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3 years ago

What is the solution of x + 1/5 (x - 1) = 1?

Mathematics

1 answer:

Tanzania [10]3 years ago

3 0

Answer:

Step-by-step explanation:

x-1+ 1 /5*( x-1)=0

(x-1)*6/5=0

x=1

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

4 years ago

Average of 2721 2557 2999 2278 4339

victus00 [196]

Answer:

Step-by-step explanation:

So we know that the average of numbers is all of the numbers added up and divided by the total amount of numbers.

2721

+ 2557

-------------------

5278

.... AND SO ON.........

=14,894 is all of the number added together!!!

Then we count up the numbers= 5

14,894/5

=2978.8

I hope this helps!!!

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4 years ago

Need to use a the table given to find the rate of change in fruit flies per day over the given intervals. Not sure how to use th

Aleksandr [31]

Given a table, with an input (x) and output (y) , you could actually use the slope formula to get the rate of change because slope is the same thing as rate of change. If you recall, the slope formula is (y2-y1)÷(x2-x1)
Just pick two points from the chart and plug them in and that is your rate of change

7 0

3 years ago

18 = 3(3x - 6)<br> Please answer with solving steps thanks!

S_A_V [24]

Answer:

jayfeather friend me

Step-by-step explanation:

(

−

)

−

Add

to both sides of the equation

Simplify

Divide both sides of the equation by the same term

Simplify

Solution

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3 years ago

Find the area and the circumference of a circle with radius 6 m.

Ratling [72]

Answer:

(a) 113.04m²

(b) 37.68m

Step-by-step explanation:

(a)

Area = πr²

=π(6)²

=36π

=113.04m²

(b)

Circumference = 2πr

2π(6) = 12π

=37.68m

6 0

3 years ago

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