a) Bisection Method MATLAB code for equation [tex]x^3 + 4x^2 - 10 = 0[/tex] in the interval [0,5]:
function root = bisection_method()
f = [tex]x^3 + 4*x^2 - 10[/tex];
a = 0;
b = 5;
tol = 1e - 6;
while (b - a) > tol
c = (a + b) / 2;
if f(c) == 0
break;
elseif f(a) * f(c) < 0
b = c;
else
a = c;
end
end
root = (a + b) / 2;
end
b) Bisection Method MATLAB code for equation [tex]x^3 - 6x^2 + 10x - 4 = 0[/tex] in the interval [0,4]:
function root = bisection_method()
f = [tex]x^3 - 6*x^2 + 10*x - 4[/tex];
a = 0;
b = 4;
tol = 1e-6;
while (b - a) > tol
c = (a + b) / 2;
if f(c) == 0
break;
elseif f(a) * f(c) < 0
b = c;
else
a = c;
end
end
root = (a + b) / 2;
end
c) Newton's Method MATLAB code for equation [tex]x^3 + 3x + 1 = 0[/tex] in the interval (-2,0]:
function root = newton_method()
f = [tex]x^3 + 3*x + 1[/tex];
df = [tex]3*x^2 + 3[/tex];
[tex]x_0[/tex] = -1;
tol = 1e-6;
while abs(f([tex]x_0[/tex])) > tol
[tex]x_0 = x_0 - f(x_0) / df(x_0)[/tex];
end
root = [tex]x_0[/tex];
end
d) Fixed-Point Method MATLAB code for equation [tex]x^3 - 2x - 1 = 0[/tex] in the interval (1.5,2]:
function root = fixed_point_method()
g = [tex](x^3 - 1) / 2[/tex];
[tex]x_0 = 2[/tex];
tol = 1e-6;
while abs([tex]g(x_0) - x_0[/tex]) > tol
[tex]x_0 = g(x_0)[/tex];
end
root = [tex]x_0[/tex];
end
e) Secant Method MATLAB code for equation 1 - 2*exp(-x) - sin(x) = 0 in the interval (0,4]:
function root = secant_method()
f = 1 - 2*exp(-x) - sin(x);
[tex]x_0[/tex] = 0;
[tex]x_1[/tex] = 1;
tol = 1e-6;
while abs(f([tex]x_1[/tex])) > tol
[tex]x_2 = x_1 - f(x_1) * (x_1 - x_0) / (f(x_1) - f(x_0))[/tex];
[tex]x_0 = x_1[/tex];
[tex]x_1 = x_2[/tex];
end
root = [tex]x_1[/tex];
end
f) Secant Method MATLAB code for equation [tex]2 - x^3 + 4*x^2 - 10 = 0[/tex] in the interval [0,4]:
function root = secant_method()
f = [tex]2 - x^3 + 4*x^2 - 10[/tex];
[tex]x_0 = 0[/tex];
[tex]x_1 = 1[/tex];
tol = 1e-6;
while abs(f([tex]x_1[/tex])) > tol
[tex]x_2 = x_1 - f(x_1) * (x_1 - x_0) / (f(x_1) - f(x_0))[/tex];
[tex]x_0 = x_1[/tex];
[tex]x_1 = x_2[/tex];
end
root = [tex]x_1[/tex];
end
How to find the MATLAB code be used to solve different equations numerically?MATLAB provides several numerical methods for solving equations. In this case, we have used the Bisection Method, Newton's Method, Fixed-Point Method, and Secant Method to solve different equations.
The Bisection Method starts with an interval and iteratively narrows it down until the root is found within a specified tolerance. It relies on the intermediate value theorem.
Newton's Method, also known as Newton-Raphson Method, approximates the root using the tangent line at an initial guess. It iteratively refines the guess until the desired accuracy is achieved.
The Fixed-Point Method transforms the equation into an equivalent fixed-point iteration form. It repeatedly applies a function to an initial guess until convergence.
