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3 years ago

Which equation has only one solution? A lx-5l=1 B l-6-2xl=8 C l5x+10l=10 D l-6x+3l=0

Mathematics

1 answer:

dem82 [27]3 years ago

5 0

Answer:

D: x = 1/2

Step-by-step explanation:

D is correct. The solution here is the solution of -6x + 3 = 0, which is x = 1/2.

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Please help!!! I'll mark you brainiest and give you as many Points as possible!!!!!

Vlada [557]

Answer:

Option C

Step-by-step explanation:

$f(x) = 40( \frac{1}{4} )^{x}$

5 0

3 years ago

Read 2 more answers

Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

What is the probability of rolling a 4 (four) on the 1st die.... and a 1 (one) on the 2nd die. Yes.. it matters which die is whi

disa [49]

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3 years ago

The table below shows the squares of different numbers:

gogolik [260]

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3 years ago

Patrick paid $275.60 for a canon printer. If he paid a sales tax of 6%, how much did the printer itself cost?

kupik [55]

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3 years ago

Read 2 more answers

Which equation has only one solution? A lx-5l=1 B l-6-2xl=8 C l5x+10l=10 D l-6x+3l=0​

Which equation has only one solution? A lx-5l=1 B l-6-2xl=8 C l5x+10l=10 D l-6x+3l=0