6. Prove the following theorem in Euclidean geometry (Euclid's Proposition III.22). If ABCD is a quadrilateral inscribed in a circle y, then the sum of the measures of the opposite angles is 180°; that is, μ(LABC) + μ(LCDA) = 180° = µ(LBCD) + µ(LDAB).
Euclid's Proposition III.22 states that if ABCD is a quadrilateral inscribed in a circle, then the sum of the measures of the opposite angles is 180°. This can be proved by considering the properties of inscribed angles and arcs.
Let ABCD be a quadrilateral inscribed in a circle with center O. We want to prove that μ(LABC) + μ(LCDA) = 180° and µ(LBCD) + µ(LDAB) = 180°.
First, consider angle LABC. This angle intercepts the arc CD. According to the inscribed angle theorem, the measure of angle LABC is equal to half the measure of the intercepted arc CD. Similarly, angle LCDA intercepts the arc AB, so μ(LCDA) = 1/2 × μ(arc AB).
Since the sum of the measures of the arcs of a circle is 360°, we have μ(arc AB) + μ(arc CD) = 360°. Therefore, 1/2 × μ(arc AB) + 1/2 × μ(arc CD) = 1/2 × 360°, which simplifies to μ(LCDA) + μ(LABC) = 180°.
Similarly, by applying the same reasoning, we can show that μ(LBCD) + μ(LDAB) = 180°.
Hence, we have proved Euclid's Proposition III.22, which states that if ABCD is a quadrilateral inscribed in a circle, then the sum of the measures of the opposite angles is 180°.
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a: b = 1:6
a:c = 3:1
How many times bigger is b than c?
Answer:
18
Step-by-step explanation:
Expressing the ratios in fractional form
[tex]\frac{a}{b}[/tex] = [tex]\frac{1}{6}[/tex] ( cross- multiply )
b = 6a → (1)
and
[tex]\frac{a}{c}[/tex] = [tex]\frac{3}{1}[/tex] ( cross- multiply )
a = 3c ← substitute into (1) , thus
b = 6 × 3c = 18c
Then b is 18 times bigger than c
B is 18 times bigger than C.
Given that,
a: b = 1:6 a:c = 3:1.Based on the above information, the calculation is as follows:
[tex]\frac{a}{b} = \frac{1}{6}[/tex]
And,
[tex]\frac{a}{c} = \frac{3}{1}[/tex]
Now we have to cross multiplied
So it comes 18
Therefore we can conclude that B is 18 times bigger than C.
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PLEASE HELP WILL MARK AS BRAINLIEST
Your savings account has a balance of $125. You add $22 a month to this balance. Which equation shows your balance, b, in m months?
A. b( m) = $125 m + $22
B.m( b) = $125 b + $22
C. m( b) = $125 + $22 b
D.b( m) = $125 + $22 m
Answer:
d
Step-by-step explanation:
you are adding 22 dollars each month and 125 is your starting balance
The equation shows your balance, b, in m months will be b( m) = $125 + $22 m.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that,
Savings account balance = $125
Money added per month = $22
The obtained equation is,
b( m) = $125 + $22 m.
Thus, the equation shows your balance, b, in m months will be b( m) = $125 + $22 m.
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hey can anyone pls asnwer dis!
Answer:
a
Step-by-step explanation:
(3) Suppose we are saving up money in an account with a yearly interest rate of 4% (compounded continuously). We will start with an initial deposit of $30,000
(a) Without any extra deposit, how much money do we expect to have in the account after 5 years?
(b) Now suppose you make constant yearly deposits of $2,000. Write down an IVP that models this problem, find its solution and estimate how much money we will have in the account after 5 years.
(c) Now suppose you are willing to increase the amount you deposit every year, calling this new fixed amount D. What is the smallest value for D be so that in 5 years we will have more than $50,000 in our account?
A)after 5 years without any extra deposit, we expect to have $36,603.86 in the account. B) we will have $79,998.77 in the account after 5 years. C) the smallest value of D to be greater than $50,000 in 5 years would be $3,800.28.
a) The formula to calculate the compound interest is given as:A=P(1+r/n)^(nt)
Here,P = Principal (initial amount) = $30,000r = Yearly Interest Rate = 4% or 0.04n = number of times the interest is compounded per year = ∞t = time (in years) = 5 yearsSo, using the above values, we get:A = 30,000(e)^(0.04×5) = $36,603.86
Thus, after 5 years without any extra deposit, we expect to have $36,603.86 in the account.
b) Now suppose you make constant yearly deposits of $2,000. Write down an IVP that models this problem, find its solution and estimate how much money we will have in the account after 5 years.
