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3 years ago

Fill in the missing term in the geometric sequence. -1, 4, -16, ____, -256

Mathematics

2 answers:

Eva8 [605]3 years ago

8 0

X times -4 is the answer

timofeeve [1]3 years ago

3 0

64, the sequence in this is X*(-4)

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hudson went into a restaurant and bought 8 hamburgers and 4 drinks, costing a total of $52. Levi went into the same restaurant a

katrin [286]

Answer:

The price of each hamburger is $5 and the price of each drink is $3.

Step-by-step explanation:

x --> the price of each hamburger
y --> the price of each drink
8x+4y=52
5x+7y=46
Solve system of equations
The intersection is (3,5)

4 0

3 years ago

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 $x(t)$ :

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

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4 years ago

Nutka1998 [239]

Answer:

Step-by-step explanation:

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3 years ago

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vovangra [49]

Answer:

2x+1

Step-by-step explanation:

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4 years ago

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alexandr1967 [171]

Answer:

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Step-by-step explanation:

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3 years ago