HELP? What percent of 33 is 99? 30% 33.3% 200% 300%

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

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

ABCD is a parallelogram the ratio of angle A and Angle B of this Parallelogram is 5 ratio 4 find the measure of Angle B.

sergij07 [2.7K]

Answer:

Mhm lemme see bou this one

Step-by-step explanation:

7 0

2 years ago

It costs Charlie's Car Repair Shop $27 to change the oil. The shop charges their costumers $40 for an oil change. What is the pe

frosja888 [35]

Cost Price for oil change =$27
Charge for the customers =$40
Markup cost = Difference between selling price and cost price =$40-$27=$13
To find the percent of markup, divide the markup cost by the cost price and multiply it by 100.
Markup percent = (13/27)*100
=48.15%

3 0

2 years ago