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Alex17521 [72]
3 years ago
6

Does anyone know how to do this

Mathematics
1 answer:
dusya [7]3 years ago
5 0

\dfrac{\mathrm dy}{\mathrm dx}=(y+2)^2\sin\left(\dfrac xe\right)

a. If y=k, then \frac{\mathrm dy}{\mathrm dx}=0, so

0=(k+2)^2\sin\left(\dfrac xe\right)\implies (k+2)^2=0\implies k=-2

b. When x=w, we're told y has a horizontal tangent, which has slope \frac{\mathrm dy}{\mathrm dx}=0. So we have

0=(y+2)^2\sin\left(\dfrac we\right)\implies\sin\left(\dfrac we\right)=0\implies\dfrac we=2n\pi\implies w=2ne\pi

where n is any integer, whose smallest positive value occurs for n=1, giving w=2e\pi.

c. The equation is separable:

\dfrac{\mathrm dy}{(y+2)^2}=\sin\left(\dfrac xe\right)\,\mathrm dx

Integrate both sides to get

-\dfrac1{y+2}=-e\cos\left(\dfrac xe\right)+C

y=-1 when x=0, so we find

-1=-e+C\implies C=e-1

Then the particular solution to the DE is

-\dfrac1{y+2}=-e\cos\left(\dfrac xe\right)+e-1\implies y=\dfrac1{e\left(\cos\left(\frac xe\right)-1\right)+1}-2

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Given right triangle jkl, what is the value of cos(l)? five-thirteenths five-twelfths twelve-thirteenths twelve-fifths
kykrilka [37]

The value of the cosine ratio cos(L) is 5/13

<h3>How to determine the cosine ratio?</h3>

The complete question is added as an attachment


Start by calculating the hypotenuse (h) using

h^2 = 5^2 + 12^2

Evaluate the exponent

h^2 = 25 + 144

Evaluate the sum

h^2 = 169

Evaluate the exponent of both sides

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The cosine ratio is then calculated as:

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3 0
2 years ago
Consider the equations 15x + 9y = 45 and 9x + 8y = 12. Solve the system of equations using elimination. Give your solution to th
True [87]

Answer:

(-5.77, 6.46)

Step-by-step explanation:

15x + 9y = 45 ----------- i

9x + 8y = 12----------------ii

Multiply equation i by 9 the coefficient of x in equ ii

And equation ii by 15 the coefficient of x in equ I

9 x 15x + 9y = 45 ----------- i

15 x 9x + 8y = 12----------------ii

135x+81y = 405

135x+120y= 180

Subtract equation ii from I

135x-135x+81y-(+120y)= 405-180

-39y=225

y = 225/-39 = -5.77

Insert the value of y in equ i

15x + 9y = 45

15x+9(-5.77) = 45

15x-51.92=45

15x = 45+51.92

15x= 96.92

x = 96.92/15= 6.46

(x,y) = (-5.77, 6.46)

x = 6.92/15

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3 years ago
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The answer is 14
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