Using the Runge-Kutta method of second order, the approximate value of y when x = 0.02 is is 1.0203045100525125.
How to apply the Runge-Kutta method of second order to approximate the value of y when x = 0.02?To apply the Runge-Kutta method of second order to approximate the value of y when x = 0.02, we can follow these steps:
[tex]y' = x^2 + y[/tex]
y(0) = 1
h = 0.01 (step size)
x = 0.02 (desired x-value)
The general formula for the second-order Runge-Kutta method is:
y(i+1) = y(i) + (k1 + k2)/2
where
k1 = h * f(x(i), y(i))
k2 = h * f(x(i) + h, y(i) + k1)
Let's calculate the values step by step:
Set x(0) = 0, y(0) = 1.
k1 = h * f(x(0), y(0))
[tex]= 0.01 * (0^2 + 1)[/tex]
= 0.01
k2 = h * f(x(0) + h, y(0) + k1)
[tex]= 0.01 * ((0 + 0.01)^2 + 1 + 0.01)[/tex]
= 0.01 * (0.0001 + 1.01)
= 0.010101
y(1) = y(0) + (k1 + k2)/2
= 1 + (0.01 + 0.010101)/2
= 1 + 0.020101/2
= 1.0100505
Let's perform the calculations iteratively:
Iteration 1:
x = 0.01
y = 1.0100505 (from Step 4)
Iteration 2:
Now we need to repeat steps 2-4 with the new x and y values:
k1 = h * f(x(1), y(1))
[tex]= 0.01 * (0.01^2 + 1.0100505)[/tex]
= 0.0102010050025
k2 = h * f(x(1) + h, y(1) + k1)
[tex]= 0.01 * ((0.01 + 0.01)^2 + 1.0100505 + 0.0102010050025)[/tex]
= 0.010307015102525
y(2) = y(1) + (k1 + k2)/2
= 1.0100505 + (0.0102010050025 + 0.010307015102525)/2
= 1.0203045100525125
After the second iteration, when x = 0.02,
we obtain y ≈ 1.0203045100525125.
Therefore, the approximate value of y when x = 0.02 using the Runge-Kutta method of second order is 1.0203045100525125.
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[tex]\sqrt15-x +\sqrt3-x=6[/tex]
As currently written, solving for [tex]x[/tex], we have
[tex]\sqrt{15} - x + \sqrt3 - x = 6[/tex]
[tex]2x = \sqrt{15} + \sqrt3 - 6[/tex]
[tex]x = \dfrac{\sqrt{15} +\sqrt3 - 6}2[/tex]
I suspect you meant to write
[tex]\sqrt{15 - x} + \sqrt{3 - x} = 6[/tex]
Move one of the roots to the other side, then take squares on both sides.
[tex]\sqrt{15 - x} = 6 - \sqrt{3 - x}[/tex]
[tex]\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2[/tex]
[tex]15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)[/tex]
[tex]12 \sqrt{3 - x} = 24[/tex]
Take squares again
[tex]\left(12\sqrt{3-x}\right)^2 = 24^2[/tex]
[tex]144 (3 - x) = 576[/tex]
[tex]432 - 144x = 576[/tex]
[tex]144x = -144[/tex]
[tex]\boxed{x = -1}[/tex]
help me w this pls thanks
Answer:
Perimeter: 4+[tex]\pi \\[/tex] mm
Area: [tex]\pi[/tex] mm^2
Step-by-step explanation:
Perimeter:
90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]
Area:
90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]
Answer: 7.14 mm and 3.14 mm²
Step-by-step explanation:
The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.
Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is
[tex]\frac{1}{2} \pi*2=\pi[/tex]
However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is
[tex]2+2=4[/tex]
By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.
The area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.
[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]
Hence, the area is [tex]\pi[/tex], or around 3.14 mm².
