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lbvjy [14]
2 years ago
10

Creating and solving formulas for geometric series:mastery test

Mathematics
1 answer:
Levart [38]2 years ago
6 0

Answer:

D. y = 5\cdot \Sigma_{i=0}^{4} \left(\frac{1}{3} \right)^{i}

Step-by-step explanation:

Let be y = \Sigma_{i = 0}^{4} \left[5\cdot \left(\frac{1}{3} \right)^{i}\right]. To find the equivalent expression we must use the following property:

y = c\cdot \Sigma_{i = 0}^{n} p(x) = \Sigma_{i=0}^{n} [c\cdot p(x)] (1)

Based on this fact, we find the following equivalence:

y = 5\cdot \Sigma_{i=0}^{4} \left(\frac{1}{3} \right)^{i}

Hence, the correct answer is D.

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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
What is the slope of the line y = -5 - 3x ?<br> o 3<br> O 5<br> 0 -3<br> 0 -8
nexus9112 [7]

Answer:

we need to see the plane

Step-by-step explanation:

but, its 0 -8

3 0
3 years ago
the formula to convert a temperature C and degrees Celsius to a temperature F in degrees fahrenheit is 1.8C+32=F. Use this equat
Arturiano [62]

Answer:

Step-by-step explanation:

sorry this one isnt an easy one. but your answr should be 1.8

3 0
2 years ago
2. Given: mZABD = rº and mZACB = yo
Ede4ka [16]

Step-by-step explanation:

the angle ABC = 180 - x, as ABD and ABC are complementary angles on top of the bottom line : all angles around a point on one side of a line are always adding up to 180 degrees.

but because we also know that the sum of all angles in a triangle is 180 degrees too, we can say

180 = ACB + ABC + CAB

180 = y + 180 - x + CAB

0 = y - x + CAB

x = y + CAB

x - y = CAB

therefore, the second answer option is correct.

3 0
2 years ago
Hallie is helping put away dishes in the school cafeteria . She is stacking bowls to put into the cupboard. If she has 62 bowls
aliina [53]

The minimum number of Halle will have 15 stacks.

3 0
2 years ago
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