The Secant Method is a modification of the Newton's Method that uses a numerical approximation of the derivative. It does not require the derivative function explicitly.
By implementing these methods in MATLAB, we can numerically solve various equations and find their roots within specified intervals.
These numerical methods are powerful tools for solving equations when analytical solutions are not feasible or not known.
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Evaluate the integral by reversing the order of integration 7/2 cosx V1+cosx dc dụ.
The evaluated integral is (7/4) (π - (3√3)/6) (rounded to an appropriate decimal approximation based on the given values of π and √3).
To evaluate the integral ∫∫(7/2 cos(x)) dV, where the region of integration is given by V: 1 ≤ c ≤ 2 and 0 ≤ x ≤ cos⁻¹(2c-1), we can reverse the order of integration.
Step 1: Write the integral with reversed order of integration:
∫∫(7/2 cos(x)) dc dx
Step 2: Determine the limits of integration for the reversed order. The variable c now varies from 1 to 2, and x varies from 0 to cos⁻¹(2c-1). Therefore, the integral becomes:
∫[1,2] ∫[0,cos⁻¹(2c-1)] (7/2 cos(x)) dx dc
Step 3: Integrate with respect to x first. The integral with respect to x is straightforward:
∫[1,2] [sin(x)] [0,cos⁻¹(2c-1)] (7/2) dc
Step 4: Evaluate the inner integral:
∫[1,2] [sin(cos⁻¹(2c-1))] (7/2) dc
Step 5: Simplify the inner integral using the trigonometric identity sin(cos⁻¹(u)) = √(1 - u²):
∫[1,2] [√(1 - (2c-1)²)] (7/2) dc
Step 6: Integrate with respect to c:
(7/2) ∫[1,2] [√(1 - (2c-1)²)] dc
Step 7: Evaluate the integral:
Using the trigonometric substitution u = sin(t), du = cos(t) dt, and the limits change to t: π/6 ≤ t ≤ π/2.
(7/4) ∫[π/6, π/2] [√(1 - sin²(t))] cos(t) dt
Step 8: Simplify the integrand:
(7/4) ∫[π/6, π/2] [cos²(t)] dt
Step 9: Apply the double-angle formula for cosine:
(7/4) ∫[π/6, π/2] [(1 + cos(2t))/2] dt
Step 10: Split the integral into two separate integrals:
(7/4) [∫[π/6, π/2] (1/2) dt + ∫[π/6, π/2] (cos(2t)/2) dt]
Step 11: Integrate each term separately:
(7/4) [(t/2) + (sin(2t)/4)] evaluated from π/6 to π/2
Step 12: Substitute the limits and simplify:
(7/4) [((π/2)/2 + (sin(2(π/2))/4) - ((π/6)/2) - (sin(2(π/6))/4)]
Step 13: Simplify further:
(7/4) [(π/4 + 0 - π/12 - (1/4)(√3/2))]
Step 14: Simplify and calculate the final value:
(7/4) [(π/4 - π/12 - (√3/8))]
= (7/4) [(3π - π - 3√3)/12]
= (7/4) [(2π - 3√3)/12]
= (7/4) (π - (3√3)/6)
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The answer is 3/4 What could the question be?
Answer:
how many brain cells do you have compared to the average person?
Step-by-step explanation:
In a study of spat dating es were asked them in the same time to What other out of the popu 23,50710090 What is the concerto? D-lichte places need was the other the contacto OA TN repostane posting tone OR Weather to the memo and on dem O. We second have the end மொயமால மாமா mg 140 Newt 0 View an example Get more help Help me solve this C M a o 0 10 1 In a study of speed dating male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractivo 10 = extremely attractive) Construct a confidence interval using a 95% confidence level What do the results tell about the mean attractiveness ratings of the population of all adult females? 6,9,3,9, 6, 6, 8, 8, 7, 10,5,9 What is the confidence interval for the population mean? [<<(Round to one decimal place as needed) west point(s) possible in a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive 10 = extremely attractive) Construct a confidence interval using a 95% confidence level What do the results tell about the mean attractiveness ratings of the population of all adult females? 6,9,3,9,6,6,8,8.7. 10,5,9 PO What is the confidence interval for the population mean? <-- (Round to one decimal place as needed) What does the confidence interval tell about the population of all adult fernales? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. ative Area from the LEF 02 O A. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females 5000 5178 03 5120 5517 5990 5871
Confidence interval are 5.9 < μ < 8.5 for the population mean.
