APPLIED MATHEMATICS
Question 1 Solve the following differential equation: dV de V coto + V3 coseco [10] Question 2 Find the particular solution of the following using the method of undetermined coefficie 64 + 8s = 4e2t w
Answers
1. The solution to the given differential equation \(V = V ln|sin(e)| - V^3 ln|cot(e) + cosec(e)| + C\) where C is an arbitrary constant.
2. The particular solution to the differential equation is \(s(t) = 0.5t^2 - 8\)
To solve the given differential equation: \(dV/de = V cot(e) + V^3 cosec(e)\), we can use separation of variables.
Starting with the differential equation:
\(dV/de = V cot(e) + V^3 cosec(e)\)
We can rearrange it as:
\(dV/(V cot(e) + V^3 cosec(e)) = de\)
Next, we separate the variables by multiplying both sides by (V cot(e) + V^3 cosec(e)):
\(dV = (V cot(e) + V^3 cosec(e)) de\)
Now, integrate both sides with respect to respective variables:
∫\(dV\) = ∫\((V cot(e) + V^3 cosec(e)) de\)
The integral of dV is simply V, and for the right side, we can apply integration rules to evaluate each term separately:
\(V = \int\limits(V cot(e)) de + \int\limits(V^3 cosec(e)) de\)
Integrating each term:
\(V = V ln|sin(e)| - V^3 ln|cot(e) + cosec(e)| + C\)
where C is the constant of integration.
2.To find particular solution of differential equation \(64 + 8s = 4e^2t\), using the method of undetermined coefficients, assume a particular solution of the form:\(s(t) = At^2 + Bt + C\), where A, B, and C are that constants which have to be determined.
Taking the derivatives of s(t), we have:
\(s'(t) = 2At + B\\s''(t) = 2A\)
Substituting derivatives into the differential equation, we get:
\(64 + 8(At^2 + Bt + C) = 4e^2t\)
Simplifying the equation, we have:
\(8At^2 + 8Bt + 8C + 64 = 4e^2t\)
Comparing coefficients of like terms on both sides, get:
8A = 4 --> A = 0.5
8B = 0 --> B = 0
8C + 64 = 0 --> C = -8
Therefore, the particular solution to differential equation: \(s(t) = 0.5t^2 - 8\).
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Related Questions
Which of the following quadrilaterals have diagonals that bisect each other?
Check all that apply.
Answers
Answer:
All A. B. C. D.
Step-by-step explanation:
A B C D are all the correct answers
¯\_(ツ)_/¯
how many cups of granulated sugar in a 5 pound bag
Answers
There are approximately 11.25 cups of granulated sugar in a 5 pound bag.
To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.
First, we multiply the number of pounds (5) by the conversion factor:
5 pounds * 2.25 cups/pound = 11.25 cups
Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.
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PLEASE HELP ASAP WILL GIVE BRAINLYEST!!
Answers
It's on the picture
It's on the picture
solve for x please help asap! will give brainlest
Answers
Answer:
80+60+3x+4=180
140+3x+4=180
144+3x=180
3x=180-144
3x=36
x=12
Answer:
x = 12
Step-by-step explanation:
All triangles equal to 180 degrees so, we can set up this expression:
180 = (3x + 4) + 80 + 60
All we have to do is solve:
180 = (3x + 4) + 80 + 60
180 = 3x + 4 + 140
180 = 3x + 144
-144 -144
36 = 3x
/3 /3
12 = x
Answer this: x=6
y=-2
-8x-4y+x
Answers
Answer:
-34
Step-by-step explanation:
first do substitution: -8 · 6 + -4 · -2 + 6
next do the multiplication: -48 + 8 + 6
add: -34
hope this helps!!!
Answer:
-34
Steps:
-8x - 4y + x
-8x + x = -7x (combine like terms)
-7x - 4y
-7(6) - 4(-2) (plug in the numbers)
-42 +8=
-34
:")
For a class he is taking, Jayson has to complete at least 35 hours of volunteer work. He has already completed 7 hours at the food bank. He wants to finish his hours at a local animal shelter, where all the shifts are 4 hours long
Answers
Jayson needs to complete at least 7 shifts of 4 hours each at the local animal shelter to fulfill his volunteer work requirement for the class.
