Answer:
y(0.1) = 0.05, y(0.2) = 0.09
what is modified Euler method?Modified Euler's method is a numerical method used to solve ordinary differential equations (ODEs). It is a variation of Euler's method that is more accurate than the original, but still relatively simple to implement. It works by taking a single iteration of the Euler method, then using the midpoint between the current and previous points to calculate the next point in the sequence. This is done in order to reduce the error.
Solution
We have, y(0) = 0
dy/dt = 1 – y
h = 0.1
Using modified Euler's method,
y(0.1) = y(0) + (1/2) h (f(t0, y0) + f(t0 + h, y0 + hf(t0, y0)))
= 0 + (1/2) (0.1) [(1 - 0) + (1 - 0 + 0.1)]
= 0.05
Similarly,
y(0.2) = 0.1 + (1/2) (0.1) [(1 - 0.05) + (1 - 0.1 + 0.1)]
= 0.0975
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Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is the following. (See the figure below for the sample space of this experiment. Enter your probability as a fraction.)
At least 11
The probability that the sum of the pips selected that is at least 11 would be = 1/12.
How to determine the probability of the selected events?To determine the probability of the selected events, the formula for problem should be used which is given below;
Probability = possible outcome/sample space
Possible outcome = at least 11 = (5,6),(6,5),(6,6)
= 3
Sample space = 36
Probability = 3/36 = 1/12
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In a standardized IQ test scores are normally distributed, with a mean score of 100 and a standard deviation of 15 what is the highest score that would still plays a person in the bottom 10% of the scores
The 68-95-99.7 Rule Example
Figure 1 illustrates how to apply the 68-95-99.7 Rule to the distribution of IQ scores. In this example, the population mean is 100 and the standard deviation is 15. Based on the 68-95-99.7 Rule, approximately 68% of the individuals in the population have an IQ between 85 and 115.
Y=2X squared -12 X +20 for quadratic formula
x = (12 ± √(-16)) / 4,The solutions would be complex numbers.
What is the quadratic formula?To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.
The quadratic formula is:
x = (-b ± √\((b^2 - 4ac)\)) / 2a
Plugging in the values for a, b, and c, we get:
x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)
Simplifying the expression inside the square root:
x = (12 ± √\((144 - 160)\)) / 4
x = (12 ± √(-16)) / 4
Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.
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Over which interval does f(t) have positive average rate of change
Answer:
i dont know im just doing this for the points
Answer: {2,4}
Step-by-step explanation: Khan Academy
make e the subject
e-5=2f
Answer:
e-5=2f
take '-5' to the other side where '2f' is
e=2f+5
What percent of 96 is 367
Answer:
96 is what percent of 367? = 26.16
Step-by-step explanation:
Que números multiplicados dan 30 y sumados dan 11
Answer:
5, 6
Step-by-step explanation:
Answer:
Los números son:
6 y 5
Step-by-step explanation:
Planteamiento:
a * b = 30
a + b = 11
Desarrollo:
De la segunda ecuación del planteamiento:
a = 11-b
Sustituyendo esta última ecuación en la primer ecuación del planteamiento:
(11-b)*b = 30
11*b + b*-b = 30
11b - b² - 30 = 0
-b² + 11b - 30 = 0
b = {-11±√((11²)-(4*-1*-30))} / (2*-1)
b = {-11±√(121-120)} /-2
b = {-11±√1} / -2
b = {-11±1} / -2
b₁ = {-11-1} / -2 = -12/-2 = 6
b₂ = {-11+1} / -2 = -10/-2 = 5
Comprobación:
6*5 = 30
6+5 = 11
A single filer had a taxable income of $90,725. Base on table, what is is the tax?
The amount that the taxpayer is owing in taxes is $2,691.05.
We have,
Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.
Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.
The tax payable will equals to:
= 15%*$11,757 + $927.50
= $1,763.55 + $927.50
= $2,691.05
Hence, The amount that the taxpayer is owing in taxes is $2,691.05.
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complete question:
Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?
if which statement must be true abcd
Answer:
A
Step-by-step explanation:
Given (√a)/(√b)=x, squaring both sides to cancel out the square roots gives a/b=x^2 which is equal to A.
Establish the identity.
(sec 0+1)(sec 0-1)= tan 0
Multiply and write the left side expression as the difference of two squares.
- Tan²θ is the left side expression as the difference of two squares in trigonometric ratios.