Given:
Let x = 6,9,3,9, 6, 6, 8, 8, 7, 10,5,9
N = 12, ∑x = 86 x = 86/12 = 7.16
[tex]s=\sqrt{\frac{(x-\bar x)^2}{N-1} } = \sqrt{\frac{(6-7.16)^2+.....+(9-7.16)}{12-1} }[/tex]
[tex]\sqrt{\frac{45.66}{11} } =2.03[/tex]
At 98% confidence interval.
[tex]z=1-\frac{95}{100} =0.05\\[/tex]
[tex]t=2.201[/tex]
Confidence interval.
[tex]\bar x \pm t\frac{s}{\sqrt{n} } = 7.16\pm 2.201(\frac{2.03}{\sqrt{12} } )[/tex]
[tex]5.9 < \mu < 8.5[/tex]
Therefore, 95% confidence interval are 5.9 < μ < 8.5
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Eugenia gasto 10 euros en el quiosco, compro 5 bocaditos, un paquete de galletas que costaba 1 euro y pagó 4 euros que debia ¿cuanto cuesta cada bocadito?
Answer:
the each snack cost is 1
Step-by-step explanation:
Let us assume the each snack cost be x
So according to the question
The following equation would be applied
5x + 1 + 4 = 10
5x + 5 = 10
5x = 5
x = 1
hence, the each snack cost is 1
So the same would be considered and relevant too
can some one please help. 4789658953 round to the nearest 10th
mean =
mean absolute deviation =
Answer:
i believe your answer is.
4,789,658,950
Step-by-step explanation:
The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. All observations were below the allowable maximum, as shown by the reported range of contaminant levels. (presumably the mean would be the midrange) Allowable Substance Range Detected Maximum Origin of Substance Chromium 0.45 to 8.61 100 Discharge from steel and pulp mills, natural erosion Barium 0.006 to 0.018 2 Discharge from drilling wastes, metal refineries, natu Fluoride 1.04 to 1.14 Natural erosion, water additive, discharge from fertil aluminum factories For each substance, estimate the standard deviation o by assuming uniform distribution and normal distribution shown in Table 8.11 in Section 8.8. (Round your answers to 4 decimal places.) Uniform Distribution Normal Distribution Chromium Barium Fluoride
(i) The uniform and normal distribution for chromium is 2.4927 and 16.5762. (ii) The uniform and normal distribution for Barium is 0.0031 and 0.3323. (iii) The uniform and normal distribution for Fluoride is 0.0289 and 0.0167
For each substance, the standard deviation o is estimated by assuming uniform distribution and normal distribution. The uniform distribution standard deviation is computed using the formula as follows:
o = (b-a) / √12
where
a is the minimum value,
b is the maximum value.
The normal distribution standard deviation is calculated using the formula as follows:
o = (b - a) / 6.
Estimate the standard deviation o for each substance. Round your answers to 4 decimal places. Substance Chromium Barium Fluoride Uniform Distribution. The range of contaminant levels for chromium is from 0.45 to 8.61. The minimum value is 0.45 and the maximum value is 8.61.
(i) Chromium
Uniform distribution
o = (b-a) / √12
= (8.61 - 0.45) / √12
= 2.4927
≈ 2.4927 (rounded to 4 decimal places)
Normal Distribution
The maximum value for chromium is 100 and the minimum value is 0.45. Thus, the standard deviation o for chromium using normal distribution is:
o = (b-a) / 6
= (100 - 0.45) / 6
= 16.5762
≈ 16.5762 (rounded to 4 decimal places)
(ii) Barium
Uniform Distribution
The range of contaminant levels for barium is from 0.006 to 0.018. The minimum value is 0.006 and the maximum value is 0.018.
