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Tju [1.3M]
3 years ago
13

The coefficients in the expansion of (x + y)4

Mathematics
1 answer:
Olenka [21]3 years ago
4 0

Answer:

A

Step-by-step explanation:

Notice:  The literal factors are all the combinations of a and b where the sum of the exponents is 4:  a4,  a3b,  a2b2,  ab3,  b4.

The degree of each term is 4.

The first term is actually a4b0, which is a4 · 1.

Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:

(a + b)5 =  ? a5 +  ? a4b +  ? a3b2 +  ? a2b3 +  ? ab4 +  ? b5

The question is, What are the coefficients?

They are called the binomial coefficients.  In the expansion of

(a + b)4, the binomial coefficients are

1  4  6  4  1

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Determine the sum of the arithmetic series: 5+18 +31 +44 + ... 161.
Finger [1]

Answer:

1079

Step-by-step explanation:

Hello,

18-5 = 13

31-18=13

44-31=13

161=5+13*12

So we need to compute

\displaystyle \sum_{k=0}^{k=12} \ {(5+13k)}\\\\=\sum_{k=0}^{k=12} \ {(5)} + 13\sum_{k=1}^{k=12} \ {(k)}\\\\=13*5+13*\dfrac{12*13}{2}\\\\=65+13*13*6\\\\=65+1014\\\\=1079

Thanks

3 0
3 years ago
Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60
TEA [102]

Answer: the rate at which the distance between the boats is​ increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

6 0
3 years ago
Polygon Q is a scaled copy of Polygon P using a scale factor of 1/2. Polygon 1 point
DiKsa [7]

Answer:

  1/4

Step-by-step explanation:

The scale factor for area is the square of the scale factor for linear dimensions.

  area scale factor = (1/2)² = 1/4

Polygon Q's area is 1/4 of the area of Polygon P.

7 0
3 years ago
HELP!<br> Find the Area of the triangle
Zigmanuir [339]

Answer:

A ≈ 65.8 m²

Step-by-step explanation:

Given 2 sides and the angle between them then the area (A) is

A = \frac{1}{2} bc sinA

   = 0.5 × 19.9 × 10.7 × sin38.17°

   ≈ 65.8 m² ( to 1 dec. place )

6 0
2 years ago
What is <br> (2ab-a+2) - (-ab-2)
Greeley [361]

Step-by-step explanation:

iknow but its hard to expalin

8 0
2 years ago
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