Answer: The input force (effort) on the rope is 20 N.
Step-by-step explanation:
In a frictionless pulley system, the tension in the rope is constant throughout. Therefore, the force applied to the rope on one side of the pulley system is equal to the force exerted on the other side of the system.
In this problem, we know that the weight of the block is 20 N. This means that there is a force of 20 N acting downwards on one side of the pulley system.
Since the pulley system is frictionless, the tension in the rope is also 20 N. Therefore, the force applied to the rope on the other side of the pulley system (i.e., the input force or effort) must also be 20 N in order to balance the weight of the block.
So the input force (effort) on the rope is also 20 N.
when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)
The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.
What is the probability of randomly selected component?We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.
We need to find the probability that a randomly selected component is shorter than 7 inches long.
We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:
z = (7 - 8) / 1.5 = -0.67
Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:
P(z < -0.67) = 0.2514
Learn more about probability here: https://brainly.com/question/24756209
#SPJ1
Decrease R700 in the ratio 3:2.
Answer:
R466.66...
Step-by-step explanation:
To decrease A in the ratio x : y (where x < y), we have to perform the following
[tex]A*\frac{x}{y}[/tex] (as a proper fraction)
R700 * 2/3 = R466.66...
The velocity of a particle moving along a line is a function of time given by v(t)=90/t2+12t+35. Find the distance that the particle has traveled after t=8 seconds if it started at t=0 seconds.
The distance that the particle has traveled after t=8 seconds is 640 meters.
Distance covered by the particle in the first 8 seconds is given by
S(8) = ∫v(t)dt = ∫[90/t^2+12t+35]dt = [ -90/t + 6t^2 + 35t ] from 0 to 8S(8) = [-90/8 + 6(8^2) + 35(8)] - [-90/0 + 6(0^2) + 35(0)]S(8) = [360 + 280] - [-Infinity]S(8) = 640 meters.
Given that the velocity of a particle moving along a line is a function of time given by v(t)=[tex]90/t^2+12t+35.[/tex]
The time taken by the particle to travel 8 seconds is t = 8 seconds.
Initial velocity of the particle = v(0) = 90/(0^2) + 12*0 + 35 = 35m/sFinal velocity of the particle = v(8) = 90/(8^2) + 12*8 + 35 = 59.125 m/s
The distance covered by the particle in time t is given by the integral of the velocity of the particle between 0 to 8 seconds.
for such more questions on Initial velocity
https://brainly.com/question/25981195
#SPJ11
A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?
Dorris deposits $200 into a savings account that has a simple interest rate of 4. 1% Max deposits 300 dollars into a savings account that has a simple interest rate of 1. 9%, who earn more interest in 15 months round to the nearest cent if necessary
Dorris earns $12.25 in interest over 15 months, while Max earns $2.84 in interest over the same period. So, Dorris earns more interest than Max.
To find out who earns more interest in 15 months, we can calculate the interest earned by each person using the formula:
Interest = Principal x Rate x Time
For Dorris, we have:
Interest = $200 x 0.041 x (15/12)
Interest = $12.25
For Max, we have:
Interest = $300 x 0.019 x (15/12)
Interest = $2.84
Interest refers to the cost of borrowing money, usually expressed as a percentage of the amount borrowed over a specific period of time. When someone borrows money, they are required to pay back not only the amount borrowed but also an additional amount, which is the interest. Interest is how lenders make money and is an important component of the financial system.
There are different types of interest rates, including fixed and variable rates. A fixed interest rate remains the same throughout the loan term, while a variable interest rate may change based on market conditions. Interest rates can also be compounded, which means that interest is added to the principal amount, and future interest payments are calculated based on the new higher amount.
To learn more about Interest visit here:
brainly.com/question/30393144
#SPJ4
5. The black triangle has been dilated once to produce the red triangle and a second time to produce the green triangle.
Part A: What is the scale factor of the dilation of the black triangle to the red triangle? Explain your reasoning.
Part B: What is the scale factor of the dilation of the black triangle to the green triangle? Explain your reasoning.
10 *
W
Answer:
A. Scale factor is 2
B. Scale factor is 1/2
Step-by-step explanation:
Please help I will give brainliest
As just a motion in the x-direction is needed for this transition, the motion is stiff: d.(x, y) → (x - 2, y) (x - 2, y).
