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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Find the equation of the plane with the given description. contains the lines r1(t) = 2, 1, 0 + t, 2t, 4t and r2(t) = 2, 1, 0 +

Genrish500 [490]

The intersection point of the two lines is (2,1,0).
The respective direction vectors are
L1: <1,2,4>
L2: <4,1,15>
Since the normal vector of the required plane is perpendicular to both direction vectors, the normal vector of the plane is obtained by the cross product of L1 and L2.
i j k
1 2 4
4 1 15
=<30-4, 16-15, 1-8>
=<26, 1, -7>

We know that the plane must pass through (2,1,0), the equation of the plane is

26(x-2)+1(y-1)-7(z-0)=0
simplifying,
26x+y-7z=52+1+0=53
or
26x+y-7z=53

Check:
Put points on L1 in the plane
26(t+2)+(2t+1)-7(4t+0)=53 ok
For L2,
26(4t+2)+(t+1)-7(15t+0)=53 ok

8 0

3 years ago

Gordon types 43 3/4 pages in 3 1/2 hours. What is his rate in pages per hour

Olegator [25]

Answer:

His rate is 12 1/2 pages per hour.

Step-by-step explanation:

Given that,

Gordon types 43 3/4 pages in 3 1/2 hours or Gordon types 175/4 pages in 7/2 hours./ We need to find its rate in pages per hour. So,

$R=\dfrac{\dfrac{175}{4}\ \text{pages}}{\dfrac{7}{2}\ \text{hour}}\\\\R=\dfrac{175}{4}\times \dfrac{2}{7}\\\\R=12.5\ \text{pages per hour}\\\\R=12\dfrac{1}{2}\ \text{pages per hour}$