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2 years ago

I need help with both preferably with the Pascal’s Triangle.

Mathematics

2 answers:

soldier1979 [14.2K]2 years ago

8 0

Check the picture below.

as you already know, the first expanded terms start off with a highest exponent, and gradually go down, likewise, the second expanded terms start off with 0 and gradually go to the highest exponent.

the Pascal triangle simply gives us the coefficient both of those expanded terms multiply by.

sdas [7]2 years ago

5 0

Answer:

(x+ 5)⁶ = x⁶ + 30x⁵ + 375x⁴ + 2500x³ + 9375x² + 18 750 + 15 625

(4x + 3)⁵ = 1024x⁵ + 3840x⁴ + 5760x³ + 4320x² + 1620x + 243

Step-by-step explanation:

Pascal's Triangle gives us the coefficients of the terms in the binomial expansion of (x+ y)ⁿ.

1. (x + 5)⁶

The exponent is 6, so we use the coefficients corresponding to that exponent:

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

Treat the 5 as if it were a single term. Then,

(x+ 5)⁶

= 1x⁶ + 6x⁵(5)¹ + 15x⁴(5)² + 20x³(5)³ + 15x²(5)⁴ + 6x¹(5⁵) + (5)⁶

= x⁶ + 30x⁵ + 375x⁴ + 2500x³ + 9375x² + 18 750 + 15 625

2. (4x + 3)⁵

The coefficients are

1, 5, 10, 10, 5, 1.

(4x + 3)⁵

= (4x)⁵ + 5(4x)⁴(3)¹ + 10(4x)³(3)² + 10(4x)²(3)³ + 5(4x)¹(3)⁴ + (3)⁵

= 1024x⁵ + 3840x⁴ + 5760x³ + 4320x² + 1620x + 243

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Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance o

g100num [7]

Answer:

The value is $k =109.6 \ miles$

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

=> $\theta_A = 40.2 ^o$

Also

$\theta_B = 32^o$

and

$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

Also

$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

=> $k =109.6 \ miles$

4 0

2 years ago

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

lara31 [8.8K]

Group first 2 and group last 2 and find factors and undistribute

(4x^3+x^2)+(-8x-2)
(x^2)(4x+1)+(-2)(4x+1)
x^2(4x+1)-2(4x+1)
answer is first one

6 0

2 years ago

Read 2 more answers

What are three collinear points on line l?

Jet001 [13]

Points A, F, and G are three collinear points on line l.

$\boxed{ \ The \ Answer \ is \ B \ }$

<h3>Further explanation </h3>

Let us consider the definition of collinear.

Collinear

Collinear points represent points that lie on a straight line. Any two points are always collinear because we can constantly connect them with a straight line. A collinear relationship can occur from three points or more, but they don’t have to be.

Noncollinear

Noncollinear points represent the points that do not lie in a similar straight line.

Given that lines k, l, and m with points A, B, C, D, F, and G. The logical conclusions that can be taken correctly based on the attached picture are as follows:

At line k, points A and B are collinear.
At line l, points A, F, and G are collinear.
At line m, points B and F are collinear.
Point A is placed at line k and line l.
Point B is placed at line k and line m.
Point F is located at line l and line m.
Points C and D are not located on any line.

Hence, the specific answer to this key question is undoubted, i.e., points A, F, and G.

All points can, also, be said to be coplanar. This is because the three lines intersect with each other and lie on a planar surface.

Coplanar

Coplanar points represent a group of points that lie on the same plane, i.e. a planar surface that extends without end in all directions. Any two or three points are always coplanar, but four or more points might or might not be coplanar.

<h3>Learn more </h3>

Determine which points are coplanar and noncollinear brainly.com/question/4165000
Finding a set of points is not coplanar in a pyramid brainly.com/question/2269323
Determining the best description of connection lines AB and CD on given rectangular prism ABCD brainly.com/question/4910705

Keywords: what are, three collinear points A, F, and G, noncollinear, located, similar straight line, definition, represents, relationship, coplanar