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insens350 [35]
3 years ago
10

Evaluate the exponential expression: (2x)2−3y2=___, if x = 5 and y = 3.

Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

  73

Step-by-step explanation:

Put the values of the variables where the variables are, then do the arithmetic.

  (2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73

___

Or, you can let a calculator or spreadsheet evaluate the function for you.

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15 points<br> I really need help with this and it’s due soon please help me and explain.
PilotLPTM [1.2K]

A square's diagonal has a length equal to √(2) times the length of its sides. So if the side length is <em>x</em>, then the diagonal is such that

√(2) <em>x</em> = 10 cm

→   <em>x</em> = 10/√(2) cm ≈ 7.07 cm

The perimeter of a square is 4 times its side length, so the perimeter is

4 (10/√(2) cm) = 40/√(2) cm ≈ 28.3 cm

which makes 28.4 cm the closest answer.

8 0
2 years ago
Read 2 more answers
9. x + 5y = 0
DedPeter [7]

there are 5 solutions. Or 4

8 0
2 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!!!

5 0
3 years ago
The sequence a1 = 6, an = 3an-1 can also be written as
wariber [46]
The question as presented is incomplete, here is the complete question with the multiple choice:

The sequence a1 = 6, an = 3an − 1 can also be written as:

1) an = 6 ⋅ 3^n
2) an = 6 ⋅ 3^(n + 1) 
3) an = 2 ⋅ 3^n
4) an = 2 ⋅ 3^(n + 1)

The correct choice is option 3) an = 2⋅3^n.

If we look at the initial sequence an = 3⋅an-1, and

a1 = 3⋅a0 = 6
a0 = 6/3
a0 = 2

We can now look at the sequence.

a0 = 2
a1 = 6
a2 = 18
a3 = 54
etc...

A common factor in each of those numbers is 2, so we can rewrite the sequence by factoring out 2.

a0 = 2⋅1
a1 = 2⋅3
a2 = 2⋅9
a3 = 2⋅27

The numbers being multiplied by 2 are all factors of 3. So we can rewrite the sequence again as:

a0 = 2⋅3^0
a1 = 2⋅3^1
a2 = 2⋅3^2
a3 = 2⋅3^3

This sequence can now be rewritten as an = 2⋅3^n.
7 0
3 years ago
2) The two rectangles shown are similar.
Citrus2011 [14]

Answer:

6\ cm

Step-by-step explanation:

First Rectangle:

length(l_1)=24\ cm\\\\Width(b_1)=9\ cm

Second Rectangle:

length(l_2)=16\ cm\\\\Let\ Width=b_2\ cm

Since\ these\ two\ rectangles\ are\ similar\\\\\frac{l_2}{l_1}=\frac{b_2}{b_1}\\\\\frac{16}{24}=\frac{b_2}{9}\\\\16\times 9=24\times b_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cross\ multiplication\\\\b_2=\frac{16\times 9}{24}\\\\b_2=6\ cm

5 0
3 years ago
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