To meet the requirement for Jayson's class, he needs to complete at least 35 hours of volunteer work.
He has already completed 7 hours at the food bank, so he still needs to complete:
35 hours (total) - 7 hours (completed) = 28 hours (remaining)
Now, Jayson wants to finish his remaining hours at the local animal shelter where each shift is 4 hours long.
To find out how many shifts he needs to complete, we can divide the remaining hours by the length of each shift:
28 hours (remaining) / 4 hours (per shift) = 7 shifts
Jayson needs to complete 7 shifts at the animal shelter to reach the required 35 hours of volunteer work for his class.
Note: Volunteering is a wonderful way to give back to your community and make a positive impact.
There are numerous opportunities available depending on your interests, skills, and the needs of your local area. Here are a few suggestions:
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Use cylindrical coordinates. Evaluate x2 + y2 dV, where E is the region that lies inside the cylinder x2 + y2 = 1 and between the planes z =-4 and z =-1.
Answers
The value is 896π/3
The spheres x² + y² + z² = 9 and x² + y² + z² = 16.
Convet into shperical coordinate
x2+y2+z2≤2z⟹ρ≤2cosϕ.
Then the volume of the element will be
Then we have
Cylindrical coordinates:
The distance from a chosen reference axis (axis L in the illustration opposite), the angle from the axis to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis are the three dimensions of a cylindrical coordinate system (plane containing the purple section). Whichever side of the reference plane faces the point determines whether the latter distance is expressed as a positive or negative value.
The location where all three coordinates may be specified as zero is the origin of the system. The reference plane and axis come together at this point. To distinguish it from the polar axis, the axis is often referred to as cylindrical or longitudinal axis.
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Suppose that an investment has 0.5% chance of a loss of $10
million and a 99.5% chance of a loss of $1 million. What is the
Value-at-Risk (VaR) for this investment when the confidence level
is 99%
Answers
To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).
Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:
Loss Amount | Probability
$10 million | 0.5%
$1 million | 99.5%
To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.
The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.
Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.
The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.
To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.
Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:
VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)
VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)
VaR = $50,000 + $995,000
VaR = $1,045,000
Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.
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If the allowable bearing stress for the material under the supports at A and B is σ
b
=840psi, determine the maximum load P
max
that can be applied to the beam. The bearing plates each have square cross sections of 4in. by 4in. The reactions at the supports are vertical. Assume w=550lb/ft,a=12ft, and b=6ft.
Answers
Answer:
Step-by-step explanation:
its 212123s\
Plz help!!! I’ll give 10 points to the first person to give me a correct answer...I need to get my grade up before the end of the semester
Answers
Answer:
A= 30
B= 60
C= 90
Step-by-step explanation:
A is already shown.
B has a right angle making it 90 degrees.
A triangle is 180 degrees 30+90= 120
180-120=60
A cylinder has a height of 15 meters and a diameter of 8 meters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Step-by-step explanation:
15+8= 23
math magician I like math but I really don't some time know how to do it but if their is wrong then you have to ask your teacher or look in your notebook
n each case, sketch the closure of the set: a) -pi < argz < pi (z not equal to 0) b)|Rez| < |z| < = 1/2 c)Re(1/z) < = 1/2 d)Re(z2)>0
Answers
The closure of set a) includes the boundary, unit circle, and origin; the closure of set b) includes the boundary, line segments, origin, and closed disk; the closure of set c) includes the boundary and origin; the closure of set d) includes the boundary, imaginary axis, origin, and closed half-plane to the right of the imaginary axis.
a) The closure of the set {-pi < arg(z) < pi, z ≠ 0} includes all points on the boundary of this region. This boundary consists of the real axis (where arg(z) = 0), the imaginary axis (where arg(z) = ±pi/2), and the unit circle centered at the origin (where |z| = 1). The closure of the set also includes the point at the origin, since this is a limit point of the set.
