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Masja [62]
3 years ago
14

To stay properly hydrated a person should drink 32 fluid ounces of water every 60 minutes of exercise how much water should Damr

on drink if you ride his bike for 135 minutes
Mathematics
1 answer:
pychu [463]3 years ago
4 0
Write and solve an equation of ratios, as follows:

32 fl oz              60 min
-----------     =     ------------
      x                  135 min

Then 60x = (32)(135) = 4320, and x = 72 oz.

damron should drink 72 fl. oz. of water if he rides 135 min.
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Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.
Lunna [17]

Answer:

The first three nonzero terms in the Maclaurin series is

\mathbf{ 5e^{-x^2} cos (4x)  }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }

Step-by-step explanation:

GIven that:

f(x) = 5e^{-x^2} cos (4x)

The Maclaurin series of cos x can be expressed as :

\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+...  \ \ \ (1)}

\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0}  \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!}  -\dfrac{x^6}{3!}+... \ \ \  (2)}

From equation(1), substituting x with (4x), Then:

\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}

The first three terms of cos (4x) is:

\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}

\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}

\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}

Multiplying equation (2) with (3); we have :

\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }

\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }

\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }

\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }

Finally , multiplying 5 with \mathtt{ e^{-x^2} cos (4x) } ; we have:

The first three nonzero terms in the Maclaurin series is

\mathbf{ 5e^{-x^2} cos (4x)  }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }

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It is the largest integer of the polynomial pf highest degree that is an exact divisor of each of two or more integers or polyno
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<u>it is the largest integer of the polynomial pf highest degree that is an exact divisor of each of two or more integers or polynomials.</u>

<u>answer</u><u> </u><u>=</u><u> </u><u> </u><u>GCF</u><u>.</u><u>.</u><u>.</u>

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3 years ago
A circle has a circumference of 16'pi' feet. What is the radius of the circle, in feet?
forsale [732]
C=16\pi ft.\\\\C=2\pi r\ (r-radius)\\\\2\pi r=16\pi\ \ \ /:2\pi\\r=8\ (ft.)\\\\Answer:C
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Which expression is equivalent to the following complex fraction?
Mamont248 [21]

i hope this will help :)

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4 years ago
Read 2 more answers
Estimate the product. Choose a method 33 X 76
Serhud [2]
Use the tens.Try 30x80. 76 rounds up to 80 and 33 rounds down to 30.
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