Consider the heat equation in a two-dimensional rectangular region 0 < x < L,0 < y < H, partial differential u/partial differential t = k(partial differential^2 u/partial differential x^2 + partial differential^2 u/partial differential y^2), subject to the initial condition u(x, y,0) = f(x, y). Solve the initial value problem and analyse the temperature as t rightarrow infinity, if the boundary conditions are a. u(0, y, t) = 0, u(L, y, t) = 0, u(x,0, t) = 0, u(x, H, t) = 0. b. partial differential u/partial differential x (0, y, t) = 0, partial differential u/partial differential x (L, y, t) = 0, partial differential u/partial differential y (x,0, t) = 0, partial differential u/partial differential y (x, H, t) = 0
Answers
The temperature approaches the steady-state solution:
\(u(x, y, t) = A_{00}\).
How to solve the initial value problem?To solve the initial value problem, we begin by assuming a solution of the form u(x, y, t) = X(x)Y(y)T(t). Plugging this into the heat equation, we obtain:
X(x)Y(y)T'(t) = k(X''(x)Y(y) + X(x)Y''(y))T(t)
Dividing both sides by k X(x)Y(y)T(t), we get:
1/T'(t) = (X''(x)/X(x) + Y''(y)/Y(y))/k
Since the left-hand side depends only on t and the right-hand side depends only on x and y, both sides must be equal to a constant, which we denote by \(-\lambda^2\):
\(1/T'(t) = -\lambda^2\)
\(X''(x)/X(x) + Y''(y)/Y(y) = -\lambda^2k\)
Solving for X(x) and Y(y) separately, we obtain:
X(x) = A \(cos(n\pi x/L)\) (n=1,2,3,...)
Y(y) = B cos(\(m\pi y/H\)) (m=1,2,3,...)
Here A and B are constants determined by the initial condition u(x, y, 0) = f(x, y), and n and m are integers.
Substituting these expressions into the previous equation and simplifying, we obtain:
\(T'(t) + \lambda^2kT(t) = 0\)
The solution to this differential equation is:
\(T(t) = C exp(-\lambda^2kt)\)
Here C is a constant determined by the initial condition u(x, y, 0) = f(x, y). Therefore, the general solution to the heat equation is:
\(u(x, y, t) = \sum A_{nm} cos(n\pi x/L)\cos(m\pi y/H)\exp(-\lambda^2knt)\)
where the sum is over all integers n and m, and \(A_{nm}\) are constants determined by the initial condition u(x, y, 0) = f(x, y).
For the boundary conditions (a), we have:
u(0, y, t) = 0
u(L, y, t) = 0
u(x, 0, t) = 0
u(x, H, t) = 0
These are homogeneous Dirichlet boundary conditions, which imply that the Fourier series of u(x, y, t) has only sine and cosine terms, with the coefficients of the sine terms being zero due to the even symmetry of the problem.
Therefore, we have:
\(u(x, y, t) = \sum A_{nm} cos(n\pi x/L)\cos(m\pi y/H)\exp(-\pi ^2knt)\)
where the sum is over all even integers n and m, and \(A_{nm}\) are constants determined by the initial condition u(x, y, 0) = f(x, y).
The constant \(\lambda^2\) is determined by the boundary conditions and is given by:
\(\lambda^2 = (n\pi /L)^2 + (m\pi /H)^2\)
As t approaches infinity, the exponential term \(exp(-\lambda^2knt)\) goes to zero for all values of n and m except n=m=0, which gives λ=0.
Therefore, the temperature approaches the steady-state solution:
\(u(x, y, t) = A_{00}\)
where \(A_{00}\) is the constant determined by the initial condition u(x, y, 0) = f(x, y).
For the boundary conditions (b), we have:
partial differential u/partial differential x (0, y, t) = 0
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Related Questions
Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as th
difference between the time a fire house receives a call and the time the first piece of fire equipment leaves the
station. The response times for fire departments in a large city are found to have an approximately Normal
distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station
response times are between 4 and 6 minutes?
