Nolan buys a $12,000, 13-week treasury bill at 5%. What’s his effective rate? Round your answer to the nearest hundredth of a percent.
Answers
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
what is interest ?Divide the original by the lending rates, the duration of time, and other factors to arrive at simple interest. Simple gain = principal + interested + hours is the marketing formula. This system makes it simpler to calculate interest. The most popular technique to figure out this is as a portion of the principal sum. He can only pay his share of the 100% interest, for example, if he borrow $100 from a friend he agrees to repay him with 5% interest. $100 (0.05) = $5. When you borrow more money, you should pay interest, and when you give it out, you must make payments. Interest is often determined as an indicator of the overall of the loan total. The interest on the loan is this percentage.
given
Simple interest = $12,000 × 0.05 × 13/52 = $150
Simple discount note = ($12,000 - $150) × 13/52 = $2962.5
Effective rate of interest = $150 / $2962.5
Effective rate of interest = 0.0506 or 5.06%
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
Related Questions
What is the line segment of BD
Answers
The vertices of triangle ABC are given: A (0;-1) B(12; -10) C(10;4)
Find:
a) the equation of the median and bisector drawn from vertex A;
b) the equation of the altitude from vertex B;
c) the point of intersection of the median and height;
d) the coordinates of the center of mass (the point of intersection of the medians).
Answers
verified
Verified by Toppr
Median bisects the line.
D≡(
2
−3+5
,
2
−9−8
)≡(1,
2
−17
)
E≡(−
2
1+5
,
2
6−8
)≡(2,−1)
F≡(−
2
1−3
,
2
6−9
)≡(−2,
2
−3
)
∴ equation of AD:(y−y
1
)=(
x
2
−x
1
y
2
−y
1
)
AD
(x−x
1
)
⇒(y−6)=
⎝
⎜
⎜
⎛
1+1
2
−17
−6
⎠
⎟
⎟
⎞
(x+1)⇒(y−6)=−
4
29
(x+1)
⇒
4
29
x+y−6+
4
29
=0
AD⇒29x+4y+5=0
equation of BE:(y+9)=(−
2+3
1+9
)
BE
(x+3)
⇒(y+9)=
5
8
(x+3)⇒5y+45=8x+24
BE⇒8x−5y−21=0
Equation of CF:(y+8)=
⎝
⎜
⎜
⎛
−2−5
−
2
3
+8
⎠
⎟
⎟
⎞
CF
(x−5)
⇒(y+8)=−
14
13
(x−5)⇒14y+112=−13x+65
CF:13x+14y+47=0
Two people are playing the game rock, paper scissors. In each round both players show rock, paper, or scissors at the same time. What is the probability that both players show rock in the first round. Show your work.
Answers
The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).
In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.
To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.
Therefore, the probability that both players show rock in the first round can be calculated as follows:
P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9
So the probability that both players show rock in the first round is 1/9 or approximately 0.111.
For more such question on probability
https://brainly.com/question/251701
#SPJ8
calculate the volume of a cylinder with a radius of 4 inches and a height of 12 inches. (V = T2h)
Answers
Answer:
603.44
Step-by-step explanation:
solution,
radius=4 inches
height=12 inches
volume=?
we know,
volume of cylinder = πr^2h
=22/7×(4)^2×12
=22/7×16×12
=603.44 inches^3#
The volume of a cylinder with a radius of 4 inches and a height of 12 inches is 602.88 cubic inches.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of cylinder whose radius of 4 inches and a height of 12
Radius r = 4 inches
Height h =12 inches
Volume=πr²h
Now plug in the values.
Volume=3.14×4²×12
=3.14×16×12
=602.88 cubic inches
Hence, the volume of a cylinder with a radius of 4 inches and a height of 12 inches is 602.88 cubic inches.
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ2
A cannonball is fired vertically upward from a height of 8 feet above the ground and with an initial velocity of 48 feet per second. The height of the cannonball after x seconds is shown in the table below. Time (seconds) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Height (feet) 8 19 28 35 40 43 44 43 40 Describe the symmetry of the height of the cannonball over time. The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds. The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 1.25 seconds is equal to the height of the cannonball at 1.75 seconds. The height of the cannonball over time is not symmetric. The height of the cannonball over time is symmetric about the line x = 1.0 seconds, which indicates the height of the cannonball at 0.75 seconds is equal to the height of the cannonball at 1.75 seconds.
