For which triangle does the equation 42 +42 = 2 apply?

What is the difference between a theorem and an axion ?

Sliva [168]

Answer:

An axiom is often a statement assumed to be true for the sake of expressing a logical sequence. ... These statements, which are derived from axioms, are called theorems. A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.

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8 0

3 years ago

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If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

As VP for operations at Méndez-Pinero Engineering, you must decide which product design, A or B, has the higher reliability.

slega [8]

Answer:

Check the explanation

Step-by-step explanation:

The overall reliability of the system provided in design A = 89.13 %

Product design B has higher reliability than design A.

Overall reliability of system provided in design B = 89.85 %.

Kindly check the attached image below to see the step by step explanation to the question above.

4 0

4 years ago

Find the lengths, if needed round to the nearest tenth

Elis [28]

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle that is made up of 2 right angle triangle.

To determine y, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

15² = y² + 12²

225 = y² + 144

y² = 225 - 144 = 81

y = √81 = 9

To determine z,

20² = z² + 12²

400 = z² + 144

z² = 400 - 144 = 256

z = √256 = 16

7 0

4 years ago

A sphere has a radius of 6 inches. What is the volume of the sphere in terms of π?

natka813 [3]

The volume of sphere in terms of $\pi$ is 288 $\pi$ cubic inches, if the sphere has a radius of 6 inches.

Step-by-step explanation:

The given is,

A sphere has a radius of 6 inches

Step:1

Formula for volume of sphere is,

$Volume, V =\frac{4}{3}\pi r^{3}$ ...........................(1)

where, r - radius of sphere

From given,

r - 6 inches

Equation (1) becomes,

$= \frac{4}{3}\pi (6)^{3}$

= $\frac{4}{3} \pi(216)$ ( ∵ $6^{3}$ = 6×6×6 =216 )

= $(1.3333)\pi (216)$

( The volume of the sphere in terms of π, So keep the value of $\pi$ )

= 288 $\pi$

= 288 $\pi$ Cubic inches

Volume of sphere, V = 288 $\pi$ Cubic inches

Result:

The volume of sphere in terms of $\pi$ is 288 $\pi$ cubic inches, if the sphere has a radius of 6 inches.

8 0

3 years ago

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