Answers
Approximately 55.61% of fire station response times are between 4 and 6 minutes.
How to solve for the percentageFor X = 4 minutes:
Z1 = (4 - 4.5) / 1.2 = -0.417 approximately.
For X = 6 minutes:
Z2 = (6 - 4.5) / 1.2 = 1.25 approximately.
Next, we look up these z-scores in a standard normal distribution table, or use a calculator or software that provides the cumulative area from -∞ to Z (which represents the proportion of data below Z).
The values we get from the z-table are:
P(Z ≤ -0.417) ≈ 0.3383
P(Z ≤ 1.25) ≈ 0.8944
P(4 ≤ X ≤ 6) = P(Z ≤ 1.25) - P(Z ≤ -0.417)
= 0.8944 - 0.3383
= 0.5561
So, approximately 55.61% of fire station response times are between 4 and 6 minutes.
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A teacher is randomly handing out tests. There are 2 different versions of the test, Test A and Test
B. If there are 8 tests in all and an equal number of each version, what is the probability that the
first 4 students will all receive Test A?
Answers
Answer:
1/2 chance or 50% probability
The population P of bacteria in a culture after t minutes is given by the equation p=p0 (1.14)^t where P0 is the initail population. If the number of the bacteria starts at 400, how long will it take for he population to incfrease to 2000
Answers
Answer:
The time taken is 4.79 minutes.
Step-by-step explanation:
\(P = Po(1.4)^{t}\)
initial Population, Po = 400
Final population, P = 2000
Let the time is t.
\(2000 = 400(1.4)^{t} \\5 = (1.4)^t\\log 5 = t log 1.4\\0.6989 = 0.146 t \\t = 4.79 minutes\)
please can yall actually help me with this?
Answers
Answers In Exact Order:
37 / 8, 91 / 20, 457 /100 (4.57), and 4543 / 1000 (4.543)
Step-by-step explanation:
In order to solve your question, we first convert the two decimals into fractions. This will be easier, since we can order fractions from least to greatest by their denominator.
1. To convert 4.57 to a fraction, we can place the decimal number over it's placed value. Like this: 0.3 - 3/10.
For this problem, we'll do the same with 4.57, like this:
457 / 100
Since 7 is in the hundredth place, the denominator will be 100.
You can also do the same with 4.543, which will be:
4543 / 1000
Like I said, 3 is in the thousandth place, and the denominator will be 1,000.
Now, since the two decimals are converted to fractions, we can do the easy part!
To order the fractions, we look at the denominator.
If you look at 37 / 8, the denominator is eight, which will go first, since it's the least.
Then take a look at 91 / 20. The denominator is twenty, and will go second.
After that, look at 457 / 100. The denominator is one hundred, and will go third.
Lastly, 4543 / 1000 will be the greatest, since the denominator is one thousand.
Hence, the order goes by:
37 / 8
91 / 20
457 / 100 (4.57)
4543 / 1000 (4.543)
Reply below if you have any questions or concerns.
You're welcome!
- Nerdworm
The amount that a charter boat captain charges a group to go deep sea fishing is $850. If the group tips the captain 17%, what is the total amount the captain receives for the fishing trip?
Answers
Answer:
Step-by-step explanation:
kl
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
17% of $850 = $144.5
The total amount the captain received for the fishing trip is $994.5
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount charged to go deep sea fishing = $850
Tip percentage = 17%
This means,
17% of 850
= 17/100 x 850
= 17/10 x 85
=17/2 x 17
= 289/2
= 144.5
Now,
The total amount the captain received for the fishing trip.
= 850 + 144.5
= $994.5
Thus,
The total amount the captain received for the fishing trip is $994.5
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There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 41.1 hours and 45.9 hours.
A. Flawed. This interpretation makes an implication about individuals rather than the mean.
B. Correct
C. Flawed. This interpretation implies that the population mean varies rather than the interval.
D. Flawed. This interpretation implies that the mean is only for last week
Answers
The correct answer is Option B.