The given amount is deposited every year, hence we have:the principal amount, P = $30,000the yearly amount added, a = $2,000Yearly interest rate, r = 4% or 0.04Number of times the interest is compounded per year, n = ∞t = 5 yearsThe general formula is: y = Ce^(kt) + (a/k) (e^(kt) - 1), where y is the total amount in the account, C is the initial amount, k is the interest rate, a is the yearly amount added, and t is the number of years.
The Initial Value Problem (IVP) is:y(0) = 30000Given, y(0) = 30000We can obtain k by differentiating the given function with respect to t to obtain:dy/dt = ky + a, with initial condition y(0) = 30000Differentiating once again gives:d^2y/dt^2 = k(dy/dt) = k(ky+a)Substituting k = 0.04, a = 2000, and y(0) = 30000 we have:y(0) = C = 30000
Using the above differential equations, we obtain:k = 0.04Then,y(t) = Ce^(0.04t) + (2000/0.04) (e^(0.04t) - 1)y(t) = 30000e^(0.04t) + 50000.00 (e^(0.04t) - 1)After 5 years, y(5) = 30000e^(0.04×5) + 50000.00 (e^(0.04×5) - 1)y(5) = $79,998.77
Thus, we will have $79,998.77 in the account after 5 years.
c) Now suppose you are willing to increase the amount you deposit every year, calling this new fixed amount D.
Let the yearly amount be D. The principal amount is P = $30,000. Yearly interest rate, r = 4% or 0.04. Number of times the interest is compounded per year, n = ∞ and t = 5 years.
So, we can use the formula y = P(e)^(rt) + D[(e)^(rt) - 1]/rto calculate the future value with yearly deposits of D dollars. We want the future value to be greater than $50,000.
Therefore, the equation we need to solve is:30,000e^(0.04×5) + D[(e)^(0.04×5) - 1]/0.04 > 50,000Solving the above equation, we get:D > 3,800.28
Therefore, the smallest value of D to be greater than $50,000 in 5 years would be $3,800.28.
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2 3 4 5 6 7 8 9 10
TIME REMAINING
07:54
Which of the following best describes the unit price of an 8-ounce bag of walnuts?
It is the number of ounces that can be bought for $1.
It is the price of one ounce.
It is the price per ounce multiplied by 8.
It is 8 divided by the price of the bag.
Answer:
It is the price of one ounce.
Step-by-step explanation:
first of all what's the Time Remaining for?
second of all unit rate when it comes to ounces is how much it cost for 1 ounce
It is the price of one ounce.
Solve equation using inverse operation
4.9 = 0.7t
Answer:
7
Step-by-step explanation:
4.9/0.7=7
5. If f(0,0) = 0 and xy f(x, y) if (x, y) = (0,0), x² + y² prove that (D₁f) (x, y) and (D₂f) (x, y) exist at every point of R², although fis not continuous at (0,0). =
The partial derivatives (D₁f) (x, y) and (D₂f) (x, y) exist at every point of R², despite f not being continuous at (0,0).
The existence of partial derivatives (D₁f) (x, y) and (D₂f) (x, y) at a point (x, y) in R² is determined by the existence of the corresponding directional derivatives. The directional derivative in the direction of the x-axis, (D₁f) (x, y), measures the rate of change of f with respect to x, while the directional derivative in the direction of the y-axis, (D₂f) (x, y), measures the rate of change of f with respect to y.
In this case, f(0,0) is defined as 0, and the expression xy f(x, y) is given as x² + y². Since the given function evaluates to 0 at (0,0), we can conclude that the function is differentiable along the x and y axes, and therefore, the partial derivatives (D₁f) (x, y) and (D₂f) (x, y) exist at every point of R².
However, it is important to note that the existence of partial derivatives does not imply the continuity of the function. In this case, although the partial derivatives exist, the function f is not continuous at (0,0) because the limit of f as (x, y) approaches (0,0) does not exist. Thus, the existence of partial derivatives alone does not guarantee the continuity of the function.