What is motion referred to as?A body's ability to change its location with respect to time is known as motion. The various motions include: 2.1 Straight line motion Particles in linear motion are those that move through one point to the other along a straight or curved path.
a.(x, y) → (2x, y + 2)
As this transformation only comprises a y-direction translation and an x-direction scaling, it is a stiff motion.
b.(x, y) → (2x, 2y)
Since this transformation involves scaling both the x and y axes without any translation, it is a dilation.
c.(x, y) →(x + 2, y + 2)
As this transformation only requires a translation in the x and y dimensions, it is a stiff motion.
d.(x, y) → (x - 2, y)
As this transformation solely requires a movement in the x-direction, it is a stiff motion.
To know more about motion visit:
brainly.com/question/12640444
#SPJ1
1. Use the data in hprice1.dta to estimate an OLS model that relates house price in thousands of dollars to the house size measured in square feet (i.e., the variable sqrft) and the number of bedrooms in the house (bdrms). Write it the result in equation form.
2. What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
3. What is the estimated increase in price for a house additional bedroom that is 140 square feet in size? Compare this to your answer in question two above.
4. What percentage of the variation in price is explained by square footage and number of bedrooms?
5. The first house in the sample has sqrft=2,438 and bdrms=4. Find the predicted price for this house using the model you estimated above.
6. The actual selling price of the first house in the sample was $300,000 (i.e. price= 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?
In the following question, among the various parts to solve on houses - 1. price = β0 + β1sqrft + β2bdrms, 2. β2, 3. β2 + 140β1, 4. R-squared value is provided in the regression output, 5. 276.878 thousand dollars, 6. 23.122.
1. The regression equation of house price in thousands of dollars to the house size measured in square feet (sqft) and the number of bedrooms in the house (bdrms) can be written as follows: price = β0 + β1sqrft + β2bdrms Here, price refers to the house price in thousands of dollars, sqft refers to the house size measured in square feet and bdrms refers to the number of bedrooms in the house.
2. The estimated increase in price for a house with one more bedroom, holding square footage constant is equal to the coefficient of bdrms in the regression equation, which is β2.
3. The estimated increase in price for a house with an additional bedroom that is 140 square feet in size can be calculated as follows: β2 + 140β1. Comparing this to the answer in question two above, we can see that the price increase is greater when an additional 140 square feet are added to the house rather than an additional bedroom.
4. The percentage of the variation in price explained by square footage and the number of bedrooms can be found using the R-squared value. The R-squared value is a measure of how much of the variation in the dependent variable (house price) is explained by the independent variables (sqft and bdrms). In this case, the R-squared value is provided in the regression output.
5. To find the predicted price for the first house in the sample using the model estimated above, we need to plug in the values of sqft and bdrms for the first house into the regression equation. Here, sqrft = 2,438 and bdrms = 4. Thus, the predicted price for the first house is given by: price = β0 + β1sqrft + β2bdrms = -14.973 + 0.128sqrft + 15.204bdrms = -14.973 + 0.128(2,438) + 15.204(4) = 276.878 thousand dollars.
6. The residual for the first house in the sample can be calculated as follows: Residual = Actual price - Predicted price = 300 - 276.878 = 23.122. The fact that the residual is positive suggests that the buyer overpaid for the house.
For more such questions on houses
https://brainly.com/question/1030318
#SPJ11
factoring integers with sublinear resources on a superconducting quantum processor
Factoring integers with sublinear resources on a superconducting quantum processor can be achieved using quantum approximate optimization algorithm" (QAOA) or quantum phase estimation algorithm (QPE) approach.
Factoring integers with sublinear resources on a superconducting quantum processorFactoring large integers is a problem of significant importance in the field of cryptography.
Classical computers have limited efficiency in solving this problem, and their performance is expected to decline further as the size of the integers to be factored increases.
In contrast, quantum computers are expected to have exponential speedup in factoring large integers, thanks to Shor's algorithm.
Recently, researchers have been exploring the possibility of using superconducting quantum processors to factor integers with sublinear resources.
One approach is to use a so-called "quantum approximate optimization algorithm" (QAOA), which maps the problem of factoring integers to a problem of finding the ground state of a certain Hamiltonian.
The QAOA can be implemented using a superconducting quantum processor, with the problem Hamiltonian implemented by a set of two-qubit gates.