Thus, the standard deviation o for barium using uniform distribution is:
o = (b-a) / √12
= (0.018 - 0.006) / √12
= 0.0031
≈ 0.0031 (rounded to 4 decimal places)
Normal Distribution
The maximum value for barium is 2 and the minimum value is 0.006. Thus, the standard deviation o for barium using normal distribution is:
o = (b-a) / 6
= (2 - 0.006) / 6
= 0.3323
≈ 0.3323 (rounded to 4 decimal places)
(iii) Fluoride
Uniform Distribution
The range of contaminant levels for fluoride is from 1.04 to 1.14. The minimum value is 1.04 and the maximum value is 1.14. Thus, the standard deviation o for fluoride using uniform distribution is:
o = (b-a) / √12
= (1.14 - 1.04) / √12
= 0.0289
≈ 0.0289 (rounded to 4 decimal places)
Normal Distribution
The maximum value for fluoride is 1.14 and the minimum value is 1.04. Thus, the standard deviation o for fluoride using normal distribution is:
o = (b-a) / 6
= (1.14 - 1.04) / 6
= 0.0167
≈ 0.0167 (rounded to 4 decimal places).
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Complete Question:
The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. Only the range is reported, not the mean.
For each substance, estimate the standard deviation σ by using one of the methods shown in Table 8.11 in section 8.8. (Round your answers to 4 decimal places.)
(i) The uniform and normal distribution is Chromium.
(ii) The uniform and normal distribution is Barium.
(iii) The uniform and normal distribution is Fluoride.
pls help i’ll give brainliest
Answer:
1/5x12 and 12/5
Step-by-step explanation:
both are dividing by five or equal to 2.4 which is the same as 1/5 of 12
Answer Of means to multiply so two correct answer would be B,D
Step-by-step explanation: hope this helps :)
Which of the following statements best describes the value of the expression 6x + 7 when x = 5?
Answer:
? is there a option?
Step-by-step explanation:
Answer:
37
Step-by-step explanation:
6x+7
6(5)+7
37
Rhonda has an extra credit protect to make a rectangular prism whit the volume of at least 24 in*3 . if the area of her base is 6 in*3 , which inequality would represent all the possible heights, h, of her prism in order to meet her teachers requirements
A. h > 4
B. h > 8
C. h < 4
D. h < 8
Find the lateral surface area.
Answer:
Step-by-step explanation:
Veterinarians often use nonsteroidal anti-inflammatory drugs (NSAIDs) to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the price is in the United States. They obtained a list of all veterinarians treating large animals, including horses. They send questionnaires to all the veterinarians on the list. Such a survey is called a cemus. The response rate was 40%. What is the population of interest? a all veterinarians Oball veterinarians treating large animals e all veterinarians in the United States treating large animals, including horses d. All of the answer options are correct.
The population of interest in this case is (d) All of the answer options are correct. It includes all veterinarians, all veterinarians treating large animals, and all veterinarians in the United States treating large animals, including horses.
The population of interest in this study is defined as all veterinarians in the United States who treat large animals, including horses. This population includes all individuals who fit this criteria, regardless of their location or any other specific characteristics.
The researchers wanted to gather information about the prevalence of using nonsteroidal anti-inflammatory drugs (NSAIDs) for treating lameness in horses among veterinarians in the United States. To do this, they obtained a list of all veterinarians who treat large animals, including horses, and sent questionnaires to each of them.
The response rate refers to the percentage of veterinarians who completed and returned the questionnaires out of the total number of questionnaires sent. In this case, the response rate was 40%, meaning that 40% of the veterinarians who received the questionnaires responded to them.
By surveying a representative sample of veterinarians, the researchers can gather information and make inferences about the larger population of veterinarians in the United States who treat large animals, including horses. The data collected from the survey can provide insights into the widespread use of NSAIDs for treating lameness in horses and contribute to the overall understanding of veterinary practices in this context.
