The expression 2x(3x^2-4x)+3(x^2-4x+6) can be written in the form ax^3 + bx^2 + cx + d.

Mathematics

1 answer:

Xelga [282]3 years ago

8 0

Answer:

$2x(3 {x}^{2} - 4x) + 3( {x}^{2} - 4x + 6) \\ 6 {x}^{3} - 8 {x}^{2} + 3 {x}^{2} - 12x + 18 \\ 6 {x}^{3} - 5 {x}^{2} - 12x + 18$

$a = 6 \\ b = -5 \\ c =- 12 \\ d = 18$

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On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angl

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In this problem, we can imagine that all the points connect to form a triangle. The three point or vertices are located on the pitcher mount, the home plate and where the outfielder catches the ball. So in this case we are given two sides of the triangle and the angle in between the two sides.

<span>With the following conditions, we can use the cosine law to solve for the unknown 3rd side. The formula is:</span>

c^2 = a^2 + b^2 – 2 a b cos θ

Where,

a = 60.5 ft

b = 195 ft

θ = 32°

Substituting the given values:

c^2 = (60.5)^2 + (195)^2 – 2 (60.5) (195) cos 32

c^2 = 3660.25 + 38025 – 20009.7

c^2 = 21,675.56

c = 147.23 ft

<span>Therefore the outfielder throws the ball at a distance of 147.23 ft towards the home plate.</span>