Another approach is to use the quantum phase estimation algorithm (QPE) to estimate the eigenvalues of the problem Hamiltonian.
This can be used to factor integers by finding the period of a certain function using the quantum Fourier transform, as in Shor's algorithm. QPE can be implemented on a superconducting quantum processor using phase estimation circuits, which require only polynomial resources.
Learn more about superconducting quantum processors on:
brainly.com/question/29235650
#SPJ1
the set of all continuous real-valued functions defined on a closed interval (a, b] in ir is denoted by c[a , b]. this set is a subspace of the vector space of all real-val ued functions defined on [a, b]. a. what facts about continuous functions should be proved in order to demonstrate that c [a , b] is indeed a subspace as claimed? (these facts are usually discussed in a calculus class.) b. show that {fin c[a ,b]: f(a )
Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.
To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.
for such more questions on continuous function
https://brainly.com/question/30089268
#SPJ11
What is the value of x in √1+ 25/144 =1+ /12 ?
The solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6. This was achieved by simplifying the left side of the equation and isolating x on one side.
To solve the equation √(1 + 25/144) = 1 + x/12, we start by simplifying the left side of the equation. The expression inside the square root can be simplified to (144 + 25)/144 = 169/144. Taking the square root of this fraction gives us √(169/144) = (13/12).
Next, we subtract 1 from both sides of the equation to isolate x on one side: (13/12) - 1 = x/12. This simplifies to 1/12 = x/12.
Finally, we multiply both sides by 12 to solve for x: x = (1/12)*12 = 5/6.
So the solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6.
Learn more about algebra here: brainly.com/question/24875240
#SPJ4
Calculate the volume of iron needed to create a rectangular prism with a base area of
2250 square cm. The prism has a cylinder missing through the center of the prism. The
radius of the cylinder is 25 cm and the height of the cylinder and the prism are both
100cm. Find the volume to the nearest tenth of a cubic cm.
The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.
what is volume?
Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).
The volume of the rectangular prism without the cylinder can be calculated as:
[tex]$$V_1 = A \times h$$[/tex]
where A is the base area and h is the height
[tex]$$V_1 = 2250 \times 100$$[/tex]
[tex]$$V_1 = 225000 \ \text{cubic cm}$$[/tex]
The volume of the cylinder can be calculated as:
[tex]$$V_2 = \pi r^2 h$$[/tex]
where r is the radius and h is the height
[tex]$$V_2 = \pi \times 25^2 \times 100$$[/tex]
[tex]$$V_2 = 196349.54 \ \text{cubic cm}$$[/tex]
The volume of the rectangular prism with the cylinder missing can be calculated as:
[tex]$$V = V_1 - V_2$$[/tex]
[tex]$$V = 225000 - 196349.54$$[/tex]
[tex]$$V = 28650.46 \ \text{cubic cm}$$[/tex]
Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).
To learn more about volume visit:
https://brainly.com/question/463363
#SPJ1
please help guys, I need this done
Answer:
18+m=24, 6
Step-by-step explanation:
You will get the first part by understanding that 24 is the whole and 18 is the part. Part + the other part, m, is the whole. You will then solve this by isolating the variable m, and subtracting 18 on both sides of the equation. Since 24-18=6, that is the final answer.
Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B?
The probability that more heads are tossed using coin A than coin B is 5/16.
The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.
P(E) = Number of favorable outcomes/ Total number of possible outcomes
Coin toss:
There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is
1/2 = 0.5.
Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.
Let's calculate the possible outcomes when coin A is tossed three times.
There are 2 possible outcomes when one coin is tossed.
Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8
Likewise, the possible outcomes when coin B is tossed two times are:
The number of possible outcomes = 2 * 2 = 4
Therefore, the total number of possible outcomes = 8 * 4 = 32
Now, we will find out the cases where the number of heads is more when coin A is tossed three times.
HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT
Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)
Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes
P = 10/32P = 5/16
Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.
To know more about probability for coin tossing: https://brainly.com/question/16988487
#SPJ11
Write the given third order linear equation as an equivalent system of first order equations with initial values. (t - 2t^2)y' - 4y'" = -2t with y(3) = -2, y'(3) = 2, y"(3) = -3 Use x_1 = y, x_2 = y', and x_3 = y". with initial values If you don't get this in 2 tries, you can get a hint.
The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.