Answers
The correct answer to the above question is option (a) The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.
What is Symmetry?Symmetry refers to a property of an object or a function that remains unchanged when transformed by a specific operation.
For example, a geometric shape is symmetric if it can be divided into parts that are mirror images of each other.
According to the given information:The answer to the above question is The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.
This is because the heights at 0.5 seconds and 2 seconds are equidistant from the line x=1.5 seconds, and they have the same magnitude but opposite signs. Therefore, the graph of the height of the cannonball over time is symmetric with respect to the vertical line x=1.5 seconds.
To know more about symmetry visit:
https://brainly.com/question/1531736
#SPJ1
UpEx delivers packages which cost $1.50 per package to deliver. The fixed cost to run the delivery truck is $198 per day. If the company charges $3.50 per package, how many packages must be delivered daily to make a profit of $32?
Answers
The number of packages that need to be delivered daily by UpEx to make a profit of $32 is 115 packages
How to find the number of packages?First, find the contribution margin of each package:
= Charge to deliver package - Cost to deliver package
= 3.50 - 1.50
= $2.00
To find the number of packages needed to make a profit of $32, the formula is:
= (Fixed cost + projected profit) / Contribution margin
= ( 198 + 32) / 2
= 230 / 2
= 115 packages
How to find the quantity to make profit at https://brainly.com/question/17929256
#SPJ1
Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
System A
x+3y=9
-x-3y=9
System B
-x-3y=-3
x+3y=3
O The system has no solution.
O The system has a unique solution:
(x, y) = (
O The system has infinitely many solutions.
They must satisfy the following equation:
y = 0
O The system has no solution.
O The system has a unique solution:
(x, y) = (D)
O The system has infinitely many solutions.
They must satisfy the following equation:
y=0
Answers
The system A has no solution.
The system B has the solution y=( 3-x )/3
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
System A:
x+3y=9..........(1)
-x-3y=9 ..........(2)
(1) => x=9-3y........(3)
Substitute (3) into (2)
(2) = > - ( 9-3y ) - 3y = 9
-9 + 3y - 3y = 9
-9 =9
This is false.
So, the system has no solution.
System B:
-x-3y=-3..........(1)
x+3y=3..........(2)
(2) => x=3-3y........(3)
Substitute (3) into (1)
-(3-3y)-3y=-3
-3+3y-3y= -3
-3=-3
This is true,
So, the solution is:
x=3-3y
=> 3y= 3-x
=> y=( 3-x )/3
To learn more about the solution of an equation from the given link
https://brainly.com/question/22688504
#SPJ1
Neptune Belvor decides to have a holiday festival at Convention Hall. There will be food and drinks for all, hotchocolate station, build your own gingerbread home competition, tree decoration station, make your ownholiday candle station and too top it all of SANTA will be there (or Coach IKE, dressed like him, real one is too busy).Tickets are selling for Students $5(under 18) and for Adults $11 (18+). The Event sold 9536 tickets and made$56,878. How many Adult tickets and how many Student tickets were sold?
Answers
Let 'x' represent the number of students tickets.
Let 'y' represent the number of adults tickets.
Two equations will be formed from the statements.
We were told that the total number of tickets sold is 9536 tickets.
\(x+y=9536\ldots\ldots\ldots1\)The total cost of the tickets is $56,878.
Given that tickets are selling for students $5(under 18) and for Adults $11(18+).
\(5x+11y=56878\ldots\ldots\ldots\text{.}.2\)Let us now combine the two equations and solve for x and y using the substitution method.
