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2 years ago

A scale on a map shows that 2 inches = 25 miles

Mathematics

1 answer:

ycow [4]2 years ago

4 0

4.4 inches because once you add 2 and 2 you 50 then add ten and you get 60

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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

2 years ago

One person can complete a typing project in 6 hours ,and another can complete the same project in 8 hours .How long will it take

Elan Coil [88]

It would take them precisely 7 hours

5 0

2 years ago

I plugged this into photo math, but apparently I have to pay to find out how to get the answer. can you guys help me out?

dimulka [17.4K]

Photo math is charging? We don't need it. We factor the difference of two squares.

$\dfrac{5t^2-500}{t+10} = \dfrac{5(t^2- 100)}{t+10} = \dfrac{5(t-10)(t+10)}{t+10} = 5(t-10) = 5t-50$

Answer: 5t-50

8 0

2 years ago

What’s slope in this graph?

aniked [119]

Answer:

1/2 !

Step-by-step explanation:

Since it's going up, we know its positive, but if you use RISE/RUN, you would go up 1, then over two, from any point. That makes it 1/2! I went up from the y axis to the next point on the line. I hope that makes sense, but the answer is 1/2!

Have a nice day :D

4 0

2 years ago

Please help! Will give brainliest answer

sergiy2304 [10]

You answer is B because supplementary is 180°

3 0

2 years ago

Read 2 more answers