7. let y=f(x) be the solution to the differential equation dy/dx = x-y-1 with the initial condition f(1)=-2. What is the approximation for f(1.4) if Euler's method is used, starting at x=1 with two steps of equal size?
The approximation for f(1.4) using Euler's method with two steps of equal size is -0.632.
Euler's method is a numerical method for approximating the solutions to differential equations. It works by approximating the derivative at each step and using it to estimate the next value of the function.
In this case, we are given the differential equation dy/dx = x-y-1 and the initial condition f(1)=-2. We want to find an approximation for f(1.4) using Euler's method with two steps of equal size, starting at x=1.
To use Euler's method, we first need to determine the step size, which is the distance between x-values at each step. Since we have two steps of equal size, the step size is (1.4-1)/2 = 0.2.
Next, we use the initial condition to find the first approximation:
f(1.2) ≈ f(1) + f'(1)*0.2
= -2 + (1 - (-2) - 1)*0.2
= -1.2
Now, we can use this approximation to find the second approximation:
f(1.4) ≈ f(1.2) + f'(1.2)*0.2
= -1.2 + (1.2 - (-1.2) - 1)*0.2
= -0.632
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HELP ME PLEASE!!!!! FAST ASAP HELP
PICTURE ATTACHED
A company logo is made up of a desire and two identical triangles as shown in this image
What is the area of the logo
The area of the logo is given as 139 cm
How to solve for the areaIn order to get the area of the shape, i would have to get the area of the triangles first
area of a triangle = 1/2 b * h
base = 9 / 2 = 4.5
h = 6
area = 1/2 * 9 * 6
= 27
Area of 2 triangle = 2 x 27
= 58
The are aof the square = a * a
= 9 * 9
= 81
The total area of the logo is given as 81 + 58
= 139 cm
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In linear regression, one variable, called a __________ variable, is related to one or more ____________ variables by a linear equation.
A. dependent; response
B. independent; dependent
C. response; dependent
D. dependent; independent
In linear regression, one variable, called a dependent variable, is related to one or more independent variables by a linear equation.
What is the relation between a function and the dependent and independent variables?A function has the following format: y = f(x).
In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.
That is, the input of the function is the independent variable and the output is the dependent variable.
In the case of multiple inputs, all the inputs are independent variables.
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Can anyone help me with this?
Answer:
a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°
A water tank is emptying at a fixed rate of 5.8 gallons of water per minute. After 5 minutes there are 71 gallons in the tank. Write an equation, in standard form, that represents the amount of water y, in gallons, after x minutes
The equation that represents the amount of water(y) present after x minutes is y = 90 - 5.8x.
What is an equation?An equation is expressing two different form of variables which are actually same.
Given a water tank has an emptying rate of 5.8 gallons of water minute and has 71 gallons after 5 minutes.
∴ In 5 minutes it can drian (5×5.8) gallons of water which is,
= 29 gallons.
So, initially the tank had ( 71 + 29) = 90 gallons of water.
Now, representing amount of water left in 'y' and time in minutes in 'x' the equation can be written as,
y = 90 - 5.8x.
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express in the form n:1
Answer:3/2
Step-by-step explanation:
\(\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}\)
85 points! Sketch the following image on a blank piece of paper and rotate triangle ABC 80 degrees. 1st pic attached: is the triangle and 2nd pic attached is what I drew.... did i do it right?
Answer:
Step-by-step explanation:
It can never be perfect, but what I see, I think yes, because u didn't rotate it 90 degrees since it's not a right triangle, but u did rotate it where it looks close to 90 degrees, so it does look like its 80 degrees as a rotation. Question, does it not say how to rotate it? Like 80 degrees clockwise, or 80 degrees counterclockwise?
Hope this helped!
15x-27=-8+30x
Show your work
Answer: Here below I attached a picture of my work.
Step-by-step explanation:
Mr. Rose randomly selects names to see who will give the first book report. There are 10 boys and 14 girls in his class. What is the probability that Mr. Rose will select a girl’s name?
Answer:
14/24 or 58%
Step-by-step explanation:
when calculating the variance, why must the deviations from the mean be squared? group of answer choices the deviations from the mean must be squared so that their sum is not greater than 100%. the deviations from the mean must be squared so that their sum is not equal to zero. the deviations from the mean must be squared so that their sum is not negative. the deviations from the mean are squared so that their sum is equal to zero.
Deviations from the mean must be squared so that their sum is not equal to zero.
The variance can be calculated using the following formula:
Variance = Sum of squared deviations from the mean / number of observations.
Deviations from the mean are calculated by subtracting the mean from each observation. Deviations can be negative or positive, depending on whether an observation is above or below the mean.
Now, coming back to the question, the reason why deviations from the mean must be squared when calculating variance is that the sum of deviations will always be zero. That means, the sum of negative deviations will cancel out the sum of positive deviations. So, to avoid that, we square each deviation, which makes them all positive. This way, we can avoid the cancellation of negative and positive deviations.