\(\begin{gathered} x+y=9536\ldots\ldots\ldots.1 \\ 5x+11y=56878\ldots\ldots\ldots.2 \end{gathered}\)Solving for x and y
Isolate x for x + y = 9536
x = 9536 - y
Substitute x = 9536 - y into equation 2
\(\begin{gathered} \begin{bmatrix}5\mleft(9536-y\mright)+11y=56878\end{bmatrix} \\ \end{gathered}\)Simplify
\(\begin{bmatrix}47680+6y=56878\end{bmatrix}\)Solve for y
\(\begin{gathered} 6y=56878-47680 \\ 6y=9198 \\ y=\frac{9198}{6}=1533 \\ \therefore y=1533 \end{gathered}\)For x = 9536 - y
\(\begin{gathered} \mathrm{Substitute\: }y=1533 \\ x=9536-1533 \\ x=8003 \end{gathered}\)The solution to the system of equations is,
\(x=8003,y=1533\)Hence, the number of tickets sold are
\(\begin{gathered} \text{Student}=8003\text{ tickets} \\ \text{Adult}=1533\text{ tickets} \end{gathered}\)
find the simple interest on 10000 from 1 July to 12 september 2007 at 5% per year calculate the interest
Answers
Answer:
Simple interest: 83.33, Final amount: 10083.33
Step-by-step explanation:
you dont get a explanation >:)
Let a, b, and c be real numbers where a ≠ b ≠ c ≠ 0. Which of the following functions could represent the graph below?
f(x) = x²(x-a)²(x-b)4(x-c)
f(x) = x³(x-a)³(x-b)(x-c)²
f(x) = x²(x-a)(x-b)³(x-c)³
f(x) = (x-a)^2(x-b)(x-c)^6
Answers
The characteristics of polynomial graphs' intercepts reveal the multiplicity's characteristics. The function is a potential representation of the graph; f(x) = x²·(x - a) (x - a) , ²·(x - b) (x - b),⁴·(x - c) (x - c).
How to find the calculation?The alternative provides a function that can represent a graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c)
Reason:
The graph's description is as follows:
Three points on the graph deviate from the x-axis.
Therefore;
The first equation is satisfied by the graph's even multiplicity at three places, such as x2, (x - a)2, and (x - b)4.
The graph once almost linearly crosses the x-axis.
Therefore;
The first equation's function contains a single zero or component, such as (x - c), so;
The function is a potential representation of the graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c).
To Learn more About polynomial graphs' intercepts refer to:
https://brainly.com/question/28576088
#SPJ1
A clothing eCommerce company has an Average Order Value of USD 65. It costs the company USD 35 to produce the clothes in the average order and USD 15 to ship it to the customer. What is the Average Order's Gross Profit?
USD 65
USD 30
USD 15
USD 50
Answers
The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;
⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit
⇒ Gross Profit = USD 65 - USD 35 - USD 15
⇒ Gross Profit = USD 15
Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ1
LarApCalc10 2.3.022. Find the marginal cost for producing x units. (The cost is measured in dollars.) C = 300(6 + 4x) dollars per unit Need Help? Read It Watch It Talk to a Tutor
Answers
The marginal cost of producing x units is equal to 300 multiplied by the sum of 6 and 4x dollars per unit.
The marginal cost for producing x units is calculated by taking the derivative of the cost equation with respect to x. The cost equation is C = 300(6 + 4x). Differentiating with respect to x, the marginal cost is found to be the derivative of the cost equation, which is equal to 300 multiplied by the derivative of the equation, 6 + 4x. The derivative of 6 + 4x is 4, so the marginal cost is 300 multiplied by 4, or 1200 dollars per unit. Therefore, the marginal cost for producing x units is 1200 dollars per unit.
Learn more about cost here
https://brainly.com/question/19075809
#SPJ4
(-5,0) with a rotation of 90° counterclockwise
Answers
Answer:
(0,-5)
Step-by-step explanation:
flipping axises casuses the points to flip
26. Tyler has been saving his winning lottery tickets. He has 23 tickets that are worth a total of $175. If each ticket is worth either $5 or $10, how many of each does he have?
Answers
In KLM, KM is extended through point M to point N,
(3x +19)°, m/LMN = (7x + 5)°, and
m/KLM = (2x+8)°. What is the value of x?
Answers
The value of the variable "x" is 11.
We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".
The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.
∠LMK + ∠LMN = 180°
∠LMK + (7x + 5)° = 180°
∠LMK = 180° - (7x + 5)°
In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.
∠K + ∠L + ∠M = 180°
(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°
3x +19 + 2x + 8 + 180 - 7x - 5 = 180
-2x + 22 = 0
2x = 22
x = 11
Hence, the value of the variable "x" is 11.
To learn more about variables, visit :
https://brainly.com/question/22277991
#SPJ9
52. Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.
Answers
The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.
Which vector is as described in the task content above?It follows that the magnitude of a vector in terms of its components in the i and j direction is;
M = √(x² + y²).
