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3 years ago

Find the value of x. Write your answer in simplest form

Mathematics

1 answer:

Naddika [18.5K]3 years ago

6 0

Answer:

The length of the hypotenuse x = x = 16√3

Step-by-step explanation:

Given

Angle Ф = 60°

To Determine

hypotenuse = x

We know the trigonometric ratio can be defined as

cos Ф = adjacent / hypotenuse

here

Ф = 60°

The side adjacent to 60° = 8√3

Hypotenuse = x

so substituting Ф = 60°, adjacent = 8√3, and hypotenuse = x

cos Ф = adjacent / hypotenuse

cos 60° = 8√3 / x

1/2 = 8√3 / x ∵ cos 60° = 1/2

x = 2 × 8√3

x = 16√3

Therefore, the length of the hypotenuse x = x = 16√3

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Find x: 3/(x-4)(x-7) + 6/(x-7)(x-13) + 15/(x-13)(x-28) - 1/x-28 = -1/20

Novay_Z [31]

The value of x<em> </em>in the polynomial fraction 3/((x-4)•(x-7)) + 6/((x-7)•(x-13)) + 15/((x-13)•(x-28)) - 1/(x-28) = -1/20 is <em>x </em>= 24

<h3>How can the polynomial with fractions be simplified to find<em> </em><em>x</em>?</h3>

The given equation is presented as follows;

$\frac{3}{(x - 4) \cdot (x - 7) } + \frac{6}{(x - 7) \cdot (x - 13) } + +\frac{15}{(x - 13) \cdot (x - 28) } - \frac{1}{(x - 28) } = - \frac{1}{20}$

Factoring the common denominator, we have;

$\frac{3\cdot(x - 13) \cdot(x - 28) + 6 \cdot(x - 4) \cdot(x - 28) + 15 \cdot(x - 4) \cdot(x - 7) - (x - 4) \cdot (x - 7)\cdot(x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}$

Simplifying the numerator of the right hand side using a graphing calculator, we get;

By expanding and collecting, the terms of the numerator gives;

-(x³ - 48•x + 651•x - 2548)

Given that the terms of the numerator have several factors in common, we get;

-(x³ - 48•x + 651•x - 2548) = -(x-7)•(x-28)•(x-13)

Which gives;

$\frac{-(x - 7) \cdot(x - 28)\cdot (x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}$

Which gives;

$\frac{-1}{(x - 4)} + = - \frac{1}{20}$

x - 4 = 20

Therefore;

x = 20 + 4 = 24

Learn more about polynomials with fractions here:

brainly.com/question/12262414

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Answer:

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Step-by-step explanation:

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so,

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so, b = 12 cm

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