b) The closure of the set {|Re(z)| < |z| ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the unit circle centered at the origin (where |z| = 1/2) and the line segments connecting this circle to the x-axis (where |z| = |Re(z)|). The closure of the set also includes the origin and the points on the closed disk centered at the origin with radius 1/2.
c) The closure of the set {Re(1/z) ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the line Re(z) = 1/2 (where the imaginary part of z can take on any value) and the point at the origin, since this is a limit point of the set.
d) The closure of the set {Re(z^2) > 0} includes all points on the boundary of this region. This boundary consists of the imaginary axis (where Re(z^2) = 0) and the rays emanating from the origin at angles ±π/4 (where Re(z^2) is positive). The closure of the set also includes the origin and the points on the closed half-plane to the right of the imaginary axis.
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Which is a diagonal through the interior of the cube?
BE
CF
DG
GF
Answers
18. A rectangular tables has a
length that is expressed as
5x + 6 and a width that is
expressed as 2x - 3. Find the
a) Area of the table
b) Perimeter of the table
Answers
Perimeter = 14x + 6
Answer:
a) 10x² - 3x - 18
b) 14x + 6
Step-by-step explanation:
Given:
length = 5x + 6
width = 2x - 3
Tables usually have rectangular shape.
a) Area of the table
Area of a rectangle
A = length × width
Insert values into formula.
A = length × width
A = (5x + 6) × (2x - 3)
A = 10x² - 15x + 12x - 18
A = 10x² - 3x - 18
b) Perimeter of the table
Perimeter of a rectangle
P = 2 × length + 2 × width
P = 2 × length + 2 × width
P = 2(5x + 6) + 2(2x - 3)
P = 10x + 12 + 4x - 6
P = 14x + 6
Help can whoever answer explain how they got the answer the steps please
Answers
Answer:
x = -1
Step-by-step explanation:
First, you factor x out of x^2 + 2x which will get you 1/x(x+2)
Next, you find the LCD of the terms in the equation and you get x(x+2)
Then, you multiply each term by x(x+2) and you simplify giving you x^2+x-1=x^2+2x
Finally you combine like terms giving you x = -1
Name the integer
1. Gained 9 kilos =
2. 32 steps backward
3. Decreased by P5 =
plesss tulungan nyo po ako parang awa nyo na plssssss.
Answers
Answer:
1. Gained 9 kilos = \(+9\)
2. 32 steps backward = \(-32\)
3. Decreased by P5 = \(-P5\)
Step-by-step explanation:
Natural numbers refer to numbers that are used for counting.
Whole numbers include 0 and natural numbers.
An integer is a collection of whole numbers and their negatives.
1. Gained 9 kilos = \(+9\)
(Gained is denoted by + )
2. 32 steps backward = \(-32\)
(backward is denoted by - )
3. Decreased by P5 = \(-P5\)
(decrease is denoted by - )
Jeremy spent a total of $79.16 on a shirt and one pair of jeans. He knows the jeans cost $49.95 but he does not know the cost of the shirt, s. He created the model shown to find the cost of the shirt.
Answers
The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.
Let the cost of shirt be x.
The jeans cost is $49.95
Now, the cost of shirt + the cost of jeans = Total cost
⇒ x+49.95=79.16
⇒ x=79.16-49.95
⇒ x=$29.21
Therefore, the cost of shirt is $29.21.
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A person places $290 in an investment account earning an annual rate of 2.2%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.
Answers
Answer:
$430.90Step-by-step explanation:
Given that the principal p= $290
rate r= 2.2% 2.2/100 =0.022
time t= 18years
by applying the expression
\(V = Pe^{rt}\)
We have
\(V = 290e^{0.022*18}\\\\V=290e^{0.396}\\\\V=290*1.48586931755\\\\V=$430.90\)
Hence after 18years the money in the account will be $430.90
The average number of games a player has appeared in the 2021 NBL games as of now is about 40 games
with a standard deviation of 10 games. Determine what percent of players have appeared in 45-56 games,
write as a percent with two decimal places.