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If a function f is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3, -2), which of the following statements must be true? (a) The graph of f has a point of inflection somewhere between x = -1 and x= 3 (b) f'(-1) = 0 (c) this is wrong (d) The graph of f has a horizontal tangent line at x = 3 (e) The graph of f intersects both axes
If a function f is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3, -2), then the following statements must be true: Option (b) f'(-1) = 0 and Option (d) the graph of f has a horizontal tangent line at x = 3
Explanation: The relative maximum of a function is the highest point in a particular set, and the relative minimum is the lowest point. If a function f is continuous for all x and has a relative maximum at (-1, 4) and a relative minimum at (3, -2), then the following statements must be true. The value of the derivative will be equal to zero at relative maximum and relative minimum points of the function. In other words, f'(-1) = 0 and f'(3) = 0. Thus, the option (b) is correct. The graph of f has a horizontal tangent line at the relative minimum and maximum points of the function. This implies that the graph of f has a horizontal tangent line at x = -1 and x = 3. Therefore, the option (d) is correct. The graph of f may or may not intersect both axes. There is no proof that the function f will intersect both axes. Therefore, option (e) is incorrect. The point of inflection is a point on a curve where the concavity of the function changes. Since the function f has a relative maximum at (-1, 4) and a relative minimum at (3, -2), there is no certainty that the graph of f has a point of inflection between x = -1 and x = 3. As a result, option (a) is incorrect. Thus, the correct options are (b) f'(-1) = 0 and (d) The graph of f has a horizontal tangent line at x = 3.
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What
is the difference between Variance and Standard Deviation?
Give
examples of how they are applied.
Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.
Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.
Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.
To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.
If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.
The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.
These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.
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220 divided by 10^2.
Answer:
Step-by-step explanation:
Please mark Brainliest when able.
The solution to the expression is A = 2.2
Given data ,
Let the expression be represented as A
Now , the value of A is
Let the first number be represented as p
The value of p = 220
Let the second number be represented as q
The value of q = 10²
So, q = 100
So, A = p/q
On simplifying the equation , we get
A = p divided by the value of q
And , A = 220/100
A = 2.2
The simplest form of the value of A = 2.2
Therefore , the value of A is 2.2
Hence , the expression is A = 2.2
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2|x - 3| - 5 = 7
“solve the equation”
Answer:
Combine solutions: x=-3 or x=9
Step-by-step explanation:
Answer:
x = - 3, x = 9
Step-by-step explanation:
Given
2| x - 3 | - 5 = 7 ( add 5 to both sides )
2|x - 3 | = 12 ( divide both sides by 2 )
| x - 3 | = 6
The absolute value function always gives a positive value, however, the expression inside the bars can be positive or negative, that is
x - 3 = 6 or - (x - 3) = 6
Solving both equations
x - 3 = 6 ( add 3 to both sides )
x = 9
or
- (x - 3) = 6
- x + 3 = 6 ( subtract 3 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
As a check
2|9 - 3| - 5 = 2|6| - 5 = 12 - 5 = 7 ← Correct
or
2|- 3 - 3| - 5 = 2|- 6| - 5 = 2 |6| - 5 = 12 - 5 = 7 ← Correct
Thus the solutions are x = - 3, x = 9
PLEASE HELP Use the graph to find domain and range minimum maximum increasing decreasing X intercept Y intercept and find f(6)
Answer:
Answer is long, so Ill put it in the explanation.
Step-by-step explanation:
Domain: -∞ ≤ x ≤ ∞ (x goes infinitely in both directions)
Range: -∞ ≤ y ≤ 1 (infinite number of negative points, or going down, but stops at positive 1 going up)
y intercept: (0,0) (where the function meets the y-axis)
x-intercepts: (0,0) and (4,0) (where the function meets the x-axis)
minimum: -∞ ( doesnt have a lowest point, essentially there isnt one)
maximum: y = 1 (this is the highest point of the function)
f(6) = -3 (this is asking: when x = 6, what does y equal?)
This parabola is decreasing (it opens downwards)
Sylvia has a weekly budget of $24, which she likes to spend on movie tickets and pizza. a. If the price of a movie ticket is $4 each, what is the maximum number of tickets she could buy in a week? b. If the price of a pizza is $12, what is the maximum number of pizzas she could buy in a week? c. What is Sylvia’s opportunity cost of purchasing a pizza?
a. Sylvia can buy a maximum of 6 movie tickets in a week.
b. Sylvia can buy a maximum of 2 pizzas in a week.
c. Sylvia can buy 6 movie tickets with her budget, the opportunity cost of purchasing a pizza is 6 movie tickets.
a. To find the maximum number of movie tickets Sylvia can buy in a week, we need to divide her weekly budget by the price of each ticket.
