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

Mathematics

1 answer:

Olenka [21]2 years ago

4 0

Answer:

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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Ms. Mwanted to estimate the height of the Republic Plaza building in downtown Denver. She has an app on

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Answer:

<em>The height of the bullding is 717 ft</em>

Step-by-step explanation:

<u>Right Triangles</u>

The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.

The tangent ratio for an internal angle A is:

$\displaystyle \tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.

The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:

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