Can someone please help me
Answer:-2.4+3.2t
Step-by-step explanation:
-3.6+1.2-1.9t+5.1t
= -2.4+3.2t
PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
The surface area of the composite figure is 524 square meters
Surface area of a figureThe given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:
Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)
Take the sum
Surface area = 2(80+20+64) + 96 + 100
Surface area = 2(164) +196
Surface area = 328 + 196
Surface area = 524 square meters
Hence the surface area of the composite figure is 524 square meters
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Find the interval in which the function is positive.
f(x)=x²-7x + 10
1. (-∞0, 2)
II. (2,5)
III. (5,00)
O I, II
O I, III
O II, III
O II only
Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
General shapeThe leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
Specific shapeThe answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
Which of the following aquatic organisms is classified as a fish?
whale
jellyfish
octopus
shark
I think the octopus is right but i am not sure !
Answer:
Shark
Step-by-step explanation:
They have gills,scales,swim bladders to float,most produce eggs and also in ectothermic.
======================================================
Further explanation:
Whales are not fish. This is a common misconception many people have (the same goes for dolphins as well). Whales are mammals that don't have gills, which is why they occasionally come to the surface for oxygen. Despite "fish" being literally right in their name, jellyfish aren't fish. It's confusing I know. Jellyfish belong to the phylum Cnidaria, while fish belong to the phylum Chordata. Octopus aren't fish either. They are molluscs and are related to animals like snails, squid, and slugs.Sharks are fish. They have gills and fins like any other fish does.Which expressions are equivalent to 2(4f+2g)-
choose three answers
A. 8f+2g
B. 2f(4 + 2g)
C. 8f+4g
D. 4(2f+g)
E. 4f+4f+4g
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using HL Theorem.
Question 2
1) [tex]\overline{PR} \perp \overline{QS}[/tex], [tex]\overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ[/tex] and [tex]\angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ[/tex] and [tex]\triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}[/tex], [tex]\overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD[/tex] and [tex]\triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
A machine manufactuers 300 nails a day. how many did it produce in the month of april 2007
The machine produces 3000 nails in the month of April 2007.
Production of Nails in the Month of April
According to the given information,
Number of nails manufactured per day by the machine, x = 300
And, we know that April is the fourth month of a year which has total 30 days.
Hence, number of days the machine is manufacturing nails in the month of April, y = 30
So, the number of nails that will be produced by the machine in the month of April is given by,
N = Number of nails produced per day × Number of days in April
N = xy
N = 300 × 30
N = 9000
Therefore, the machine produces 9000 nails in the April month of year 2007.
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Which rule describes the translation below? on a coordinate plane, triangle s t u is shifted 3 units down and 5 units to the left to form triangle s prime t prime u prime. (x, y) right-arrow (x minus 5, y minus 3) (x, y) right-arrow (x 5, y 3) (x, y) right-arrow (x minus 3, y minus 5) (x, y) right-arrow (x 3, y 5)
If f(x)=2x-6, which of these is the inverse of f(x)?
○ A. f-¹(x) = 1 +6
X-6
○ B. f-¹(x) = x=6
2
○ C. f-¹(x) = X+6
2
○ D. f¹(x) = -6
Answer:
f-¹(x) = (x + 6)/2
Step-by-step explanation:
Replace f(x) with y.
y = 2x – 6
Interchange x and y.
x = 2y – 6
Solve for y.
y = (x + 6)/2
Replace y with f-¹(x)
f-¹(x) = (x + 6)/2
in this triangle, cosA/cosB =
AB = 4.24
BC= 3
AC = 3
<C 90deg.
Answer:
1
Step-by-step explanation:
[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]
Write the standard form of the equation of the line trough the given point with the given slope.
Step-by-step explanation:
we use the point-slope approach :
y - y1 = m(x - x1)
m is the slope, and (x1, y1) is a point on the line.
so,
1.
y - 2 = 7(x - 1) = 7x - 7
y = 7x - 5
2.
y - -1 = -1×(x - 3) = -x + 3
y + 1 = -x + 3
y = -x + 2
3.
y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)
y = -4x - 3
4.
y - 5 = 5/3 × (x - 3) = 5x/3 - 5
y = 5x/3 or 5/3 × x
Answer:
1. [tex]7x-y=5[/tex]
2. [tex]x+y=2[/tex]
3. [tex]4x+y=-3[/tex]
4. [tex]5x-3y=0[/tex]
Step-by-step explanation:
Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.
