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2 years ago

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Which equation does the graph of the systems of equations solve? two linear functions intersecting at 4, 1 the answers are one f

ourthx + 2 = 2x − 7 one fourthx + 2 = −2x − 7 −one fourthx + 2 = 2x − 7 −one fourthx + 2 = −2x − 7

2 answers:

Airida [17]2 years ago

5 0

-1/4x + 2 = 2x - 7.....this has been broken down...ur system of equations is : y = -1/4x + 2 and y = 2x - 7

-1/4x + 2 = 2x - 7
7 + 2 = 2x + 1/4x
9 = 8/4x + 1/4x
9 = 9/4x
9 * 4/9 = x
4 = x

y = 2x - 7
y = 2(4) - 7
y = 8 - 7
y = 1

solution is : -1/4x + 2 = 2x - 7 <==

Mandarinka [93]2 years ago

4 0

1/4x + 2 = 2x - 7.....this has been broken down...ur system of equations is : y = -1/4x + 2 and y = 2x - 7
-1/4x + 2 = 2x - 77 + 2 = 2x + 1/4x9 = 8/4x + 1/4x9 = 9/4x9 * 4/9 = x4 = x
y = 2x - 7y = 2(4) - 7y = 8 - 7y = 1
solution is : -1/4x + 2 = 2x - 7 letter c

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Let y(t) be the solution to y˙=3te−y satisfying y(0)=3 . (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4

OLEGan [10]

Answer:

$y(0.2)=3$ , $y(0.4)=3.005974448$ , $y(0.6)=3.017852169$ , $y(0.8)=3.035458382$ , and $y(1.0)=3.058523645$

The general solution is $y=\ln \left(\frac{3t^2}{2}+e^3\right)$

The error in the approximations to y(0.2), y(0.6), and y(1):

$|y(0.2)-y_{1}|=0.002982771$

$|y(0.6)-y_{3}|=0.008677796$

$|y(1)-y_{5}|=0.013499859$

Step-by-step explanation:

<em>Point a:</em>

The Euler's method states that:

$y_{n+1}=y_n+h \cdot f \left(t_n, y_n \right)$ where $t_{n+1}=t_n + h$

We have that $h=0.2$ , $t_{0}=0$ , $y_{0} =3$ , $f(t,y)=3te^{-y}$

We need to find $y(0.2)$ for $y'=3te^{-y}$ , when $y(0)=3$ , $h=0.2$ using the Euler's method.

So you need to:

$t_{1}=t_{0}+h=0+0.2=0.2$

$y\left(t_{1}\right)=y\left(0.2)=y_{1}=y_{0}+h \cdot f \left(t_{0}, y_{0} \right)=3+h \cdot f \left(0, 3 \right)=$

$=3 + 0.2 \cdot \left(0 \right)= 3$

$y(0.2)=3$

We need to find $y(0.4)$ for $y'=3te^{-y}$ , when $y(0)=3$ , $h=0.2$ using the Euler's method.

So you need to:

$t_{2}=t_{1}+h=0.2+0.2=0.4$

$y\left(t_{2}\right)=y\left(0.4)=y_{2}=y_{1}+h \cdot f \left(t_{1}, y_{1} \right)=3+h \cdot f \left(0.2, 3 \right)=$

$=3 + 0.2 \cdot \left(0.02987224102)= 3.005974448$

$y(0.4)=3.005974448$

The Euler's Method is detailed in the following table.

<em>Point b:</em>

To find the general solution of $y'=3te^{-y}$ you need to:

Rewrite in the form of a first order separable ODE:

$e^yy'\:=3t\\e^y\cdot \frac{dy}{dt} =3t\\e^y \:dy\:=3t\:dt$

Integrate each side:

$\int \:e^ydy=e^y+C$

$\int \:3t\:dt=\frac{3t^2}{2}+C$

$e^y+C=\frac{3t^2}{2}+C\\e^y=\frac{3t^2}{2}+C_{1}$

We know the initial condition y(0) = 3, we are going to use it to find the value of $C_{1}$

$e^3=\frac{3\left(0\right)^2}{2}+C_1\\C_1=e^3$

So we have:

$e^y=\frac{3t^2}{2}+e^3$

Solving for <em>y</em> we get:

$\ln \left(e^y\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y\ln \left(e\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y=\ln \left(\frac{3t^2}{2}+e^3\right)$

<em>Point c:</em>

To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:

Find the values y(0.2), y(0.6), and y(1) using $y=\ln \left(\frac{3t^2}{2}+e^3\right)$

$y(0.2)=\ln \left(\frac{3(0.2)^2}{2}+e^3\right)=3.002982771$

$y(0.6)=\ln \left(\frac{3(0.6)^2}{2}+e^3\right)=3.026529965$

$y(1)=\ln \left(\frac{3(1)^2}{2}+e^3\right)=3.072023504$

Next, where $y_{1}, y_{3}, \:and \:y_{5}$ are from the table.

$|y(0.2)-y_{1}|=|3.002982771-3|=0.002982771$

$|y(0.6)-y_{3}|=|3.026529965-3.017852169|=0.008677796$

$|y(1)-y_{5}|=|3.072023504-3.058523645|=0.013499859$

3 0

3 years ago

What is least perimeter of a rectangle with an area 32 square feet

Aleks04 [339]

If you have a rectangle with an area of 32 square feet, it means that the sides are
A=L x W, 32= 8*4, where
L=8, W=4
other options are
L=16, W=2 and the last one is
L=32, W=1
You need to find the least perimeter , and you know that the perimeter is P= 2(L+W)
Perimeter (1)= 2(8+4)=2*12=24
Perimeter(2)= 2(16+2)=2*18=36
Perimeter (3)=2(32+1)=2*33=66

The least perimeter is 24, with the sides L=8 and W=4

5 0

3 years ago

Which of the following statements is consistent with the scatterplot?

Snezhnost [94]

I would say the answer is B my good sir

8 0

3 years ago

If f(x)=2x^2+5sqrt(x-2),complete the following statement f(6)=_____

Anon25 [30]

Answer:

f(3)=

Step-by-step explanation:

4 0

3 years ago

Distance between points 3,3 and 5,7?

ohaa [14]

Answer: d = 4√5 or 4.47

Step-by-step explanation:

To find the distance of two-point, we can use the distance formula:

$d=\sqrt{(x_{2} -x_{1} )^2 +(y_{2} -y_{1} )^2}\\\\d=\sqrt{(5 -3 )^2+ (7 -3)^2}\\\\d=\sqrt{(2)^2+ (4)^2}\\\\d=\sqrt{4+16}\\\\d=\sqrt{20}\\\\d = \sqrt{4*5}\\\\\\d = 4\sqrt{5}\\\\\\$ or d ≈ 4.47

7 0

2 years ago