What do trigonometric ratios represent?
As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. Trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.Review the sine, cosine, tangent, cotangent, secant, and cosecant trigonometric ratios.When calculating unknown distances from known or measured angles in geometric figures, trigonometric functions are used.(sec θ+1)(sec θ-1)= tan² θ
use ( a+ b ) ( a - b) = a² - b²
= 1² - sec²θ { we know that 1 + tan²θ = sec²θ}
= 1 - sec²θ
= - tan²θ
LHS = RHS
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WHAT IS THE SLOPE OF THE LINE
6X + 3Y = 18?
Can anyone actually help me work it out please
3y=6x=18 the equation must look like this y=mx+b where m is the slope in this case it is 2 and b is the y-intercept 18 hope it helps
just divide every term by 3 to isolate y
\(GraceRosalia\)
Answer:
\(6x + 3y = 18 \\ \\ y = - 2x + 6 \\ \\ x = 3\)
HELPPP
PLLS
DUE RN
WILL
GIVE BRAINLIST
X
X
X
X
Answer:
33% of the people preferred onions
can i get brainliest now lol
Elsa, Chang, and Bob have a total of 104 in their wallets. Chang has 3 times what Bob has. Elsa has 6 more than Bob. How much does each have?
Answer:
Bob=19.60
Elsa=25.60
Chang=58.80
Step-by-step explanation:
(E)lsa + (C)hang + (B)ob=104
C=3B
E=B+6
substitute
(B+6)+3B+B=104
5B+6=104
5B=98
5B/5=98/5
B=19.60
E=19.60+6=25.60
C=3(19.60)=58.80
Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so that the coefficient of x2 is 1.
Answer:
The equation is \(x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0\)
Step-by-step explanation:
From the question we are told that
The diameter endpoints is (-8, -3, -10) and (-6, 1, -4)
Generally the equation of a sphere with center coordinates (a, b , c ) and radius r is mathematically represented as
\((x - a )^2 + (y -b )^2 + (z -c)^2 = r^2\)
Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows
\((a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ]\)
\((a, b , c) = [ -7 , -1.5 , -7 ]\)
Now the length of the diameter is evaluated as
\(|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }\)
\(|d| = \sqrt{56 }\)
\(|d| = \sqrt{4 * 14 }\)
\(|d| = 2 \sqrt{ 14 }\)
Now the radius is mathematically represented as
\(r = \frac{|d|}{2}\)
\(r = \frac{ 2 \sqrt{14} }{2}\)
\(r = \sqrt{14}\)
So
\((x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2\)
\((x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14\)
\(x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14\)
\(x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0\)
A worm is at the bottom of a ravine. Every day it climbs up 5 feet, but every night while it is sleeping, it falls back 3 feet. a) How long will it take the worm to crawl up the ravine if it is 20 ft high? b) What if the ravine is 97 feet high?
Answer:
a) 9 days
b) 47 days
Step-by-step explanation:
Given information:
Distance worm climbs each day = 5 ftDistance worm falls back each night = 3 ftPart (a)\(\begin{array}{|c|r|c|r|}\cline{1-4} \sf Day & \sf Height\:{(ft) & \sf Night & \sf Height\:(ft) \\\cline{1-4} 1 & 5 & 1 & 5 - 3 = 2\\\cline{1-4} 2 & 2 + 5 = 7 & 2 & 7 - 3 = 4 \\\cline{1-4} 3 & 4 + 5 = 9 & 3 & 9 - 3 = 6 \\\cline{1-4} 4 & 6 + 5 = 11 & 4 & 11 - 3 = 8 \\\cline{1-4} 5 & 8 + 5 = 13 & 5 & 13 - 3 = 10 \\\cline{1-4} 6 & 10 + 5 = 15 & 6 & 15-3=12\\\cline{1-4} 7 & 12 + 5 = 17 & 7 & 17 - 3 = 14 \\\cline{1-4} 8 & 14 + 5 = 19 & 8 & 19-3=16\\\cline{1-4} 9 & 16 + 5 = 21 &&\\\cline{1-4}\end{array}\)
On the first day the worm climbs 5 ft, but slips back 3 ft during the first night.
On the second day the worm climbs a further 5 ft, so is now at 7 ft, but slips back 3 ft during the second night. Therefore, it starts the third day at a height of 4 ft.