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Please help!!! I really need to get this lesson done
The probability of choosing a green tile and then a blue tile is given as follows:
1/7.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
For each outcome, the probabilities are given as follows:
Green tile: 2/7.Blue tile: 3/6 = 1/2.Hence the probability is given as follows:
2/7 x 1/2 = 1/7.
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This measure of central tendency can be considered the most precise.
a. mode
b. median
c. mean
d. average
This measure of central tendency can be considered the most precise in option c. mean
The mean is a measure of central tendency that calculates the average of a set of values. It is often considered the most precise measure because it takes into account all the values in the dataset and provides a balanced representation.
The mean is calculated by summing all the values and dividing by the total number of values. Unlike the mode, which only identifies the most frequently occurring value, and the median, which represents the middle value, the mean incorporates all the values and provides a comprehensive summary of the dataset.
However, it is important to note that the mean can be sensitive to extreme values or outliers in the data.
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U3U please help me asap U3U
the question is:
How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain.
hate to be that person but what she said
g(a)=3a-2
find g(-9)
help!
The length of one edge of a cube is 7 units. What is the volume of this cube in cubic units? HELPPPPPP JUSTIFY THE ANSWER PLEASEEE
Answer:
Step-by-step explanation:
A cube has an edge length of 5 inches
When I know the side length of a cube, I can find its surface area and express it using appropriate units.
I can write and explain the formula for the surface area of a cube.
The volume of a cube with edge length \(S^{}\) is .\(S^{3}\)
A cube has 6 faces and they are all identical squares. The surface area of a cube with edge length \(S^{}\) is. 6 DIVIDE \(S^{2}\)
Kristen is solving a radical equation and determines that the equation has no solution. Which equation is Kristen attempting to solve? 00= 6x â 2 O14-1 +9= 0 OV= 90 â 1 â 2 O V27 + 6x = 2
Kristen is attempting to solve the equation \(0=\sqrt{6x}-x\). Hence, option b. is the correct answer.
A radical equation has no solution if the square root of a negative number is involved in the equation. The left-hand side of equation b, √(6x), is always non-negative. But the right-hand side, -x, can be negative. So, there is no value of x that can satisfy the equation.
In other words, there is no real number x that would make the left-hand side equal to the right-hand side, so equation b has no solution.
Hence, Kristen is attempting to solve equation 0 = √(6x) - x.
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The complete question is -
Kristen is solving a radical equation and determines that the equation has no solution. Which equation is Kristen attempting to solve?
a. \(\sqrt{27+6x} =x\)
b. \(0=\sqrt{6x}-x\)
c. \(\sqrt{4-x}+9=0\)
d. \(\sqrt{\frac{x}{8}} = \sqrt{90-x}\)
pls help if you can asap!!!!
Answer: A
Step-by-step explanation: I would say A because the angle is greater than 90 degrees
Answer:
We have supplementary angles.
76 + 3x + 2 = 180
3x + 78 = 180
3x = 102
x = 34
help pls :) geometry makes me want to " :K eep M yself S afe " :)
Answer:
z = 103
x = 20
Step-by-step explanation:
See photo for steps. You got this… don’t give up. I believe you can do this. Comment if u need me to explain more :)
imagine an island that is 1 square mile. the island has a population of 1950 people. although the island is not perfectly square, the image below can help us imagine the situation. 1
ANSWER:
a. 1950 people per square mile
b. The island's area got smaller
c.
\(\frac{1950\text{ people}}{0.5\text{ square mile}}\)STEP-BY-STEP EXPLANATION:
Population density is the average number of people living per unit area. It is calculated by dividing the total number of population of a geographical unit (in this case it is the island) by the total amount of surface.
a.
Therefore:
\(Density=\frac{1950\text{ people}}{1\text{ square mile}}=1950\text{ people per square miles}\)b.
Since the size of the island is halved without losing any people, we can conclude that the area has become smaller.
Therefore:
The island's area got smaller
c.
Since it is half the area, the new density would be:
\(Density=\frac{1950\text{ people}}{0.5\text{ square mile}}\)A two-inch cube ($2\times2\times2$) of silver weighs 3 pounds and is worth $\$200$. How much is a three-inch cube of silver worth
The three-inch cube would be worth \(9\text{ lb}\times $20/\text{lb} = $180$.\)
Since the cube is made of silver, we know that the ratio of volume to weight is constant, meaning that the density of silver is the same throughout the cube. Therefore, if a two-inch cube of silver weighs 3 pounds, then its volume is \($(2\text{ in})^3=8\text{ in}^3$\) and its density is \(3\text{ lb}/8\text{ in}^3 = 0.375\text{ lb/in}^3$.\)
Now let's consider a three-inch cube. Its volume is \($(3\text{ in})^3=27\text{ in}^3$\), which is 3 times the volume of the two-inch cube. Since the density is the same, the weight of the three-inch cube will be 3 times the weight of the two-inch cube, or \(3\times 3\text{ lb}=9\text{ lb}$.\)
To find the value of the three-inch cube, we need to know the price of silver per pound. Let's assume it's \($$20$\) per pound (this is just an example). Then the three-inch cube would be worth \(9\text{ lb}\times $20/\text{lb} = $180$.\)
In general, the value of the three-inch cube would be proportional to the weight and the price of silver per pound.
