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3 years ago

Solve 1/x-1/x-5=1/3x

Mathematics

1 answer:

Arada [10]3 years ago

3 0

9514 1404 393

Answer:

x = -10

Step-by-step explanation:

We assume your equation is ...

$\dfrac{1}{x}-\dfrac{1}{x-5}=\dfrac{1}{3x}$

Subtracting the right side, then expressing with a common denominator gives ...

$\dfrac{3}{3x}-\dfrac{1}{3x}-\dfrac{1}{x-5}=0\\\\\dfrac{2}{3x}-\dfrac{1}{x-5}=0\\\\\dfrac{2(x-5)-3x}{3x(x-5)}=0\\\\\dfrac{-x-10}{3x(x-5)}=0\\\\\boxed{x=-10} \qquad\text{equate the numerator to 0 and add $x$}$

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Suppose that you take 120 mg of an antibiotic every 4 hr. The half-life of the drug is 4 hr (the time it takes for half of the

vodomira [7]

Answer:

The steady state amount of antibiotic in the bloodstream when t --> ∞ is 240 mg.

Step-by-step explanation:

Let the amount of antibiotic in one's bloodstream be given as Aₙ (where n = the number of half lives since the start of usage)

Let's follow the time line of events.

At t = 0 hr, the drug is taken

A₀ = 120 mg

At t = 4 hrs, n = 1, the drug is taken again

A₁ = (0.5×A₀) + 120

A₁ = (0.5×120) + 120 = 180 mg

At t = 8 hrs, n = 2, the drug is taken again,

A₂ = (0.5×A₁) + 120

A₂ = (0.5×180) + 120 = 210 mg

At t = 12 hrs, n = 3, the drug is taken again

A₃ = (0.5×A₂) + 120

A₃ = (0.5×210) + 120 = 225 mg

At this point, it becomes evident that at t = 4n hrs, n = n i.e. n half lives later, the general formula for the amount of the antibiotic in the bloodstream is

Aₙ = 0.5Aₙ₋₁ + 120

where Aₙ₋₁ = The amount of antibiotic in the bloodstream at the time t = 4(n-1) and (n-1) half lives later.

For infinite series, that are increasing in this order, as the value of n --> ∞,

Aₙ = Aₙ₋₁ = K

And our general formula becomes

K = 0.5K + 120

0.5K = 120

K = (120/0.5)

K = 240 mg

Hence, the steady state amount of antibiotic in the bloodstream when t --> ∞ is 240 mg.

Hope this Helps!!!

5 0

3 years ago

A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the

liq [111]

If the number of downloads of the standard version is x, and the high quality is x, 2.1*x+4.1*y=2761 (not 1010 due to that this is multiplied by 2.1 and 4.1, therefore representing the total amount of megabytes) In addition, there are 1010 total downloads, and it's either 2.1 MB or 4.1 MB, so x+y=1010.

We have
2.1x+4.1y=2761
x+y=1010

Multiplying the second equation by -2.1 and adding it to the first equation, we get 2y=2761-1010*2.1=640 and by dividing both sides by 2 we get y=320 downloads of the high quality version

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3 years ago

Mrs. Chip bought 2 sheets and a blanket and paid $41. Mrs. Dale bought a sheet and 4 blankets and paid $80.

Katyanochek1 [597]

Answer:

Sheet = $12
Blanket = $17

Step-by-step explanation:

Let the cost of a sheet be s and cost of a blanket be b

2s + b = 41
s + 4b = 80

From the first equation we get:

b = 41 - 2s

Substitute in the second equation

s + 4*(41 - 2s) = 80
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Then

b = 41- 2*12 = 17

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3 years ago

Write an equation of the line that is perpendicular to 3x - 4y equals 9 + contains (-4, -5)

Inga [223]

Slope-Intercept Form: y = mx+b, with m = slope and b = y-intercept

So perpendicular lines have slopes that are negative reciprocals to each other, but firstly we need to find the slope of the original equation. The easiest method to find it is to convert this standard form into slope-intercept.

Firstly, subtract 3x on both sides of the equation: $-4y=-3x+9$