What is confidence interval?The given statement is an interpretation of a confidence interval, which is a statistical range of values that has a certain level of confidence of containing the true population parameter, in this case, the population mean of hours worked by adults in the previous week.
The interpretation correctly states that there is a 95% chance that the mean number of hours worked by adults in the previous week falls within the interval of 41.1 to 45.9 hours. This interpretation does not make any implication about individuals, but rather the population mean, which is the parameter of interest in this case. It also does not imply that the population mean varies, but rather that the true value of the mean is somewhere within the given interval with a 95% level of confidence. Finally, it does not imply that the mean is only for last week, but rather that the interval estimate is for the mean number of hours worked by adults in the previous week.
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100 POINTS GEOMETRY QUESTION PLEASE ANSWER !!!!!!
Answers
Answer:
Step-by-step explanation:
ABC have sides: 5, 7 and 10
5^2 + 7^2 = 25+47 = 72 < 10^2
so triangle ABC is obtuse
JKL has sides: 12, 35 and 37
12^2 + 35^2 = 144 + 1225 = 1369 = 37^2
so triangle JKL is right-angled
PQR has sides 12, 10 and 16
12^2 + 10^2 = 144 + 100 = 244 > 16^2
so triangle PQR is acute
Answer:
Step-by-step explanation:
missing the Q: it asks 2 classify the triangles.
so the ans:
ABC - obtuse
JKL - right-angled
PQR - acute
Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then
decreases its speed, as time increases?
Speed (miles per minute)
Time (minutes)
х
(miles per minute)
Answers
Answer:
The top one would be the answer
A parabolic TV antenna is construoted by taking a flat sheet of metal and bending it into a parabolic shape. If the cross section of the antenna is a parabola which is 50 centimeters wide and 30 centimeters deep, where should the receiver be placed to maximize reception?
Answers
Therefore, the receiver should be placed at a distance of 30/2 = 15 centimeters from the vertex, in the direction of the focus, to maximize reception.
To maximize reception, the receiver should be placed at the focus of the parabolic antenna. In a parabola, the focus is located at a distance equal to half the focal length from the vertex.
In this case, the width of the parabolic antenna is 50 centimeters, which means the distance from one side to the vertex is 25 centimeters. Since the parabola is symmetric, the vertex is at the center, and the focal length is equal to the depth of the parabola, which is 30 centimeters.
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what is the value of x
1. 124
2. 62
3. 112
4. 68
explain why the answer is correct
Answers
Answer:
3.112 because 56+56=112Answer:
The answer is 4. 68
Step-by-step explanation:
since equal sides of triangle,it has equal angle at the base of triangle.So, the two angles of triangle at base is 56. The sum of angles in a triangle is 180.Therefore,56+56+x=180
x=180-112
x=68
WILL GIVE BRAINLIEST- Geometric Proofs
Answers
Answer:
Angle ACE and Angle ABE are congruent because they both share a side of Line Segment AE
Step-by-step explanation:
Please help me ASAP! These are my last points and I really need help. Thank you!
What is the area of the composite figure?
A. 69 cm²
B. 90 cm²
C. 3168 cm²
D. 33 cm²
Answers
Required area of the composite figure is 69 cm²
What is area of a composite shape?
the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.
Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.
Here in this figure, we have two figures.
First one is rectangle and second one is triangle.
Length and breadth of the rectangle are 12 cm and 4 cm respectively.
So, area = Length × Breadth = 12 × 4 = 48 cm²
Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.
So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²
Now if we add both area of rectangle and triangle then we will get area of the composite figure.
So, required area of the composite figure is ( 48+21) = 69 cm²
Therefore, option A is the correct option.
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There are 7 women and 5 men in a department. How many ways can a committee of 4 people be selected? How many ways can this committee be selected if there must be 2 men and 2 women on the committee? How many ways can this committee be selected if there must be at least 2 women on the committee?
Answers
There are 420 ways to select a committee of 4 people with at least 2 women.