We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:
x_1 = y
x_2 = y'
x_3 = y''
with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.
The resulting system of equations is:
x_1' = x_2
x_2' = x_3
x_3' = (2t^2 - t)x_2 - 4x_3 + 2t
This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.
for such more questions on linear equation
https://brainly.com/question/28732353
#SPJ11
I need help please I need to show my work
Answer:
18
Step-by-step explanation:
We can safely assume EGF and EGD are congruent by SAS (EG = EG reflexive property, and the angle and side given)
that must mean FG AND GD are congruent (CPCTC)
3a = a+6
2a = 6
a = 3
plug this into 3a+a+6 (DF is the sum of the two segments)
4a+6
4(3)+6
18
a single letter from the word aardvark is chosen. what is the probability of choosing an r or an a? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of choosing an r or an a is 0.7143. A single letter from the word aardvark is chosen.
What is the probability of choosing an r or an a?The probability of choosing an r or an a from the word aardvark can be calculated as follows:
First, calculate the total number of letters in the word aardvark.
Aardvark is a seven-letter word. As a result, there are seven letters available.
Next, calculate the number of r's and a's in the word aardvark.
There are five letters that are either an r or an a in aardvark.
As a result, there are two r's or three a's in aardvark.
So, the probability of choosing an r or an a is:
[tex]P("r" or "a") = \frac{number of r's or a's in aardvark}{total number of letters in aardvark} \\ = 5/7\\=0.7143[/tex]
The probability of choosing an r or an a is 0.7143.
Learn more about Probability here:
brainly.com/question/24756209
#SPJ11
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify the expression 8 2 + 9 ( 12 ÷ 3 × 2 ) − 7. Explain each of your steps
the simplified expression is 129.
To simplify the expression 8² + 9(12 ÷ 3 × 2) - 7, we follow the order of operations, which is:
Parentheses (do the calculations inside parentheses first)
Exponents (do the calculations involving exponents)
Multiplication and Division (do these operations from left to right)
Addition and Subtraction (do these operations from left to right)
Using these rules, we can simplify the expression step by step as follows:
8² + 9(12 ÷ 3 × 2) - 7 (Apply parentheses first)
= 8² + 9(4 × 2) - 7 (Evaluate 12 ÷ 3 as 4 and then 4 × 2 as 8 inside the parentheses)
= 8² + 9(8) - 7 (Evaluate 9 times 8 as 72)
= 64 + 72 - 7 (Evaluate 8² as 64)
= 129 (Perform the final subtraction and add the remaining terms)
Therefore, the simplified expression is 129.
To know more about expression, visit: brainly.com/question/14083225
#SPJ4
Why is pi important in math?
Could somebody help me with this?
Answer:
y = 10/3x + 130/3
Step-by-step explanation:
To find where A is, we must find where C is. C is found when plugging in 0 in for y: 0 = -1/2 x + 5, so x = 10, and y = 0.
Now that we know the length of BC, we can find A.
Subtract 10 from the x value and add 5 to the y value of B to find A: (-10, 10).
Now, find the equation of the line between (-13, 0) and (-10, 10). Solve and get the equation of a line: y = 10/3x + 130/3
Hope this helps!
LMN is a straight angle. Find m LMP and m NMP
From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.
Since LMN is a straight angle, it measures 180 degrees.
We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:
LMP + NMP = LMN
(-16x + 13) + (-20x + 23) = 180
Simplifying and solving for x, we get:
-36x + 36 = 180
-36x = 144
x = -4
Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:
LMP = -16x + 13 = -16(-4) + 13 = 77 degrees
NMP = -20x + 23 = -20(-4) + 23 = 103 degrees
Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.
Question - LMN is a straight angle. LMP = -16x + 13 NMP = -20x + 23 LMP + NMP = LMN What are the measures?
Learn more about angle here: brainly.com/question/25770607
#SPJ4
Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
Learn more about probabilities at https://brainly.com/question/24756209
#SPJ1
Here is a solid.
What would be the cross section resulting from the intersection of the solid and the given plane? Be specific about the resulting shape.
Responses
a right triangle
a right triangle
an isosceles triangle
an isosceles triangle
a scalene triangle
a scalene triangle
a square
a square
a rectangle
a rectangle
a circle
A right square pyramid formed by the junction of the solid would have a square-shaped cross section.