On this note, since the i and j components are equal; x = y and hence, we have;
3 = √(x² + x²).
3² = 2x²
x² = 9/2
x = 3/√2
x = 3√2/2
On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.
Read more on vector components;
https://brainly.com/question/26187714
#SPJ1
Pls help me I really nee it pls pls pls pls
Answers
The area of a rectangle is 40 square inches. The rectangle is 8 inches long. How wide is the rectangle?
A. 3 inches
B. 32 inches
C. 5 inches
D. 13 inches
Answers
Answer:
C. 5 inches
Step-by-step explanation:
I’m area you have to multiply L • W
But since we don’t know the width we can divide the length by the area.
40/8 = 5
So the answer would be 5.
Another way to solve this problem is with using guess and check.
I hope it helps! Have a great day!
Anygays~
Answer:
C. 5 inches
Step-by-step explanation:
Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.
40/8 = 5
ANSWER: 5 inches
I hope it helps! Have a great day!
PLEASE ANSWER ASAP!!!!!
Answers
Answer:
\(\huge\boxed{\sf r = 5}\)
Step-by-step explanation:
Given that,
7(q + 5) = (q + r)7Distribute7q + 35 = 7q + 7r
Subtract 7q from both sides7q - 7q + 35 = 7q - 7q + 7r
35 = 7r
Divide both sides by 735/7 = r
5 = r
OR
r = 5\(\rule[225]{225}{2}\)
Answer:
r = 5
Step-by-step explanation:
Given statement,
→ 7(q + 5) is equivalent to (q + r)7.
Forming the equation,
→ 7(q + 5) = 7(q + r)
Now we have to,
→ Find the required value of r.
Then the value of r will be,
→ 7(q + 5) = 7(q + r)
Applying Distributive property:
→ 7(q) + 7(5) = 7(q) + 7(r)
→ 7q + 35 = 7q + 7r
Cancelling 7q from both sides:
→ 35 = 7r
→ 7r = 35
Dividing the RHS with number 7:
→ r = 35/7
→ [ r = 5 ]
Therefore, the value of r is 5.
Confirm my selection please
Answers
They are both the bottom of the trapezoid
if you rolled two dice, what is the probability that you would roll a sum of 2
Answers
Answer:
2.78%
Step-by-step explanation:
Theres only one number combination you could get for the sum of 2 ( 1 and 1) but there is 36 different outcomes on the 2 dice that you could get for all the numbers.
1/36=.02777.. =.0278 but since its a percentage you move it over 2x to the right from the decimal point which would give you 2.78%
Why is the interest rate of a loan one of the most important things to consider when shopping around for loans?
a.
The interest rate should be ignored, because there’s nothing a consumer can do to change it.
b.
The interest rate is essentially how long you have to pay off your loan, and the shorter the better.
c.
The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.
d.
The interest rate does not change, even between banks, so choosing the right time to borrow is essential.
Answers
Answer:
C
Step-by-step explanation:
trust me c is the correct answer
a rectangle has a length of 8m and a width of 4.5m. A parallelogram has a length of 6 m. The area of the parallelogram is twice the area of the rectangle. What is the height of the parallelogram
Answers
Answer:
12m
Step-by-step explanation:
work out the area of the rectangle then times it by 2 because the parallelogram is twice the area of the rectangle. 8 × 4.5m = 36m². 36 ×2 = 72cm². Now you do 72 ÷ 6 = 12 . the answer is 12m.
The height of the parallelogram is 12 meters.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The area of a rectangle is given by the formula A = lw, where l is the length and w is the width.
The area of the rectangle is A1 = lw = (8 m)(4.5 m) = 36 m².
The area of a parallelogram is given by the formula A = bh, where b is the base and h is the height.
Since the area of the parallelogram is twice the area of the rectangle, we have:
2A1 = A2
2(36 m²) = 72 m²
So the area of the parallelogram is A2 = 72 m².
We are given that the length of the parallelogram is 6 m, so we can use the formula for the area to solve for the height:
A2 = bh
72 m² = (6 m)h
h = 12 m
Therefore,
The height of the parallelogram is 12 meters.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ3
A(-2,-2) B(-1,2) C(2,1) / A (-4,-4) (-2,4) C(4,2)
Answers
Answer:
umm lettders dont go in math pst this in englash
Step-by-step explanation
yeet
Find the value of x in the parallelogram
Answers
The value of x in the parallelogram is 112°.
