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3 years ago

In the rhombus, what are m angle 1, m angle 2, and m angle 3? The diagram is not drawn to scale.

Mathematics

1 answer:

Rus_ich [418]3 years ago

5 0

Angle 1 = 128
Angle 2 = 64
Angle 3 = 64

If you'd like an explanation, let me know!
Hope this helps!! :)

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Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

3 years ago

Directions: The marketing research department at the Fresno Mall plans to survey teenagers about a newly developed soft drink. E

emmainna [20.7K]

The experiment is the development of a new soft drink

A possible outcome is "Prefer this new drink"
A possible event is "The event that 5 of 10 teenagers prefer this new drink to their favourite drink"
A new survey is about children vaccination

<h3>The experiment</h3>

From the question, we understand that:

The Fresno Mall plans to survey teenagers about a newly developed soft drink

This implies that the experiment is the survey of teenagers for a new soft drink

<h3>A possible outcome</h3>

Also from the question, we have:

The teens will be asked to compare it with their favourite soft drink

In terms of preference, one outcome could be "Prefer this new drink"

<h3>A possible event</h3>

Also from the question, we have:

The teens will be asked to compare it with their favourite soft drink

In terms of preference, one event could be "The event that 5 of 10 teenagers prefer this new drink to their favourite drink"

<h3>A new survey</h3>

Using the question as a guide, a survey could be:

<em>In a survey of 500 randomly selected adults, 68% of the respondents think that the government should require parents to have their children vaccinated.</em>

Here, we have:

Experiment: Children vaccination
Outcome: Outcome that a parent supports parent should have their children vaccinated
Event: Event that 5 of 10 individuals think that the government should require parents to have their children vaccinated

<h3>Importance of probability</h3>

Probabilities, in this scenario are used to determine the proportions of outcomes, events and it is used to make informed decisions