[tex]y-k=m(x-h)[/tex]
[tex]y-2=7(x-1)[/tex]
[tex]y-2=7x-7[/tex]
[tex]7x-y=5[/tex]
[tex]y+1=-1(x-3)[/tex]
[tex]y+1=-x+3[/tex]
[tex]x+y=2[/tex]
[tex]y-5=-4(x+2)[/tex]
[tex]y-5=-4x-8[/tex]
[tex]4x+y=-3[/tex]
[tex]y-5=\frac{5}{3} (x-3)[/tex]
[tex]y-5=\frac{5}{3}x-5[/tex]
[tex]3y-15=5x-15[/tex]
[tex]5x-3y=0[/tex]
If f is greater than 0 but less than or equal to 90, and cos(22f-1)=sin(7f+4), what is the value of f?
The value of f from the given expression is 3
Sine and cosine functionGiven the expression below
cos(22f-1) = sin(7f+4),
This can also be expressed
cos(22f-1) = cos(90-7f-4)
cos(22f-1) = cos(86-7f)
22f - 1 = 86 - 7f
Collect the like terms
22f+7f = 86 + 1
29f = 87
f = 3
Hence the value of f from the given expression is 3
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Find the missing angle.
The missing angle of the right trapezoid is 126°.
Quadrilaterals
There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. The trapezoid is a quadrilateral that presents at least one set of parallel sides and the sum of the internal angles is 360°. The trapezoid classifications are:
Right trapezoid - it presents two right angles.Isosceles trapezoid - it presents the congruent non-parallel sides.Scalene trapezoid - it is one in which the non-parallel sides are not congruent.From the figure, it is possible to see that the image has two right angles. Thus, you have a right trapezoid.
Therefore, from the sum of internal angles, you can find the missing angle:
u+54+90+90=360
u=360-234
u=126
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Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
[tex] \frac{y}{x} = \frac{1}{ - 3} \\ - 3y = x[/tex]
[tex] - 3(2) = 6 = x[/tex]
( - 6 , 2 ) Option a3 quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Mr.Royal, tysm for the help!
#1
h(t)=-16t²+58t+2h(2.5)
-16(2.5)²+58(2.5)+2-16(6.25)+145+2147-10047ftAfter 2.5s the ball was at 47ft
#2
g(x)=x²-9g(0)
-9g(4)
4²-9=16-9=6g(7)
7²-949-940Range
{-9,6,40}#3
f(-3)=5f(0)=0f(1)=-3am bad at this type of geomtry
pls haIp
x =x=x, equals
^\circ
∘
degrees
Answer:
15
Step-by-step explanation:
The blue angle and the yellow angle form a linear pair, so they are supplementary (angle measures add up to 180).
180 - 165 = 15
PLEASE HELP HURRYYYYY
Answer:
See below
Step-by-step explanation:
Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear
Determine the perimeter of the figure.
Answer: 2x + 6y + 22 units
Step-by-step explanation:
The perimeter of a figure is the total length of all the sides of a figure.
Therefore, the perimeter can be found by adding up all the lengths of the figure.
Suppose that P is the perimeter of this figure, then
[tex]P = x+4+x+4+3y+7+7+3y\\[/tex]
Combining like terms, we get
[tex]P = 2x + 6y + 22[/tex]
Since we do not have any information on what the variables are, this is the perimeter of the figure.
What is the slope of line m? please help
POINTS!!!! PLS HELP LOOK AT PIC
Answer:
first option
Step-by-step explanation:
two solutions means 2 cutting points
A wall is in the shape of a trapezoid. The lengths of the parallel bases are 8 feet and 20 feet. The height of the room is 8 feet. How much paint is needed to cover the wall? 80 ft2 112 ft2 160 ft2 224 ft2
The amount of paint needed to cover the wall is 112 square feet
How to determine the amount of paint?The given parameters are:
Parallel bases = 8 feet and 20 feet
Height = 8 feet
The area is calculated as:
Area = 0.5 * (Sum of parallel bases) * Height
So, we have;
Area = 0.5 * (8 + 20) * 8
Evaluate
Area = 112
Hence, the amount of paint needed to cover the wall is 112 square feet
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area of the ceiling of a room 4 metre high is 48 metre square if the area of four walls of the room is 112 m square calculate the length and breadth of a room.