In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.
To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.
Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.
Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.
Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.
This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.
For the given question, we know x° + 68° = 180°.
Then x° = 180° - 68°
x° = 112°
For more such questions on parallelogram
https://brainly.com/question/20526916
#SPJ8
Please help. I'm really confused on how to solve this.
Answers
Explanation
556/650 is the original price over the new one, because it was bumped up from the original. 100/p means 100 percent of the price = 556, p, the new percentage, = 650
Two different red-light-running signal systems were installed at various intersection locations with the goal of reducing angle-type crashes. Red-Light-Running System A resulted in 60% angle crashes over a sample of 720 total crashes. Red-Light-Running System B resulted in 52% angle crashes over a sample of 680 total crashes. Was there a difference between the proportions of angle crashes between
Answers
Complete Question
Two different red-light-running signal systems were installed at various intersection locations with the goal of reducing angle-type crashes. Red-Light-Running System A resulted in 60% angle crashes over a sample of 720 total crashes. Red-Light-Running System B resulted in 52% angle crashes over a sample of 680 total crashes. Was there a difference between the proportions of angle crashes between the two red-light-running systems installed? Use an alpha of 0.10.
Answer:
Yes there is a difference between the proportions of angle crashes between the two red-light-running systems installed
Step-by-step explanation:
From the question we are told that
The first sample proportion is \(\r p_ 1 = 0.60\)
The second sample proportion is \(p_2 = 0.52\)
The first sample size is \(n_1 = 720\)
The second sample size is \(n_2 = 680\)
The level of significance is \(\alpha = 0.10\)
The null hypothesis is \(H_o : \r p_1 - \r p_2 = 0\)
The alternative hypothesis is \(H_a : \r p_1 - \r p_2 \ne 0\)
Generally the pooled proportion is mathematically represented as
\(p_p = \frac{(\r p_1 * n_1 ) + (\r p_2 * n_2)}{n_1 + n_2 }\)
=> \(p_p = \frac{(0.6 * 720) + ( 0.52 * 680)}{720 +680 }\)
=> \(p_p = 0.56\)
Generally the test statistics is evaluated as
\(t = \frac{ ( \r p_1 - \r p_2 ) - 0 }{ \sqrt{ (p_p (1- p_p) * [ \frac{1}{n_1 } + \frac{1}{n_2 } ])} }\)
\(t = \frac{ (0.60 - 0.52 ) - 0 }{ \sqrt{ (0.56 (1- 0.56) * [ \frac{1}{720} + \frac{1}{680 } ])} }\)
\(t = 3.0\)
The p-value obtained from the z-table is
\(p-value = P(Z> t ) = 0.0013499\)
From the question we see that \(p-value < \alpha\) so the null hypothesis is rejected
Hence we can conclude that there is a difference between the proportions
Which functions are increasing?; How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions?
Answers
Linear, polynomial, and quadratic functions can be both increasing or decreasing functions. Exponential function is monotonically increasing function. The derivative of a function may be used to determine whether the function is increasing or decreasing. Exponential functions eventually exceed all other increasing functions.
Function, in mathematics, refers to an expression or rule that describes a relationship between two or more variables. A function is said to be an increasing function when the y-value increases as the x-value increases and vice versa. In order to determine whether the function is increasing or decreasing, the derivative of a function may be used on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. From the given function options, Exponential functions eventually exceed all other increasing functions as the one of variable is in the exponential leading an exponential increase and not a constant increase.
Note: The question is incomplete. The complete question probably is: From the following, Which functions are increasing? How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions? A) linear B) exponential C) polynomial D) quadratic.
Learn more about Function:
https://brainly.com/question/22340031
#SPJ4
solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Answers
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
Read more about Partial Differential Equations at: https://brainly.com/question/28099315
#SPJ1
its 0 degrees outside at midnight the temperature of the air drops 20° in the morning hours then gains 3° as soon as the sun comes up what is the temperature after the Sun comes up
Answers
Answer:
It is -17 degrees.
Step-by-step explanation:
Because:
0 degrees - 20 degrees=-20 degrees
-20 degrees +3 degrees =-17 degrees.