Answers
what is the scale factor from ABC to DEF
Answers
Answer:
the scale factor from triangle ABC to triangle DEF would be 8
Step-by-step explanation:
the triangle DEF was actually flipped from triangle ABC
1.line AB corresponds to line EF
AB = 6 , and EF = 48
we multiply 6 by "8" to get to 48
2.line BC corresponds to line ED
BC = 6 , and ED = 48
we multiply 6 by "8" to get to 48
3.line AC corresponds to line FD
AC = 6 , and FD = 48
we multiply 4 by "8" to get to 32
I hope this help
when a distribution is bell-shaped, approximately what percentage of data values will fall within 1 standard deviation of the mean?
Answers
When a distribution is bell shaped, the percentage of the data values which will fall within 1 standard deviation of the mean is= 68%
What does standard deviation mean in plain English?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
According to empirical rule, which is also known as three-sigma rule or 68-95-99.7 rule, it is a rule of statistics which says that all observed data will fall within three standard deviations of the mean or average for a normal distribution.
1.68% falls within first standard deviation .
2.95% falls within the first two standard deviations.
3.99.7% falls within the first three standard deviations.
Therefore,
When a distribution is bell shaped, the percentage of the data values which will fall within 1 standard deviation of the mean is= 68%
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Analytically show that the equations below represent trigonometric identity statements. 1. sec²θ (1-cos²θ) 2. cosx(secx-cosx) = sin²x 3. cosθ + sinθtanθ = secθ 4. (1- cos∝)(cosec∝+cot∝)= cos∝ tan∝
Answers
To show that the given equations represent trigonometric identity statements, we will simplify each equation and demonstrate that both sides of the equation are equal.
Starting with sec²θ(1 - cos²θ):
Using the Pythagorean identity sin²θ + cos²θ = 1, we can rewrite sec²θ as 1 + tan²θ. Substituting this into the equation, we get:
(1 + tan²θ)(1 - cos²θ)
= 1 - cos²θ + tan²θ - cos²θtan²θ
= 1 - cos²θ(1 - tan²θ)
= sin²θ
Thus, the equation simplifies to sin²θ, which is a trigonometric identity.
For cosx(secx - cosx) = sin²x:
Using the reciprocal identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the equation as:
cosx(1/cosx - cosx)
= cosx/cosx - cos²x
= 1 - cos²x
= sin²x
Hence, the equation simplifies to sin²x, which is a trigonometric identity.
Considering cosθ + sinθtanθ = secθ:
Dividing both sides of the equation by cosθ, we obtain:
1 + sinθ/cosθ = 1/cosθ
Using the identity tanθ = sinθ/cosθ, the equation becomes:
1 + tanθ = secθ
This is a well-known trigonometric identity, where the left side is equal to the reciprocal of the right side.
Simplifying (1 - cos∝)(cosec∝ + cot∝):
Expanding the expression, we have:
cosec∝ - cos∝cosec∝ + cot∝ - cos∝cot∝
= cot∝ - cos∝cot∝ + cosec∝ - cos∝cosec∝
= cot∝(1 - cos∝) + cosec∝(1 - cos∝)
= cot∝tan∝ + cosec∝sec∝
= 1 + 1
= 2
Thus, the equation simplifies to 2, which is a constant value.
In summary, we have analytically shown that the given equations represent trigonometric identity statements by simplifying each equation and demonstrating that both sides are equal.
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If f(x)=√x-10 +3, which inequality can t
x-10+3, which inequality can be used to find the domain of f(x)?
O
√√x20
0x20
Ox-1020
O
√√x-10+320
Answers
The inequality used to determine the domain of the function is greater than equal to and the domain is [10, ∞).
What is domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. The values in this set
Hence, once we input an x value, the function returns. The y values are those.
The given expression is:
\(\sqrt{x- 10} + 3\\\)
The value in the square root must be greater than or equal to 0 to ensure that the number is real.