Answer:
Breadth=8
Length=6
OR
breadth = 6
length=8
Step-by-step explanation:
Area of 4 walls = 2(l+b)h
112=2.4(l+b)
112/8=l+b
14=l+b
l=14-b
Area of base or ceiling=l x b
48=(14-b).b
48=14b-b²
b²-14b+48=0
factorize it and we get
(b-6)(b-8)=0
taking b-6=0
b=6
l=14-6
l=8
Lie is solving the quadratic equation by completing the square. 3x2 18x – 8 = 0 3x2 18x = 8
Answer: The answer is factor 3 out the variable terms
Step-by-step explanation:
Briefly, describe the distribution in context. Recall, categorical variables are summarized by counts and/or percents
Thus, distribution is a function that shows the possible values for a variable and how often they occur and categorical values are summarized by counts and/or percents
In statistics, the distribution is a function that shows the possible values for a variable and how often they occur.
The distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest. Therefore we take a sample. This sample is used to make conclusions about the whole data set.
The categorical variable is a data in which individuals are placed into groups or categories.
One way to summarize categorical data is to simply count (frequency), or tally up, the number of individuals that fall into each category. Another way is to show the percentage of individuals who fall into each category, thereby creating a relative frequency.
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what is the scale factor from ABC to DEF
Answer:
the scale factor from triangle ABC to triangle DEF would be 8
Step-by-step explanation:
the triangle DEF was actually flipped from triangle ABC
1.line AB corresponds to line EF
AB = 6 , and EF = 48
we multiply 6 by "8" to get to 48
2.line BC corresponds to line ED
BC = 6 , and ED = 48
we multiply 6 by "8" to get to 48
3.line AC corresponds to line FD
AC = 6 , and FD = 48
we multiply 4 by "8" to get to 32
I hope this help
How do I solve question 6 through 8?
Solve for me
The equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
How to determine the functions?A quadratic function is represented as:
y = a(x - h)^2 + k
Question #6
The vertex of the graph is
(h, k) = (-1, 2)
So, we have:
y = a(x + 1)^2 + 2
The graph pass through the f(0) = -2
So, we have:
-2 = a(0 + 1)^2 + 2
Evaluate the like terms
a = -4
Substitute a = -4 in y = a(x + 1)^2 + 2
y = -4(x + 1)^2 + 2
Question #7
The vertex of the graph is
(h, k) = (2, 1)
So, we have:
y = a(x - 2)^2 + 1
The graph pass through (1, 3)
So, we have:
3 = a(1 - 2)^2 + 1
Evaluate the like terms
a = 2
Substitute a = 2 in y = a(x - 2)^2 + 1
y = 2(x - 2)^2 + 1
Question #8
The vertex of the graph is
(h, k) = (1, -2)
So, we have:
y = a(x - 1)^2 - 2
The graph pass through (0, -3)
So, we have:
-3 = a(0 - 1)^2 - 2
Evaluate the like terms
a = -1
Substitute a = -1 in y = a(x - 1)^2 - 2
y = -(x - 1)^2 - 2
Hence, the equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
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Am what I’m writing is correct? I put 2+-2=0
The diagram ends at -2
The equation would be 2-4 = -2
Answer:
Step-by-step explanation:
Start on point 2
Ends on point -2
Then:
2 + a = -2
a = -2 - 2
a = -4
then the equation is:
2 + (-4) = 0
2 - 4 = 0
Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). For what percentage of great lakes states would you expect the economic impact from fishing to be between $234.5 and $401.5 (in millions of dollars)? ( Hint use the empirical rule)
The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.
Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.
We have to calculate the percentage of great lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.
Because we have not given the sample size taken so we will use any test.We are using z test.
We know that,
z=X-μ/σ
where μ is population mean and σ is population standard deviation.
We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.
P value between $234.5 and $318:
z=234.5-318/83.5
=-83.5/83.5
=-1
p value of -1 is 0.1587
P value between $318 and $401.5:
z=401.5-318.5/83.5
=83.5/83.5
=1
p value of z=1 is 0.3413
Total p value=0.1587+0.3413
=0.5
Total percentage=0.5*100
=50%
Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.
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