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3 years ago

About how many more people lived in California than in Texas in the year 2013?

Mathematics

1 answer:

EleoNora [17]3 years ago

7 0

Answer:

D - ten million

Step-by-step explanation:

California had a population of 38.26 million in 2013

Texas had a population of 26.48 million in 2013

38.26-26.48 is closest to 10 million

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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

Graph y - 3 = 1/2 (x + 2)

SashulF [63]

Answer:

Step-by-step explanation:

y - 3 = 1/2 (x + 2)

y - 3 = x/2 + 1

y = x/2 + 4

slope: 1/2

y-intercept: (0, 4)

x | y

-8 | 0

0 | 4

4 0

3 years ago

I need help on number 5 ASAP

Alex

Answer:

540°

Step-by-step explanation:

If a triangle (3 sides) has 180 degrees then we can figure out the degrees in a pentagon.

180° + 360° = 540°

How? The "top" part could be seen as a triangle (180 degrees), and we know that a quadrilateral's angles add up to 360 degrees, so when we add them together we get out answer!

6 0

3 years ago

Read 2 more answers

If sound travels 2 miles and 10 seconds how far does sound travel in 2 minutes

AnnZ [28]

Answer:

24 miles

Step-by-step explanation:

2 miles:10 seconds

? miles: 120 seconds

120 divided by 10 =12

12 x 2 =24