Number of movie tickets = Weekly budget / Price of a movie ticket
Number of movie tickets = $24 / $4
Number of movie tickets = 6
Sylvia can buy a maximum of 6 movie tickets in a week.
b. To find the maximum number of pizzas Sylvia can buy in a week, we need to divide her weekly budget by the price of each pizza.
Number of pizzas = Weekly budget / Price of a pizza
Number of pizzas = $24 / $12
Number of pizzas = 2
Sylvia can buy a maximum of 2 pizzas in a week.
c. The opportunity cost of purchasing a pizza refers to the value of the next best alternative that Sylvia gives up when choosing to buy a pizza. In this case, since Sylvia has a fixed budget, the opportunity cost of purchasing a pizza would be the number of movie tickets she could have bought instead.
Since Sylvia can buy 6 movie tickets with her budget, the opportunity cost of purchasing a pizza is 6 movie tickets.
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Solve for x . Round to the nearest tenth , if necessary
The value of x in the given right triangle is determined as 1.36.
What is the value of x?The value of x is calculated by applying trig ratios as follows;
The trig ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The value of x is calculated as follows;
tan (23) = opposite side / hypothenuse side
tan (23) = x / 3.2
x = 3.2 x tan (23)
x = 1.36
Thus, the value of x is determined by applying trigonometry ratios.
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-10x+6=-144 ? I have a quiz tomorrow and this is on the review
Answer:
.-10x + 6 = -144-10x = (-144-6)-10x = -150divide -10 both sides.
x = 15Step-by-step explanation:
The negatives are counciled
THERE ARE A NUMBER of students SITTING IN A
circle. They ARE EVENly spaced and the 7th
STUDENT IS SEATED directly ACROSS FROM THE
18th student
How many students are there altogether
Answer:
7x18=x
solve for x , X= 127
answer = there are 127 students all together
hope this helpes
What is 87,200,000 written in scientific notation?
Answer:
8.72 • 10^7
Step-by-step explanation:
The graph of y=-3x+ 4 is:
Answer: x=4/3
Step-by-step explanation:
What is the angular position in radians of the minute hand of a clock at 3:30? Express your answer using three significant figures. θ =__ rad
Answer:
The angular position of the minute hand at 3:30 is 2π radians.
Step-by-step explanation:
In a clock, the minute hand completes one full revolution (360 degrees) in 60 minutes or 2π radians.
At 3:30, the minute hand is at the 6 o'clock position, which corresponds to 180 degrees or π radians.
Since 3:30 is halfway between the 3 and 4 on the clock, the minute hand has moved halfway between the 6 o'clock position and the 12 o'clock position.
Therefore, the angular position of the minute hand at 3:30 is:
θ = π + (1/2) * (2π) = π + π = 2π radians.
Hence, the angular position of the minute hand at 3:30 is 2π radians.
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Two surveys were independently conducted to estimate a population mean, mu. Denote the estimators and their standard errors by X_1 X_2 and sigma X_1 and sigma X_2. Assume that X_1 and X_2 are unbiased. For some alpha and beta, the two estimators can be combined to give a better estimator: X = alpha X_1 + beta X_2. Find the conditions on a and 0 that make the combined estimator X unbiased. What choice of a and alpha minimizes the variance of beta, subject to the condition of unbiasedness?
The choice of a and α that minimizes the variance of β, subject to the condition of unbiasedness, is given by α =
σ(X2)^2/[σ(X1)^2 + σ(X2)^2] and β = σ(X1)^2/[σ(X1)^2 + σ(X2)^2].
The estimators X1 and X2 with their standard errors were used to independently conduct two surveys to estimate a
population mean μ. Denote the estimators and their standard errors by X_1 X_2 and sigma X_1 and sigma X_2.
Assume that X_1 and X_2 are unbiased, and they can be combined to give a better estimator X = αX1 + βX2 for some α
and β.The conditions on α and β that make the combined estimator X unbiased are obtained as follows: Expectation of
X = E(X) = E(αX1 + βX2)E(X) = αE(X1) + βE(X2)Since X1 and X2 are unbiased, E(X1) = μ and E(X2) = μThus, E(X) = αμ + βμ =
μα + μβSolving for α, we have α + β = 1 α = 1 - βThis implies that the unbiased estimator X is given by X = (1 - β)X1 + βX2.