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find the equation of the line that goes through the point ( 0 , -3 ) and is perpendicular to the line y= -2/5x + 6
Answer:
y = 5/2 - 3
Step-by-step explanation:
y = - 2/5x + 6
Slope: - 2/5 (slope of the perpendicular line: 5/2)
Point (0, -3)
y - - 3 = 5/2(x -0)
y + 3 = 5/2x
y = 5/2x - 3
4. A safe slope for a ladder is 1 ft of run for every 4 ft of rise. Vincent needs to use a
ladder to reach a window sill that is 22 ft above the ground. How far from the house
should the base of the ladder be?
Answer:
5.5 ft
Step-by-step explanation:
because its 4ft for every 1ft there's a ratio of 1:4 so 22 represents the 4 part of the ratio, hence 22 divided by 4 gives us 5.5 on the base
A toy rocket is launched straight up so that its height, s, in metres, at time t, in seconds, is given by s(t) = -5t² + 30t + 2. Determine a simplified equation for the velocity (IROC) for any value of t using the difference quotient.
The simplified equation for the velocity (IROC) for any value of t using the difference quotient is v(t) = -10t + 30.
The velocity of an object is the rate of change of its position with respect to time. The derivative of the position function gives the velocity function.
To find the velocity function for the given rocket, we need to take the derivative of its position function, which is s(t) = -5t² + 30t + 2.
v(t) = s'(t) = lim(h→0) [s(t+h) - s(t)]/h
Plugging in the values of s(t+h) and s(t), we get:
v(t) = lim(h→0) [(-5(t+h)² + 30(t+h) + 2) - (-5t² + 30t + 2)]/h
Simplifying the expression, we get:
v(t) = lim(h→0) [-10th - 5h² + 30h]/h
v(t) = lim(h→0) [-10t - 5h + 30]
Taking the limit as h approaches 0, we get:
v(t) = -10t + 30
Therefore, the simplified equation for the velocity (IROC) for any value of t using the difference quotient is v(t) = -10t + 30.
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Solve for x.
a. 16
b. 11
c. 6
Taki keeps all of her black and white photos in portfolio folders. She
was recently asked to show the photos at an upcoming exhibit. She
notices as she sorts through the photos that, in each folder, two out of
every five photos are landscapes.
1. If Taki has 70 black and white photos in one of her portfolio folders,
how many of them are landscapes?
There are 28 landscapes.
From the question, we have
In five photos = 2 landscapes.
In 70 photos = 2/5*70
=28 landscapes.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Please I need help the answer please
Answer:-72
Step-by-step explanation:
(6)*(-12)
-72
Answer:
Negative times positive = negative
negative x negative = positive
6 x 12 = 72
6 x -12 = -72
Hope this helps
Step-by-step explanation:
in rectangle QRST , QS = 5x-31 and RT= 2x+11. Find the lengths of the diagonals of QRST
Answer:
11.7
Step-by-step explanation:
I just solved and added them all-
Choose the number that makes the comparison true.
85.04 >
85.9
85.006
85.72
85.051
85.08
Answer:
85.006
hope this helps
have a good day :)
Step-by-step explanation:
Find the value of :
\(5 { }^{2} +2 {}^{5} \)
I need help filling in the missing blanks.
The degree measure of each angle in the triangle are:
m angle l = 18.4
m angle J = 57.6
m angle K = 93
What is the Degree Measure?
The degree measure, also known as an angle measure, is a way to quantify the size of an angle in mathematics. The degree measure of an angle is typically represented by the symbol "degrees" (°) or simply "deg" and it is a unit of measurement.
In a triangle, the degree measure of all angles add up to 180 degrees. Therefore, we can use this property to find the degree measure of each angle in the triangle.
m angle l = (x + 5) deg
m angle J = (4x + 7) deg
m angle K = (7x) deg
So we can use the following equation:
m angle l + m angle J + m angle K = 180
(x + 5) + (4x + 7) + (7x) = 180
12x + 19 = 180
12x = 161
x = 13.4
Hence, the degree measure of each angle in the triangle are:
m angle l = (x + 5) deg = (13.4 + 5) = 18.4
m angle J = (4x + 7) deg = (413.4 + 7) = 57.6
m angle K = (7x) deg = (713.4) = 93
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