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3 years ago

What's is the least common multiple of 4&13

Mathematics

2 answers:

marusya05 [52]3 years ago

8 0

The least common multiple of 4 & 13 is 52 :)

Snowcat [4.5K]3 years ago

6 0

It's equal multiple of 4 and 13

LCM = 4*13 = 52

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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

if you have 10 fish and three died in 8 more got put in the fish tank then two died how many fish in the tank now

Juli2301 [7.4K]

you have 10 fish and 3 died (must not have been taking very good care of them ?), but it didnt say that you cleaned them out ...

so you still have 10 fish in the tank

8 more got put in, so 10 + 8 = 18 fish

2 died but you STILL didnt take them out, so you have 18 fish in the tank now.

6 0

3 years ago

B(x) is the function that multiplies the input by 100 and then subtracts 5

Tanzania [10]

Answer:

$B(x) = 100x - 5$

Step-by-step explanation:

Required

Determine the formula of B(x)

B(x) implies that B is a function of x and the input is x

Taking the instructions in the question 1 at a time:

Multiplies the input by 100: $100 * x = 100x$

Subtracts 5 : $100x - 5$

Hence;

$B(x) = 100x - 5$

4 0

3 years ago

What is the sun made of (by mass)?

tresset_1 [31]

B. 70 percent hydrogen, 28 percent helium, 2 percent other elements

4 0

3 years ago

Pls help!!!! Find the center, vertices, foci, and asymptotes of the hyperbola. 9y^2-36x^2=324

ICE Princess25 [194]

Answer:

Center: (0, 0)

Vertices: (0, 6), (0, -6)

Foci: (0, 3√5), (0, -3√5)

Asymptotes: y = 2x, y = -2x

Step-by-step explanation:

7 0

2 years ago