To solve these problems, we can use the formula for combinations. The number of ways to choose k items from a set of n items is given by:
C(n, k) = n! / (k! * (n - k)!)
where "!" denotes the factorial function.
To select a committee of 4 people from a pool of 12 people, we can use the formula:
C(12, 4) = 12! / (4! * 8!) = 495
So there are 495 ways to select a committee of 4 people without any additional criteria.
To select a committee of 4 people with 2 men and 2 women, we can first count the number of ways to choose 2 men from the 5 men and 2 women from the 7 women. This gives us:
C(5, 2) * C(7, 2) = (5! / (2! * 3!)) * (7! / (2! * 5!)) = 10 * 21 = 210
So there are 210 ways to select a committee of 4 people with 2 men and 2 women.
To select a committee of 4 people with at least 2 women, we can count the number of committees with exactly 2 women, 3 women, or 4 women, and add them together.
The number of committees with exactly 2 women is:
C(7, 2) * C(5, 2) = 21 * 10 = 210
The number of committees with exactly 3 women is:
C(7, 3) * C(5, 1) = 35 * 5 = 175
The number of committees with all 4 women is:
C(7, 4) = 35
So the total number of committees with at least 2 women is:
210 + 175 + 35 = 420
Therefore, there are 420 ways to select a committee of 4 people with at least 2 women.
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2/3x5/9
This needs 20 charesters to send so haw yall doin
Answers
Answer:
Hello! have a good day!
Exact Form:
10/27
Decimal Form:
0.370
In assuming we are doing (2/3)*(5/9) not 2/(3*5)/9 we can conclude that the answer is 10/27 by multiplying the numerator and denominator of the 2 fractions.
Also I'm doing very well and it would make my day even better if you give me brainlliest.
Use the SOLVE Process to determine the missing coefficient
of a given polynomial. P(x)=x^4 - 3x^3 +ax^2 - 6x + 14
Answers
Answer:
To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:
S: Write down the given information and identify the problem.
We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".
O: Organize the information and decide on a plan.
To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.
L: Carry out the plan.
For example, let's say we substitute x = 2 into the polynomial. We get:
P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14
= 16 - 24 + 4a - 12 + 14
= -4 + 4a + 2
= 4a - 2
We are given that P(2) = 4a - 2 = 0, so 4a = 2.
Solving for a, we get:
a = 2 / 4
= 0.5
V: Check the solution.
We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.
P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14
Substituting x = 2 and a = 0.5, we get:
P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14
= 16 - 24 + 1 - 12 + 14
= 0
Since P(2) = 0, our solution appears to be correct.
Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.
The perimeter of a semicircle is 35. 98 millimeters. What is the semicircle's radius Use 3. 14 for a. Millimeters Submit explain
Answers
If the perimeter of a semicircle is 35. 98 millimeters, 7 mm is the semicircle's radius.
A semi-circle refers to half of the circle. The circle is cut along the diameter to form a semi-circle.
A diameter is a line segment that passes through the center of the circle and touches the boundary of the circle from both ends.
The perimeter of the semi-circle is the sum of the length of the diameter and the circumference of the semi-circle.
P = 2r + πr
where P is the perimeter
r is the radius
P = 35.98 mm
35.96 = 2r + 3.14r
35.96 = 5.14r
r = 7 mm.
