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3 years ago

A 6-pound bag of sugar costs $7.98. What is the unit price?

Mathematics

2 answers:

Shtirlitz [24]3 years ago

7 0

Answer:

1.33

Step-by-step explanation:

Akimi4 [234]3 years ago

3 0

Lets start by making a quick equation:

Total cost is y, or 7.98, with the weight being 6 pounds. We are looking for the unit price, which will be our x.

7.98 = 6x

Divide 6 by both sides:

7.98 / 6 = 6x / 6

This gets rid of the 6 on the right, so we are left with:

1.33 = x

So the unit price is $1.33 per pound.

I hope this helps! :)

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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

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

7 0

3 years ago

The original price of a skateboard was $63.99. The owner of the store marked it 15% off. Calculate the discount and sale price.

aleksandr82 [10.1K]

$63.99 *0.85=$54.40 ($54.3915)<span> rounded = Sale Price
$63.99-54.40= </span> $9.60 $9.59 rounded = Discount

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3 years ago

Write 5.9% as a decimal?

Bingel [31]

$5.9\% \to5\frac{9}{10} \%\to\frac{59}{10}\% \to \frac{59}{10}*\frac{1}{100} \to\frac{59}{1.000}\to\boxed{0,059}$

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Solve the system using the substitution method<br> 6x - 2y = -4<br> y= 3x + 2

Anit [1.1K]

Answer:

Step-by-step explanation:

6x - 2y = -4

y= 3x + 2

We see that y = 3x + 2 so we can use that value of Y everytime we see i in the other equation.

6x - 2(3x +2) = -4

Now usually we'd we simply solve for X.

6x - 6x -4 = -4

This clearly does not work as we cannot get rid of X

Therefore, this system of equations has no solution we can find through substitution

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The average temperature at the South Pole is – 45º F. The average temperature on the Equator is 92º F. How much warmer is the av

iVinArrow [24]

Answer:

-45 to 0 = 45

45 + 92 = 137 degrees

It is 137 degrees hotter on the equator

Step-by-step explanation:

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