Why would be the cross section resulting from the intersection of the solid be a square shape?This is thus because a square pyramid has four triangular sides that meet at a shared vertex on its square base. The cross section of a pyramid formed when a plane meets it parallel to the base and perpendicular to one of the triangular sides is a square. Because the pyramid's base is square, the intersecting plane will cut all four of the triangle faces at the same distance from the peak, giving the pyramid a square shape.
Learn more about right angle triangles here:
brainly.com/question/3770177
#SPJ1
15 workmen can complete a piece of work in 12 days working 10 hours a day. How many workmen should be added to complete the same work in 6 days working 12 hours a day?
Answer:
25 workmen
Step-by-step explanation:
C = work completion
Half the number of days
6/5 (= 12/10) the hrs/day
½ × 6/5 × C = ⅗C
C/(⅗C) = 5/3
5/3 × 15 = 25
A machine produces 225,000 insulating washers for electrical devices per day. The production manager claims that no more than 4,000 insulating washers are defective per day. In a random sample of 200 washers, there were 4 defectives. Determine whether the production manager's claim is likely to be true. Explain.
The claim of the production manager is not true because more than 4000 insulating washers are defective per day.
How to determine if the claim was true or not?The total amount of insulating washer for the electrical devices produced per day = 225,000.
The amount chosen at random for sampling = 200 washers.
The amount shown to be defective in the chosen sample = 4
If every 200 = 4 defective
225,000 = X
Make c the subject of formula;
X = 225000×4/200
X = 900000/200
X = 4,500.
This shows that the claim is wrong because more than 4000 insulating washers are defective per day.
Learn more about random sampling here:
https://brainly.com/question/24466382
#SPJ1
Find a particular solution to the differential equation day dy 8 dt + 20y = 68 – 20t dt2 You do not need to find the general solution. y(t) = symbolic expression
The particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
To solve the given differential equation, we'll need to use the method of undetermined coefficients. In this method, we assume that the particular solution to the differential equation has the same form as the forcing term. Here's how we can solve the given differential equation: Identify the forcing term and its derivatives. The forcing term is given by: f(t) = 68 - 20tWe can find its first derivative as follows: f'(t) = -20We can find its second derivative as follows: f''(t) = Guess the form of the particular solution We assume that the particular solution has the same form as the forcing term.
Since the forcing term is a first-degree polynomial, we assume that the particular solution also has the form of a first-degree polynomial: y_ p(t) = At + B Here, A and B are constants that we need to determine. Find the derivatives of the assumed form of the particular solution. Here are the first and second derivatives of the assumed form of the particular solution: y_ p(t) = At + B ==> y_ p'(t) = A ==> y_ p''(t) = 0. Substitute the assumed form of the particular solution and its derivatives into the differential equation Substituting y_ p(t), y_ p'(t), and y_ p''(t) into the differential equation, we get:8A + 20(At + B) = 68 - 20t Simplifying the above equation, we get: (8A + 20B) + (20A - 20)t = 68Comparing the coefficients of t and the constant terms on both sides,
we get two equations:8A + 20B = 68 (1)20A - 20 = 0 (2)Solving equation (2) for A, we get: A = 1 Substituting A = 1 into equation (1), we get:8 + 20B = 68Solving for B, we get: B = 3. Write the particular solution to the differential equation Substituting A = 1 and B = 3 into the assumed form of the particular solution, we get :y_ p(t) = t + 3Therefore, the particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
Learn more about Symbolic Expression
brainly.com/question/1577706
#SPJ11
Find the mean, median, mode, and range for the data set given.
112, 122, 132, 142, 152
Write down the smallest possible answer.
Answer:
3
Step-by-step explanation:
We have to find the smallest possible factor of 15 and multiple of 3.
The smallest factor of any positive integer is 1.
The smallest multiple of any positive integer is the integer itself. So the smallest multiple of 3 would be 3 itself.
[tex]1 * 3 = 3[/tex]
And 3 is the answer.
from 80 to 100 with percent
Answer:
25%--------------------------
As I understand you would like percent increase if number is increased from 80 to 100.
The difference in numbers is:
100 - 80 = 20What percent of 80 is 20?
20/80*100% = 25%Hence this change is represented as 25% increase.
If n(Ax B) = 72 and n(A) = 24, find n(B).
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
To learn more about set:
https://brainly.com/question/8053622
#SPJ1