The progression continues this way so that the worm starts the 9th day at a height of 16 ft. As it climbs 5 feet during the day, it will reach the height of 20 ft during the 9th day, and so will climb out of the ravine before it sleeps for the night.
Therefore, it will take 9 days for the worm to crawl up a 20 ft ravine.
This can be modeled as an arithmetic sequence:
\(y=a+(x-1)d\)
where:
y = height of ravinex = number of daysa = initial height after the first dayd = common difference = 2Therefore:
\(\implies y=5+(x-1)2\)
\(\implies y=5+2x-2\)
\(\implies y=3+2x\)
Part (b)To calculate how long it will take the worm to crawl up the ravine if it is 97 ft high, substitute y = 97 into the equation and solve for x:
\(\implies 3+2x=97\)
\(\implies 3+2x-3=97-3\)
\(\implies2x=94\)
\(\implies \dfrac{2x}{2}=\dfrac{94}{2}\)
\(\implies x=47\)
Therefore, it will take 47 days for the worm to crawl up a 97 ft ravine.
428÷31 round answer to the nearest thousandth
428/31
31• 10 + 31• 3= 403
Then
428 - 403= 25
So then
428 = 31• (10+3) + 25
And result
428/31= 13 + 25/31 = 13 + 0.806
428/31= 13.806
simplify 3[(5-2)3+4)
Answer:
39
Step-by-step explanation:
there are 147 third grade students going to the theater. Each row at the theater has ten seats. How many rows of seats will the third grade students fill?
Answer:
157
Step-by-step explanation:
Using the graph determine the coordinates of the zeros of the parabola
Answer:
-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,
find the value
any help
Which parallelogram has an area of 60 units?
¿Como se escribe siete millones setecientos cuarenta mil novecientos treinta y dos?
Drag each equation to the value that makes it true.
The solution of the equations are given below.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equations are b + 6 = 15, 17.5 - b = 12.5, 4.b = 14, 3/2 + b = 5 and 27/b = 3.
Solve the equations one by one.
b + 6 = 15
Solve the equation,
b = 15 - 6
b = 9
17.5 - b = 12.5
Solve the equation,
b = 17.5 - 12.5
b = 5
4.b = 14
Solve the equation,
b = 14/4
b = 7/2
3/2 + b = 5
Solve the equation,
b = 5 - 3/2
b = 7 / 2
27/b = 3
Solve the equation
b = 27/3
b = 9
Equation 17.5 - b = 12.5 gives value 5.
Equations b + 6 = 15 and 27/b = 3 gives value 9.
And equations 4.b = 14 and 4.b = 14 gives value 7/2.
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X+ 4y = 3
3x - 2y = -5
Which is the correct solution to the system?
a) (2, 2)
b) (5,-5)
c) No Solution
d) (-1, 1)
Answer:
The answer is d
Step-by-step explanation:
A test was given to a group of students. The grades and gender are summarized below
A B C Total
Male 3 10 12 25
Female 14 2 13 29
Total 17 12 25 54
If one student is chosen at random from those who took the test,
Find the probability that the student got a 'A' GIVEN they are male.
The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.
To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:
P(A | Male) = P(Male | A) × P(A) / P(Male)
We can find the values of the terms in the formula using the information given in the table:
P(Male) = (25/54) = 0.46 (the proportion of all students who are male)
P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')
P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')
Therefore, plugging these values into the formula:
P(A | Male) = 0.18 × 0.31 / 0.46
P(A | Male) ≈ 0.12
So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.
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model 12 more than 35 on the number line
Few families can survive on a single salary.
Please select the best answer from the choices provided
T
F
Few families can survive on a single salary is true statement
Many families rely on dual incomes to make ends meet, especially in areas with high living costs.
However, there are still many families that rely on a single salary to support themselves.
While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.
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which property of exponents must you apply to the express p 1/2 to derive p as the result
The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.
The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.
The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.
For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.
Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.
So we have derived p as the result using the Power of a Power Property.
In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.
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8m > 67
Which value of m satisfies the inequality?
A.5
B.6
C.8
D.9
Answer:
D
Step-by-step explanation:
A is wrong because 8 x 5 = 40
40 < 67
B is wrong because 8 x 6 = 30
48 < 67
C is wrong because 8 x 8 = 64
64 < 67
D is correct because 72 > 67
Hope this helps!! ♥︎
Out of 250 racers who started the marathon, 222 completed the race, 19 gave up, and 9 were disqualified. What percentage did not complete the marathon