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daser333 [38]
2 years ago
11

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.

We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want. Write a function g g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n n. (Notice that g ( 0 )
Mathematics
1 answer:
kobusy [5.1K]2 years ago
8 0

Answer:

  g(n) = 0.05·2^n

Step-by-step explanation:

The paper with no folds is 0.05 mm thick. Each fold multiplies the thickness by 2, so the function is ...

  g(n) = 0.05·2^n

_____

<em>Comment on paper folding</em>

In practice, where the paper must bend around the fold, it is impossible to fold an ordinary piece of paper 9 times. You may be able to fold a very large, very thin piece of paper that many times.

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Given two vectors a⃗ =4.00i^+7.00j^ and b⃗ =5.00i^−2.00j^ , find the vector product a⃗ ×b⃗ (expressed in unit vectors). what is
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The vector product of \boxed{a \times b =  - 43\hat k} and the magnitude of a \times b is \boxed{43}.

Further explanation:

Given:

Vector a is \vec a = 4.00\hat i + 7.00\hat j.

Vector b is \vec b = 5.00\hat i - 2.00\hat j.

Explanation:

The cross product of a \times b can be obtained as follows,

\begin{aligned}a \times b &= \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k} \\4&7&0\\5&{ - 2}&0 \end{array}}\right|\\&= \hat i\left( {0 - 0} \right) - \hat j\left( {0 - 0} \right) + \hat k\left( { - 9 - 35} \right)\\&= 0\hat i - 0\hat j - 43\hat k\\&= - 43\hat k\\\end{aligned}

The vector can be expressed as follows,

a \times b =  - 43\hat k

The magnitude of a \times bcan be obtained as follows,

\begin{aligned}\left| {a \times b} \right| &= \sqrt {{0^2} + {0^2} + {{\left( { - 43} \right)}^2}}\\&= \sqrt {{{43}^2}}\\&= 43\\\end{aligned}43404

The vector product of \boxed{a \times b =  - 43\hat k} and the magnitude of a \times b is \boxed{43}.

Learn more:

  1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Vectors

Keywords: two vectors, vector product, expressed in unit vectors, magnitude, vector a, vector b, a=4.00i^+7.00j^, b=5.00i^-2.00j^, unit vectors, vector space.

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