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dimulka [17.4K]
2 years ago
7

If zn = z√, what value of n makes this equation true?

Mathematics
2 answers:
GarryVolchara [31]2 years ago
4 0

Answer:

zn\:=\:z\sqrt{n^2}

Step-by-step explanation:

zn = z√?

√? = \frac{zn}{z}

√? = n

? = n²

Therefore z√n² makes the statement zn true

elena55 [62]2 years ago
3 0

Solution:

<u>Note that:</u>

  • Given equation: zn = z√x (x = unknown value)

<u>Simplify the equation and solve for the variable n.</u>

  • zn = z√x
  • z(n) = z(√x)
  • => n = √x

The <u>value of n</u> to make the equation <u>(zn = z√x {x = unknown value})</u> true is √x.

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A sequence is defined by f(0) = -20, f(n) = f(n-1) - 5 forn &gt; 1.
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1. Proved down

2. proved down

3. f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5

Step-by-step explanation:

Let us explain how to solve the question

∵ f(0) = -20, f(n) = f(n - 1) - 5 for n > 1

→ That means we have an arithmetic sequence with constant

   difference -5 and first term -20

1. → f(1) means we need to find the second term, which equal the

      term - 5

∵ f(1) means n = 1

∴ f(1) = f(1 - 1) - 5

∴ f(1) = f(0) - 5

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∴ f(1) = -20 - 5 → Proved

2. → f(3) means we need to find the third term, which equal the

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∵ f(3) means n = 3

∴ f(3) = f(3 - 1) - 5

∴ f(3) = f(2) - 5

→ f(2) = f(1) - 5

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∴ f(3) = [-20 - 5 - 5] - 5

∴ f(3) = -20 - 5 - 5 - 5 → Proved

3. → From 1 and 2 we notice that the number of -5 is equal to n,

      at n = 1 there is one (-5), when n= 3 there are three (-5)

∵ n = 10

∴ There are ten (-5)

∴ f(10) = -20 - 5(10)

∴ f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 → Proved

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