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2 years ago

Is the binomial theorem and pascal's formula the same?

1 answer:

3 0

They are closely related. The Binomial Theorem expands (a+b)ⁿ as the sum of a series of terms involving progressive powers of a and b with a coefficient based entirely on the exponent n. Coefficients of consecutive terms in the series are the same as the nth rows of Pascal’s Triangle. This means that the formula used for calculating the coefficients in the Binomial expansion is the same one used to calculate the numbers in the corresponding row of Pascal’s Triangle. The nomenclature ⁿcᵣ for the number of ways of combining r objects out of n objects invokes this formula.

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Which number is the smallest?

Natalka [10]

Answer:

E D C are the answers for the questions

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2 years ago

If sin3X+cos3X=1/2.<br>Find the value of X.

-BARSIC- [3]

Step-by-step explanation:

Solve for xsin3⁡x+cos3⁡x=1" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; box-sizing: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">xsin3x+cos3x=1xsin3⁡x+cos3⁡x=1

sin3⁡x+cos3⁡x=1(sin⁡x+cos⁡x)(sin2⁡x−sin⁡x⋅cos⁡x+cos2⁡x)=1(sin⁡x+cos⁡x)(1−sin⁡x⋅cos⁡x)=1" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; box-sizing: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">sin3x+cos3x=1(sinx+cosx)(sin2x−sinx⋅cosx+cos2x)=1(sinx+cosx)(1−sinx⋅cosx)=1

6 0

2 years ago

Amanda is having new tile installed in her kitchen. TileAll charges a flat fee of $378.00 plus $15.00 per tile. Kitchen Plus cha

myrzilka [38]

Answer:

$C = 495 + 13.05x$

60 tiles.

Step-by-step explanation:

$15.00 per tile plus a flat fee of $378.00 that charges Tile All.

Therefore, for x number of tiles, the total cost of installation will be

C = 378 + 15x ........... (1)

Again, $14.50 per tiles plus a flat fee of $550.00 that charges Kitchen Plus. Amanda has at Kitchen Plus, a 10% discount coupon.

Therefore, for x tiles installation the charges will be

$C = (550 + 14.5x)(1 - \frac{10}{100}) = 495 + 13.05x$ .......... (2) (Answer)

Now, if for x number of tiles both the company charges the same, then

378 + 15x = 495 + 13.05x (From equations (1) and (2)}

⇒ 1.95x = 117

⇒ x = 60 tiles. (Answer)

3 0

2 years ago

given a geomatric progression 2,6,18,54... find the smallest value of n such that the nth term is greater than 100000

stiks02 [169]

Answer:

hello,

Step-by-step explanation:

$u_1=2=2*3^0\\u_2=6=2*3^1\\u_3=18=2*3^2\\u_4=54=2*3^3\\\\....\\u_n=2*3^{n-1}\geq 100000\\\\3^{n-1}\geq 50000\\\\(n-1)*ln(3)\geq ln(50000)\\\\n-1\geq 9,848586...\\\\n\geq 10.848586....\\\\\boxed{n=11}\\$

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2 years ago

Which lines are parallel in the regular pentagonal prism

Pepsi [2]

Answer:

We have rectangle HCDE CD ║ HE.

And the other rectangle is ABCH AB ║ HC...

Step-by-step explanation:

In the given figure notice that:

We have two rectangles in the figure.

Opposite sides of any rectangular face are parallel, because opposite sides of a rectangle are parallel.

We have rectangle HCDE CD ║ HE.

And the other rectangle is ABCH AB ║ HC...

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2 years ago