faculty member Overall: Average Overall Quality Rating (1-5 scale, lowest to highest) Easiness: Average Easiness Rating (1-5 scale, hardest to easiest) We are going to use Minitab to make some graphs for this data. Specifically, we are going to look at the average easiness rating of Foothill-De Anza Community College instructors, and we will use the 700 instructors as a sample. First, let's ask some questions about this data.
What is the average easiness rating of Foothill-De Anza Community College instructors? What are the distributions of easiness ratings for instructors with a photo, chili pepper, and no chili pepper? Is there a relationship between gender and easiness ratings?
To answer these questions, we first need to open the MINITAB file rateMP.mpj. Upon opening the file, we can see that it contains data on 700 instructors from Foothill-De Anza Community College, including the college they teach at, their gender, the department and division they teach in, the number of ratings they have received, their overall quality rating, and their easiness rating. To answer the first question, we can use the average function on the easiness column to find the overall average easiness rating of Foothill-De Anza Community College instructors. To answer the second question, we can use a bar chart to compare the distributions of easiness ratings for instructors with a photo, chili pepper, and no chili pepper. To answer the third question, we can use a two-way table to examine the relationship between gender and easiness ratings. After creating these graphs and tables, we can then interpret our results.
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On 21/04 the service fee for depositing the amount of R2239.10 was 31.74. Determine the service fee as a percentage of the deposited amount
To determine the service fee as a percentage of the deposited amount, we can use the following formula:
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Service fee percentage = (Service fee / Deposited amount) x 100
In this case:
Service fee percentage = (31.74 / 2239.10) x 100 = 1.41%
So, the service fee for depositing the amount of R2239.10 was 1.41% of the deposited amount.
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Find an equation of the form y=f(x) for a curve with x-intercept 1 whose tangent line at any point (x, y) has slope xe^-y.
y=___
y = ln( [tex]\frac{x^2+1}{2}[/tex]) is the required equation.
What is x-intercept?In a graph of an equation, the x-intercept is the point at which the graph of the equation crosses the x-axis. It is the point where the y-coordinate is equal to 0. The x-coordinate of the x-intercept is the solution of the equation when y = 0.
Given that the slope at point (x,y)
and we know that slope at any find is dy/dx
so dy/dx = [tex]xe^-^y[/tex]
=> dy/[tex]e^-^y[/tex] = xdx
=> [tex]e^y[/tex] dy = x dx
intergrating both side we get:
[tex]e^y[/tex] = x²/2 + c
where c is a constant
given x intercept is 1
[tex]e^0[/tex] = 1²/2 + c
=> 1 = 1/2+c
=> c= 1/2
so [tex]e^y[/tex] = x²/2 + 1/2
taking ln on both side we get:
y = ln( [tex]\frac{x^2+1}{2}[/tex]) is the required equation.
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