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On this homework sheet, there are a total of 8 shapes that are rectangles or right triangles. You agree to help check their work. You decide to use your handy dandy MATLAB skills to create a script that you can run once to calculate the area of all 8 shapes on the assignment. You are to do the following: - Start by writing an algorithm. While you might not need one for this particular assignment, it is absolutely necessary in more difficult coding problems and is a must-have habit to develop. - Write your code with enough comments that someone who doesn't know how to code can understand what your code does. - Check your code. Include a short description of how you verified that your code was working correctly after your algorithm. Here are some tips to get you started: - For each shape, the script should ask the user to input a character that signifies what shape it is and also ask them to input the relevant dimensions of the shape. - Assume all dimensions are known and all units are in inches. You may also assume that the user does not make any incorrect inputs. - Output each answer to the command window with no more than two decimal places, including the units. Question 3 (6 points) With people carrying less cash than they used to, finding an actual coin for a coin toss can be difficult. Write a MATLAB script so that as long as you have your laptop with you, you can simulate flipping a coin. The script should do the following: - Prompt the user to enter an H for heads or T for tails. - If the user does not enter an H or T, throw an error with an appropriate message. - Randomly generate a 1 or 2 to stand for heads or tails, respectively. - Compare the guess to the "flipped" coin and display a message to the screen indicating whether the guess was correct or not.
Answers
Compare the calculated areas with the output of the script.
Ensure that the script produces the correct total area by adding up the individual areas correctly.
Algorithm to create a MATLAB script for calculating the area of all 8 shapes on the assignment:
Initialize a variable totalArea to 0.
Create a loop that will iterate 8 times, once for each shape.
Within the loop, prompt the user to input a character representing the shape ('R' for rectangle, 'T' for right triangle).
Based on the user's input, prompt them to enter the relevant dimensions of the shape.
Calculate the area of the shape using the provided dimensions.
Add the calculated area to the totalArea variable.
Repeat steps 3-6 for each shape.
Output the totalArea with two decimal places to the command window, including the units.
Now, let's write the MATLAB code based on this algorithm:
matlab
Copy code
% Step 1
totalArea = 0;
% Step 2
for i = 1:8
% Step 3
shape = input('Enter shape (R for rectangle, T for right triangle): ', 's');
% Step 4
if shape == 'R'
length = input('Enter length of rectangle (in inches): ');
width = input('Enter width of rectangle (in inches): ');
% Step 5
area = length * width;
elseif shape == 'T'
base = input('Enter base length of right triangle (in inches): ');
height = input('Enter height of right triangle (in inches): ');
% Step 5
area = 0.5 * base * height;
end
% Step 6
totalArea = totalArea + area;
end
% Step 8
fprintf('Total area: %.2f square inches\n', totalArea);
To verify that the code is working correctly, you can run it with sample inputs and compare the output with manual calculations.
For example, you can input the dimensions of known shapes and manually calculate their areas.
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Now we're going to apply these same principles of
with/without replacement to a simple game with a bag
of marbles.
John chooses a marble without replacing it. He then
choose a second marble. In the bag, there are 8 red, 6
blue, 8 white, and 5 yellow. Find the probability for each
of the outcomes listed in the table.
Keep each answer in DECIMAL form, rounding to 3
decimal places.
Answers
Answer:
In bold, see below
Step-by-step explanation:
P(Red, Blue) means that there's an 8/27 chance of selecting a red marble, and then a 6/26 chance of selecting a blue marble after eliminating the red marble we just grabbed. Therefore, multiplying the probabilities, (8/27)(6/26) = 48/702 = 0.068 would be the probability of selecting a red marble followed by a blue without replacement.
P(Red, Red) means that there's an 8/27 chance of selecting a red marble, and then a 7/26 chance of selecting a red marble after eliminating the first red marble we just grabbed. Therefore, multiplying the probabilities, (8/27)(7/26) = 56/702 = 0.08 would be the probability of selecting a red marble followed by a red without replacement.
P(Blue, White) means that there's a 6/27 chance of selecting a blue marble, and then an 8/26 chance of selecting a white marble after eliminating the first blue marble we just grabbed. Therefore, multiplying the probabilities, (6/27)(8/26) = 48/702 = 0.068 would be the probability of selecting a blue marble followed by a white without replacement.