The variance of X can be found as follows: Var(X) = Var[(1 - β)X1 + βX2]Since X1 and X2 are independent, we have
Var(X) = [(1 - β)^2 Var(X1)] + [β^2 Var(X2)]Var(X) = (1 - β)^2 σ(X1)^2 + β^2 σ(X2)^2Since we need to find the values of α and
β that minimize Var(X), we need to differentiate Var(X) with respect to β and equate it to zero. Hence, d[Var(X)]/dβ = 2(1
- β)σ(X1)^2 - 2βσ(X2)^2 = 0On solving for β, we haveβ = σ(X1)^2/[σ(X1)^2 + σ(X2)^2]Thus, α = 1 - β = σ(X2)^2/[σ(X1)^2 +
σ(X2)^2]Therefore, the choice of a and α that minimizes the variance of β, subject to the condition of unbiasedness, is
given by α = σ(X2)^2/[σ(X1)^2 + σ(X2)^2] and β = σ(X1)^2/[σ(X1)^2 + σ(X2)^2].
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Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient. PLs help 25 points!
Answer:
[tex]2\frac{1}{3}[/tex] ÷ 7 = [tex]\frac{1}{3}[/tex]
[tex]\frac{12}{14}[/tex] ÷ [tex]\frac{7}{6}[/tex] = [tex]\frac{36}{49}[/tex]
[tex]\frac{3}{5}[/tex] ÷ 5 = [tex]\frac{3}{25}[/tex]
[tex]\frac{22}{33}[/tex] ÷ [tex]\frac{6}{9}[/tex] = 1
[tex]\frac{1}{12}[/tex] ÷ [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Hope that helps.
PLEASE HELP I DONT WANT TO FAIL EITHER: The weight of four puppies are shown in pounds 9.5 9 3/8 9.125 or 9 3/4 which list shows thses weights form greatest to least?
Answer:9.125, 9 3/8, 9.5, 9 3/4
Step-by-step explanation:
Value of (256)0.16 X (256)0.0
Answer:
0
Step-by-step explanation:
Value of (256)0.16 X (256)0.0 = 0
What do millennials around the world want in a job? A Deloitte survey of millennials on work-life challenges found that millennials are looking for stability in an uncertain world, with 67% of millennials preferring a permanent, full-time job rather than working freelance or as a consultant on a flexible or short-term basis. Suppose you select a sample of 100 millennials. Answer parts (a) through (d).
a. What is the probability that in the sample fewer than 71% prefer a permanent, full-time job? (Round to four decimal places as needed.)
b. What is the probability that in the sample between 61% and 71% prefer a permanent, full-time job? (Round to four decimal places as needed.)
c. What is the probability that in the sample more than 69% prefer a permanent, full-time job? (Round to four decimal places as needed.)
d. If a sample of 400 is taken, how does this change your answers to (a) through (c)? (Round to four decimal places as needed.)
The probability that in the sample fewer than 71% prefer a permanent, full-time job is
The probability that in the sample between 61% and 71% prefer a permanent, full-time job is
The probability that in the sample more than 69% prefer a permanent, full-time job is
The binomial distribution assumes that each sample is independent and the probability of success remains constant throughout the sampling process.
To solve these probability questions, we can use the binomial distribution formula. Let's define the following variables:
p = Probability of preferring a permanent, full-time job = 0.67
n = Sample size = 100
a. To find the probability that fewer than 71% prefer a permanent, full-time job, we need to calculate the cumulative probability from 0% to 70% (0.71):
P(X < 0.71 * 100) = P(X < 71) = Σ (nCr) * p^r * (1-p)^(n-r) for r = 0 to 70
b. To find the probability that between 61% and 71% prefer a permanent, full-time job, we need to calculate the cumulative probability from 60% (0.6) to 70% (0.71):
P(0.6 * 100 ≤ X ≤ 0.71 * 100) = P(60 ≤ X ≤ 71) = Σ (nCr) * p^r * (1-p)^(n-r) for r = 60 to 71
c. To find the probability that more than 69% prefer a permanent, full-time job, we need to calculate the cumulative probability from 70% (0.7) to 100% (1):
P(X > 0.7 * 100) = P(X > 70) = Σ (nCr) * p^r * (1-p)^(n-r) for r = 71 to 100
d. If a sample of 400 is taken, the only change is the value of n. We will use n = 400 to recalculate the probabilities in (a), (b), and (c) using the same formulas.
