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2 years ago

Find cos ⁡ ( 2 ⋅ ∠ A B C ) cos(2⋅∠ABC)

Mathematics

1 answer:

Pavlova-9 [17]2 years ago

3 0

The value of the cosine function is -0.385

<h3>How to determine the measure of the cosine function?</h3>

The figure that completes the question is added as an attachment

From the figure, we have the following sides

AB = √13

AC = 3

BC = 2

The triangle is a right triangle.

The angle B is calculated as:

cos(B) = 2/√13

Evaluate

cos(B) = 0.5547

Take the arccos of both sides

B = 56.31

This means that:

cos(ABC) = cos(56.31)

Multiply ABC by 2.

So, we have:

cos(ABC * 2) = cos(56.31 * 2)

Evaluate the product

cos(ABC * 2) = cos(112.62)

Evaluate the cosine

cos(ABC * 2) = -0.385

Hence, the value of the cosine function is -0.385

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5-(x/3)when x=12<br><br> What’s the answer

notka56 [123]

Answer:

When x is 12<em>, </em> $5-(\frac{x}{3})=1$

Step-by-step explanation:

$5-(\frac{x}{3} )$

Insert the given value of x:

$5-(\frac{12}{3} )$

Simplify the expression. Divide 12 by 3:

$5-4$

Simplify subtraction:

$1$

:Done

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3 years ago

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Kobotan [32]

Answer:

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2 years ago

Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is

olganol [36]

<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25 ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0 [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2) To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25 [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0

4 years ago

Akira and Hideo are twins with different jobs. Akira earns five-eighths of what Hideo earns, but Akira’s expenses are half of Hi

aleksklad [387]

9514 1404 393

Answer:

25%

Step-by-step explanation:

Apparently, we're to assume that anything not spent is saved.

Let Hideo's income be 1. Then Akira's income is 5/8. Akira's expenses are 60% = 3/5 of that value, so ...

Akira's expenses = (3/5)(5/8) = 3/8 . . . . . of Hideo's income

Hideo's expenses are twice this amount, so ...

Hideo's expenses = (2)(3/8) = 3/4 . . . . . of Hideo's income

That means Hideo saves 1 -3/4 = 1/4 = 25/100 = 25% of his income.

Hideo saves 25% of his income.

4 0

3 years ago

Negative 3 xy minus 4 xy

Oksanka [162]

Since -3xy and negative 4xy are like terms, subtract 4xy from -3xy to get -7xy

-7xy is your answer

3 0

4 years ago