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chubhunter [2.5K]
3 years ago
10

Under the USMCA agreement, exports will increase to both Canada&Mexico

Mathematics
1 answer:
tekilochka [14]3 years ago
7 0

Answer:

exports will increase to both Canada&Mexico

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Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8
Kitty [74]
Substitute z=\ln x, so that

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}

\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)

Then the ODE becomes


x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0
\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0

which has the characteristic equation r^2+1=0 with roots at r=\pm i. This means the characteristic solution for y(z) is

y_C(z)=C_1\cos z+C_2\sin z

and in terms of y(x), this is

y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)

From the given initial conditions, we find

y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1
y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8

so the particular solution to the IVP is

y(x)=\cos(\ln x)+8\sin(\ln x)
4 0
3 years ago
What is the unit rate of $46 for 5 toys
natita [175]
$46 divided by 5 which equals $9.50
8 0
3 years ago
Read 2 more answers
Please help i dont understand thank you
Alenkasestr [34]

Answer:

Part a)

We need to find the equation of a straight line passing through two given points in slope-intercept form

Part b)

The information given; we are given two points where the line passes through; (0, -4) and (-2, 2)

Part c)

We shall first determine the slope of the line using the formula;

change in y/change in x. Next, we determine the value of the y-intercept using the general form of the equation of a straight line in slope-intercept form; y = mx+c

Part d)

The slope of the line is calculated as;

(2--4)/(-2-0) =6/-2 = -3

The equation of the line in slope-intercept form becomes;

y = -3x +c

We use the point (0, -4) to determine the value of c;

-4 = -3(0)+c

c = -4

Part e)

Final solution thus becomes;

y=-3x-4

8 0
3 years ago
Jack likes to go fishing. While waiting for the fishes to bite, he formulates the following model for the process: fishes bite a
gogolik [260]

Answer:

a) 0.122

b) 3.35 × 10⁻⁴

c) 0.1071

Step-by-step explanation:

Here we have the Poisson process given by

P(N(t) = k) = \frac{e^{-\lambda t} (\lambda t)^k }{k!}

Where:

λ = Rate = 4 bites/hour and

t = Length of time that is

Mean = λt

Where k = 6 fishes bites and t = 2 hours we have

P(N(2) = 6) = \frac{e^{-4 \times 2} (4 \times 2)^6 }{6!} = 0.122

b) The probability that he fails to catch any fishes during the first two hours is the probability t that he catches 0 fish as follows

P(N(2) = 0) = \frac{e^{-4 \times 2} (4 \times 2)^0 }{0!} = 3.35 \times 10^{-4}

(c) Here we have

P(N(2) = 6) =  0.122

For 1 fish caught in two times we have first time no fish and second time he caches a fish gives

0.122×(1-0.122) = 0.1071

4 0
3 years ago
Which one?? help please for a grade!! due today
dimulka [17.4K]

Answer:

its 10

Step-by-step explanation:

because all you have to do is add a zero for each place you go

6 0
3 years ago
Read 2 more answers
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