\(\sqrt{x - 10} \geq 0\)
Taking squares on both sides of the equation:
x - 10 ≥ 0
x ≥ 10
The domain of the given inequality is [10 , ∞).
Hence, the inequality used to determine the domain of the function is greater than equal to and the domain is [10, ∞).
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A company produces a special new type of TV. The company has fixed costs of $467,000, and it costs $1500 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850TV s. If the company wants to sell 900TVs, however, it must lower the price to $2000. Assume a linear demand. What price should the company charge to earn a profit of $833,000? It would need to charge 9 (Round answer to nearest dollar. If more than one answer, separate with a comma.)
Answers
To determine the price the company should charge to earn a profit of $833,000, we need to calculate the total revenue and subtract the total cost.
Let's break down the problem step by step:
Fixed costs: $467,000
Variable cost per TV: $1500
Number of TVs projected to be sold at a price of $2300: 850
Total revenue at this price: $2300 * 850 = $1,955,000
Number of TVs needed to be sold to earn a profit of $833,000:
Total revenue needed: Total cost + Profit
Total revenue needed: $467,000 + $833,000 = $1,300,000
Determine the price required to sell 900 TVs:
Let's assume the price is P.
Total revenue at this price: P * 900
Set up an equation based on the linear demand:
Total revenue = Total cost + Profit
P * 900 = $1,300,000
Solve the equation for P:
P = $1,300,000 / 900 ≈ $1444.44
Therefore, the price the company should charge to earn a profit of $833,000 is approximately $1444.44.
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frank is going to plant d vegetable seeds in one garden and 3d + 9 vegetable seeds in another. How many seeds is Frank going to plant?
Answers
Answer:
If Frank is planting b seeds in one and 5b + 10 in the other, the expression showing the total is b + (5b + 10), or 6b + 10 seeds.
brainliest?
PLEASE ANSWER THE FOLLOWING QUESTION GIVEN THE CHOICES!!!
Answers
Answer: 3/52
Step-by-step explanation:
You want to pick a diamond jack, diamond queen or diamond king
There are only 3 of those so
P(DJ or DQ or DK) = 3/52 There are 3 of those out of 52 total
Harrison has 12 coins in quarters and nickels. He determines that they have a total value of $2.00.
a) Write a system of equations that could be used to find the number of each coin he has.
Answers
Answer:
See belowStep-by-step explanation:
Let the number of nickels is n, number of quarters is q.
We know that:
Nickel = 5¢, quarter = 25¢, $2 = 200¢As per given we can set the following system:
n + q = 125n + 25q = 200Solving this we get:
n = 5, q = 7What is the equation of this line?
A)y=1/4x
B)y= -4x
C)y= -4x
D)y=4x
Answers
Answer:
the answer is -1/4x which isn't on there
Step-by-step explanation:
Find the midpoint and distance for each:
1. A(0, 0) & B(8,4)
Answers
The midpoint between two points A(0,0) and B(8,4) is (4,2)
The distance between two points A(0,0) and B(8,4) is 4√5
To find the midpoint of two points,
We need to take an average of both the x and y components of both points
Two points A(x ₁,y₁) and B(x₂ ,y₂) are (0,0) and (8,4) respectively
Let M be the mid-point M(x, y),
x = x₁+x₂/2
= 0+8/2
= 8/2
= 4
Similarly
y = y₁+y₂/2
= 0+4/2
= 4/2
= 2
So, the midpoint of the two points A(0,0) and B(8,4) is (4,2)
To find the distance between two points,
We need to take the square root of the difference square of x and y, which is
d² = Δx² + Δy²
d = √(Δx²+Δy²)
Δx = x₂-x₁
= 8-0
= 8
Δy = y₂-y₁
= 4-0
= 4
Thus,
d = √(8²+4²)
d = √(64 + 16)
d = √80
d = 4√5
So the distance between the two points is 4√5
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6 divied by 6.48 how to slove it
Answers
Answer:
0.93
Step-by-step explanation:
6/6.48 = 0.92592592592592592592592592592593
Answer:0.92
Step-by-step explanation:
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