P(Yellow, Red) means that there's a 5/27 chance of selecting a yellow marble, and then an 8/26 chance of selecting a red marble after eliminating the first blue marble we just grabbed. Therefore, multiplying the probabilities, (5/27)(8/26) = 40/702 = 0.057 would be the probability of selecting a yellow marble followed by a red without replacement.
show that the wave function y=e^(b(x-vt)) is a solution of the linear wave equation (eq. 16.27), where b is a constant
Answers
To show that the wave function y=e^(b(x-vt)) is a solution of the linear wave equation (eq. 16.27), we need to plug the wave function into the equation and see if it satisfies the equation.
The linear wave equation (eq. 16.27) is given by:
∂^2y/∂x^2 = (1/v^2) ∂^2y/∂t^2
Plugging in the wave function y=e^(b(x-vt)) into the equation, we get:
∂^2(e^(b(x-vt)))/∂x^2 = (1/v^2) ∂^2(e^(b(x-vt)))/∂t^2
Taking the second derivative with respect to x, we get:
b^2 e^(b(x-vt)) = (1/v^2) ∂^2(e^(b(x-vt)))/∂t^2
Taking the second derivative with respect to t, we get:
b^2 e^(b(x-vt)) = (1/v^2) b^2 v^2 e^(b(x-vt))
Simplifying, we get:
b^2 e^(b(x-vt)) = b^2 e^(b(x-vt))
This shows that the wave function y=e^(b(x-vt)) satisfies the linear wave equation (eq. 16.27) and is therefore a solution of the equation.
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For f(x) = -x² -2x-4, find f(x + h) - f(x) / h
f(x + h) - f(x) / h =
Answers
To find the expression for (f(x + h) - f(x)) / h for the function f(x) = -x² - 2x - 4, we substitute f(x + h) and f(x) into the formula and simplify the expression.
Using the derivative formula we derive the expression.We start by evaluating f(x + h) and f(x) individually. For f(x + h), we substitute x + h into the function: f(x + h) = -(x + h)² - 2(x + h) - 4. Expanding and simplifying, we get f(x + h) = -x² - 2hx - h² - 2x - 2h - 4.
Next, we substitute x into the function f(x): f(x) = -x² - 2x - 4.
Now, we can calculate the numerator of our expression, f(x + h) - f(x). Substituting the corresponding values, we have (-x² - 2hx - h² - 2x - 2h - 4) - (-x² - 2x - 4). Simplifying this expression, we get -2hx - h² - 2h.
Finally, we divide the numerator by h to get our desired expression: (-2hx - h² - 2h) / h. By canceling out h terms, we simplify it further to -2x - h - 2. Thus, the expression (f(x + h) - f(x)) / h for f(x) = -x² - 2x - 4 is -2x - h - 2.
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Directions: Solve for x. Round your answer to the nearest tenth. Make sure you calculator
is in degree mode!
11
35
Answers
Answer:
its 10 because chu papi munenu
suppose that two people standing 2 miles apart both see the burst from a fireworks display. after a period of time, the first person standing at point a hears the burst. one second later, the second person standing at point b hears the burst. if the person at point b is due west of the person at point a and if the display is known to occur due north of the person at point a , where did the fireworks display occur?
Answers
The fireworks display occurred due north of the person at point A. This can be determined by calculating the direction and speed of sound. Assuming the speed of sound is approximately 343 meters per second, the fireworks display must have occurred approximately 0.58 seconds away from point A, which is approximately 343 meters due north of point A. This means that the fireworks display occurred somewhere between the two points.
To double-check the calculations, we can look at the two points and the direction in which the sound traveled. Point A is due north of the fireworks display, and point B is due west. This means that the sound traveled both north and west, which is consistent with the calculations.
Therefore, we can conclude that the fireworks display occurred due north of point A.
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how do you guys do this
Answers
Answer: B. 4, 5, 2
Step-by-step explanation:
Scale factor is very simple. You just take the side lengths of your prime (starting) triangle and divide/multiply by the factor. Since the scale factor is 1/7, you could choose to multiply each side by 1/7 or divide each side by 7. Both will leave you with the same answers.
stuck on this its super hard
Answers
Explanation:
Divide shape into one rectangle and one triangle.
