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3 years ago

Determine if Set of Points is a Function

Mathematics

1 answer:

Lemur [1.5K]3 years ago

3 0

Answer:

{(-5, 7), (-4, -9), (–5, – 4), (2, -6)}

Step-by-step explanation:

In a function, no two points can have the same x-coordinates. In other words, all x-coordinates of the points must be different.

{(5, -6), (-1, - 2), (2, –9), (–8, -2)} : All x-coordinates are different: 5, -1, 2, -8. This is a function.

{(-5, 7), (-4, -9), (–5, – 4), (2, -6)} : Two x-coordinates are the same: -5, -5. This is not a function.

{(-4,2), (-2,8), (-1,6), (5,6)} : All x-coordinates are different: -4, -2, -1, 5. This is a function.

{(2,2), (-4,9), (9, -3), (-3, 2)}: All x-coordinates are different: 2, -4, 9, -3. This is a function.

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Washer B can wash 144 loads in 3 days. At this rate, how many loads can Washer B wash in 10 days?

sineoko [7]

The answer is 480 because 144/3 is 48. You multiply 48 and 10 to get 480

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3 years ago

Find the general solution of the differential equation. (use c for the constant of integration.) dr dt = 8et 1 − e2t

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Try this solution:
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3 years ago

The difference of three and the reciprocal of a number is equal to the quotient of 20 and the number. Find the number.

Monica [59]

Equation to find number: $\frac{1}{n}$ - 3 = $\frac{20}{n}$

Number's value: n = $-\frac{19}{3}$

Step-by-step explanation:

Let n be the unknown number.

The reciprocal basically makes the number (n in this case) a fraction. So, that being said, the reciprocal of n would be $\frac{1}{n}$ .

The difference of three and the reciprocal of a number ( $\frac{1}{n}$ ) would be $\frac{1}{n}$ - 3.

The quotient of 20 and the number (n) would be $\frac{20}{n}$ .

So, with this information we've gathered so far, we can come up with an equation to find what the number equals.

Equation: $\frac{1}{n}$ - 3 = $\frac{20}{n}$

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3 years ago

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!!!

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3 years ago

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astraxan [27]

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