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3 years ago

The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.

2 answers:

5 0

Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1

Ksivusya [100]3 years ago

5 0

Answer:

1, 6, 15, 20, 15, 6, 1

Step-by-step explanation:

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Tommy has 5 jars of marbles. Each jar is 2/3 filled with marbles. If Tommy decided to combine the marbles completely fill the ja

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Answer:

Step-by-step explanation:

to find this answer we will then have to do 5 x 2/3

since we our multiplying by a fraction we will then have to change the fraction to a decimal.

2/3 = 0.6

this will then give us the equation of 5 x 0.6

this will give us the sum of 3 jars that had were able to be filled woth marbles.

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3 years ago

a) Estimate the volume of the solid that lies below the surface z = 7x + 5y2 and above the rectangle R = [0, 2]⨯[0, 4]. Use a Ri

SSSSS [86.1K]

In the $x$ direction we consider the $m=2$ subintervals [0, 1] and [1, 2] (each with length 1), while in the $y$ direction we consider the $n=2$ subintervals [0, 2] and [2, 4] (with length 2). Then the lower right corners of the cells in the partition of $R$ are (1, 0), (2, 0), (1, 2), (2, 2).

Let $f(x,y)=7x+5y^2$ . The volume of the solid is approximately

$\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy\approx f(1,0)\cdot1\cdot2+f(2,0)\cdot1\cdot2+f(1,2)\cdot1\cdot2+f(2,2)\cdot1\cdot2=\boxed{164}$

###

More generally, the lower-right-corner Riemann sum over $m=\mu$ and $n=\nu$ subintervals would be

$\displaystyle\sum_{m=1}^\mu\sum_{n=1}^\nu\left(7\frac{2m}\mu+5\left(\frac{4n-4}\nu\right)^2\right)\frac{2-0}\mu\frac{4-0}\nu=\frac83\left(101+\frac{21}\mu+\frac{40}{\nu^2}-\frac{120}\nu\right)$

Then taking the limits as $\mu\to\infty$ and $\nu\to\infty$ leaves us with an exact volume of $\dfrac{808}3$ .

7 0

3 years ago