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Solve X
[tex] {16}^{ \frac{1}{5} } \times {2}^{x} = {8}^{ \frac{3}{4} } [/tex]
I got X= 9/10
am I right?
16^1/5 = 2^4/5 .. & .. 8^3/4 = 2^9/4
____________
2^4/5 × 2^x = 2^9/4
2^16/20 × 2^x = 2^45/20
2^[ ( 16/20 ) + x ] = 2^45/20
16/20 + x = 45/20
x = 45/20 - 16/20
x = 29/20
Im not sure how to do this can someone please help me only answer if you know
Answer:
57%
Step-by-step explanation:
FORMULA:LESS/TOTAL × 100%
=52/92 × 100%
=56.52 %
ROUND OFF TO NEAREST WHOLE NUMBER
56.52%=57%
(because the 5 after the (.) is near 1)
when comparing the f(x) = x2 2x and g(x) = log(2x 1), on which interval are both functions negative? (–[infinity], –2) (–2, 0) (–1, 1) (–[infinity], [infinity])
To find out on which interval are both functions f(x) = x^2 + 2x and g(x) = log (2x + 1) negative, we need to analyze the intervals of negative values of both functions.
We can plot their graphs to have a better understanding:
Graphs of f(x) = x² + 2x and g(x) = log(2x + 1)
Now, we need to observe the intervals where both functions lie below the x-axis: The function f(x) = x^2 + 2x is below the x-axis on the interval (-∞, -2).
The function g(x) = log(2x + 1) is below the x-axis on the interval (-1/2, 0).
Therefore, the interval on which both functions are negative is (-2, 0).Thus, the correct option is (–2, 0).
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PLEASE HELP HARD FOR ME BUT EASY FOR OTHERS
The curb weight of a new car is 3,347 pounds. How much does the car weigh?
Answer: 3,347 pounds
Step-by-step explanation:
Curb weight is simply the weight of a car with no passengers, cargo, or anyting other than the standard base model options.
Basically it's the weight of a base model car sitting on the dealership lot. Curb weight would be different if ANYTHING is added to the base model car such as a passenger, any cargo, or any upgrades aftermarket or otherwise.
Answer:
Not sure if this the correct type of way your looking but its between 1 and 2 tons which is 1000
Step-by-step explanation:
I think...
PLSSS HELP IF YOU KNOW THISS:))
Find the area of the shaded sector.
write a quadratic function with leading coefficient 1 that has roots ofp.
A quadratic function with leading coefficient 1 and roots of p can be expressed as f(x) = (x - p)(x - p), which simplifies to f(x) = x^2 - 2px + p^2.
To construct a quadratic function with leading coefficient 1 and roots of p, we utilize the relationship between the roots and the factors of a quadratic equation. Since p is a root, the factors of the quadratic function would be (x - p) and (x - p). By multiplying these factors together, we obtain the quadratic function f(x) = (x - p)(x - p). Simplifying further, we can expand the expression:
f(x) = (x - p)(x - p) = x^2 - px - px + p^2 = x^2 - 2px + p^2
Hence, the quadratic function with leading coefficient 1 and roots of p is given by f(x) = x^2 - 2px + p^2. This form allows for easy identification of the coefficients and reveals that the constant term of the quadratic is p^2.
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how many yards are in 1 foot?
correct=brainliest
Answer:
0.333333
Step-by-step explanation:
0.333 yards are in one foot
y= 5x - 9; domain = { 1,3,7 }
what is the range values?