Base of triangle:
15 - 9 = 6 cm
Height of triangle:
11 - 6 = 5 cm
Area if triangle (1/2 • base • height):
1/2 • 6 • 5 = 15 square centimeters
Area of rectangle (length • width)
15 • 6 = 90 square centimeters
ADD THE AREA OF BOTH SHAPES:
90 + 15 = 105 square centimeters
Hope this helps!
-SpaceMarsh
Kellie has 6/7 as many paper clips as Junjie. Minghua has 3 times as many paper clips as Kellie. Given that Minghua has 2552 more paper clips than Junjie. (a) how many paper clips do the 3 children have in total? (b) how many paper clips does Minghua have?
Answers
Answer: 6,192 paperclips, 3,826 paperclips
Step-by-step explanation:
a) To find the sum of all the children's paperclips, you must find each of them.
First, to start off, create some equations that represent this information:
k = j * \(\frac{6}{7}\)
m = 3k
m = j + 2552
Then, for starts you can use the equation m = 3k and plug in for the variables
m = 3k
(j+2552) = 3(j * 6/7)
j + 2552 = 3j + 2.57
2549.43 = 2j
j = 1274.715
j = 1274 (round down because you can't have a fraction of a paper clip)
Next, use j to solve the other equations
m = j + 2552
m = 1274 + 2552
m = 3826
k = j * 6/7
k = 1274 * 6/7
k = 1092
sum = k + j + m
sum = 1092 + 1274 + 3826
sum = 6,192 paperclips
b) We already know m, which is 3826.
3,826 paperclips
HURRY I NEED HELP!!!!!
State the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots, be sure to show all work!
(equations are in the image below)
Answers
Answer:
Both have 4 imaginary rootsStep-by-step explanation:
1)
(x^2 + 9)(x^2 + 6) = 01.
x^2 + 9 = 0x^2 = - 9x = ± √-9x = ± 3i2.
x^2 + 6 = 0x^2 = -6x = ±√-6x = ± i√6It has 4 imaginary roots and no real roots
2)
(x^2 + 7)(x^2 + 5) = 01.
x^2 + 7 = 0x^2 = -7x = ± √7x = ± i√72.
x^2 + 5 = 0x^2 = - 5x = ± √-5x = ± i√5It has 4 imaginary roots and no real roots
#1
(x²+9)(x²+6)=0First
x²=-9x=±3isecond
x²=-6x=±√6i4complex roots
#2
(x²+7)(x²+5)=0first
x²=-7x=±√7iSecond
x²=-5x=±√5i4 complex roots
!!!URGENT!!! I WILL GIVE 100 points
Can someone please answer this?
Answers
Ans hope its the green
but i need better info
May 03, 8:12:38 PM
A group of friends wants to go to the amusement park. They have no more than $725
to spend on parking and admission. Parking is $19, and tickets cost $20.25 per
person, including tax. Which inequality can be used to determine p, the maximum
number of people who can go to the amusement park?
O 725 < 20.25p + 19
O 725 < 20.25 + 19p
Submit Answer
725 > 20.25 + 19p
O 725 > 20.25p + 19
Type here to search
Answers
Answer:
725 > 20.25p +19
Step-by-step explanation:
Help please giving points to right answer JUST NEED THE NUMBER TO FILL IN BLANK !!
Answers
Answer:
We have the proportion: 8/10 = 100/y
We can solve for y by cross-multiplying.
That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000
Dividing both sides by 8 to solve for y, y = 125
Hence, the value of y is 125.
Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5
Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4
Therefore, y = 4√5The value of y is 4√5.
Step-by-step explanation:
Hope this helps!! Have a good day/night!!
Ezra surveyed some students at his school about their favorite classes.
Art: 3
History: 7
Choir: 5
What is the experimental probability that the next student Ezra talks to will pick choir?
Write your answer as a fraction or whole number.
Answers
Answer:
1/3
Step-by-step explanation:
total number of students = 15
students that chose choir as their favourite class= 5
P(choir)= 5/15 = 1/3