Note: The binomial distribution assumes that each sample is independent and the probability of success remains constant throughout the sampling process.
Please note that calculating these probabilities requires performing multiple calculations and it would be more suitable to use statistical software or a calculator with binomial distribution capabilities to obtain the precise results.
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A contestant on a game show has 30 points. She answers a quest on correctly to win 15 points. Then she answers a question incorrectly and loses 25 points. What is the contestant's final score?
Answer:
20 points
Step-by-step explanation:
First you add 30 + 15, which equals 45.
Then, you subtract 25 from 45, (45-25) which equals 20
y' = (2 +y)y - x on [0, 1], y(0) =0, h = 0.2 e. y = y sin x on [0, 7],
y (0) = 1, h = 4
For the first equation y' = (2 + y)y - x on [0, 1] with y(0) = 0 and h = 0.2, and the second equation y' = y sin(x) on [0, 7] with y(0) = 1 and h = 4
The given problem consists of two separate differential equations. In the first equation, y' = (2 + y)y - x on the interval [0, 1], with an initial condition of y(0) = 0 and a step size of h = 0.2. In the second equation, y' = y sin(x) on the interval [0, 7], with an initial condition of y(0) = 1 and a step size of h = 4.
For the first equation, we can solve it using numerical methods such as Euler's method or Runge-Kutta methods. By applying Euler's method with the given step size, we can approximate the values of y at different points within the interval [0, 1].
Starting with the initial condition y(0) = 0, we can calculate the values of y at subsequent points using the formula y_i+1 = y_i + h*f(x_i, y_i), where f(x, y) = (2 + y)y - x represents the given differential equation. By repeating this process for each step, we can generate an approximation of the solution y(x) within the specified interval.
For the second equation, y' = y sin(x), we can also use numerical methods such as Euler's method or Runge-Kutta methods. Similarly, by applying Euler's method with the given step size, we can approximate the values of y at different points within the interval [0, 7]. Starting with the initial condition y(0) = 1, we can calculate the values of y at subsequent points using the formula y_i+1 = y_i + h*f(x_i, y_i), where f(x, y) = y sin(x) represents the given differential equation. By repeating this process for each step, we can generate an approximation of the solution y(x) within the specified interval.
In summary, for the first equation y' = (2 + y)y - x on [0, 1] with y(0) = 0 and h = 0.2, and the second equation y' = y sin(x) on [0, 7] with y(0) = 1 and h = 4, we can use numerical methods like Euler's method to approximate the solutions of the differential equations within the respective intervals.
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4.16 X 10 to the 3rd power
Answer:
4,160
Step-by-step explanation:
your welcome
Jorge solves the equation 4 x minus (x + 2) + 6 = 2 (3 x + 8) using the steps below. Step 1: 4 x minus x + 2 + 6 = 6 x + 16 Step 2: 3 x + 8 = 6 x + 16 Step 3: 8 minus 16 = 6 x minus 3 x Step 4: Negative 8 = 3 x Step 5: Negative StartFraction 8 Over 3 EndFraction = x Jorge verifies his solution by substituting Negative StartFraction 8 Over 3 EndFraction into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge's error?
Answer:
Kindly check explanation
Step-by-step explanation:
Give the steps used in solving the equation :
4x - (x + 2) + 6 = 2 ( 3x + 8)
Step 1:
4 x - x + 2 + 6 = 6 x + 16
Step 2:
3 x + 8 = 6 x + 16
Step 3:
8 - 16 = 6x - 3x
Step 4:
- 8 = 3 x
Step 5:
- 8 / 3 = x
Jorge's error was made in STEP 1:
4x - (x + 2) + 6 = 2 ( 3x + 8)
OPENING THE BRACKET SHOULD GIVE :
4x-x-2 +6 = 6x+16 AND NOT 4x - x+2+6 = 6x+ 16
Hence,
4x - x - 2 + 6 = 6x+16
3x + 4 = 6x + 16
4 - 16 = 6x - 3x
- 12 = 3x
-12 / 3 = x
-4 = x
Answer:
Jorge distributed incorrectly.
Step-by-step explanation:
For a 36-gon what is the sum of the exterior angles
Answer: It is 360°
Explanation:
For any polygon the sum of the exterior angles is always 360°