Answer:
Step-by-step explanation:
range = [-4,6,26]
Step-by-step explanation:
y = 5x - 9.....domain = [1,3,7]....the domain is ur x values, and I am assuming ur looking for the y values that go with the x ones
y = 5x - 9.....when ur domain (ur x) = 1
y = 5(1) - 9
y = 5 - 9
y = -4
y = 5x - 9...when ur domain (x) = 3
y = 5(3) - 9
y = 15 - 9
y = 6
y = 5x - 9...when ur domain(x) is 7
y = 5(7) - 9
y = 35 - 9
y = 26
so ur range (ur y valus) = [-4,6,26]
Someone help what would my average be if I got 100% on my both of my tests? I just wanna know
Answer:
To figure out your average, you add them together then divide by2
Step-by-step explanation:
Please help !!!!!!!!!
Answer:
5
Step-by-step explanation:
3x -12 = -36
-36 ÷ -3 = 12
-7 + 12 = 5
Answer:
The value of -7 + 3(-12) ÷ (-3) is 5
Step-by-step explanation:
First: -7 + -36 ÷ (-3)
Second: -7 + 12
Third: = 5
Therefore your value of this equation is 5.
your welcome.
e. 15 = 1.5t t=? Solve please
Answer:
E Z
10
Step-by-step explanation:
15 = 1.5t
so t = 15/1.5
= 10
Answer: t = 10
1. Switch sides
- 1.5t = 15
2. Multiply both sides by 10
- 15t = 150
3. Divide both sides by 15
4. Simplify
t = 10
Use the function f=d+1 to find the value of f when d=5.
Answer:
f = 6
Step-by-step explanation:
Plug in what you know then solve:
f = d + 1
f = 5 + 1
f = 6
PLEASE HELP THIS IS MATHHHHH
what inequality??????
f(x) = 9x-7. If f(x)= -7, find x.
Answer: the answer is 56
Step-by-step explanation: since the f(x) is -7 it would be 9 times -7 then minus 7 and get the answer.
Can somebody help me please no links
Answer:
Lololololo9lolo9lkiujyhgdfbhjkifewkjuhgsdvcgfh
Step-by-step explanation:
g(x) = -3x-8g(x)=−3x−8g, left parenthesis, x, right parenthesis, equals, minus, 3, x, minus, 8
g\Big(g(g, left parenthesis
\Big)=10)=10
Answer:
try your best
Step-by-step explanation:
Suppose X is an exponential random variable, show that E(X²) = 2/λ²
The exponential distribution is a continuous probability distribution that is widely used in probability theory and statistics. In probability theory, an exponential random variable is a continuous random variable that represents the waiting time between events in a Poisson process.
Suppose X is an exponential random variable. We have to show that E(X²) = 2/λ². We can show this by using the definition of expectation that is, E(X) = ∫[0,∞] xf(x) dx
where f(x) is the probability density function of X.
Similarly, E(X²) = ∫[0,∞] x²f(x) dx
We know that the probability density function of an exponential distribution with parameter λ is given by f(x) = λe^(-λx)So, E(X²) = ∫[0,∞] x²λe^(-λx) dx
Using integration by parts, we have ∫[0,∞] x²λe^(-λx) dx= [-x²e^(-λx)/λ] + [2xe^(-λx)/λ²] + [(-2/λ³)e^(-λx)]∞ 0= (2/λ²)
E(X²) = 2/λ².
The exponential distribution is a continuous probability distribution that is widely used in probability theory and statistics. In probability theory, an exponential random variable is a continuous random variable that represents the waiting time between events in a Poisson process.
Suppose X is an exponential random variable. We have to show that E(X²) = 2/λ². We can show this by using the definition of expectation that is, E(X) = ∫[0,∞] xf(x) dx
where f(x) is the probability density function of X.
Similarly, E(X²) = ∫[0,∞] x²f(x) dx
We know that the probability density function of an exponential distribution with parameter λ is given by f(x) = λe^(-λx)So, E(X²) = ∫[0,∞] x²λe^(-λx) dx
Using integration by parts, we have ∫[0,∞] x²λe^(-λx) dx= [-x²e^(-λx)/λ] + [2xe^(-λx)/λ²] + [(-2/λ³)e^(-λx)]∞ 0= (2/λ²)Therefore, the main answer to this question is E(X²) = 2/λ².
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