Buying a new car can create a financial challenge because car

In Exercises 5-7, find all the exact t-values for which the given statement is true,

bearhunter [10]

Answer: See Below

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

NOTE: You need the Unit Circle to answer these (attached)

5) cos (t) = 1

Where on the Unit Circle does cos = 1?

Answer: at 0π (0°) and all rotations of 2π (360°)

In radians: t = 0π + 2πn

In degrees: t = 0° + 360n

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$6)\quad sin (t) = \dfrac{1}{2}$

Where on the Unit Circle does $sin = \dfrac{1}{2}$

<em>Hint: sin is only positive in Quadrants I and II</em>

$\text{Answer: at}\ \dfrac{\pi}{6}\ (30^o)\ \text{and at}\ \dfrac{5\pi}{6}\ (150^o)\ \text{and all rotations of}\ 2\pi \ (360^o)$

$\text{In radians:}\ t = \dfrac{\pi}{6} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{6} + 2\pi n$

In degrees: t = 30° + 360n and 150° + 360n

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$7)\quad tan (t) = -\sqrt3$

Where on the Unit Circle does $\dfrac{sin}{cos} = \dfrac{-\sqrt3}{1}\ or\ \dfrac{\sqrt3}{-1}\quad \rightarrow \quad (1,-\sqrt3)\ or\ (-1, \sqrt3)$

<em>Hint: sin and cos are only opposite signs in Quadrants II and IV</em>

$\text{Answer: at}\ \dfrac{2\pi}{3}\ (120^o)\ \text{and at}\ \dfrac{5\pi}{3}\ (300^o)\ \text{and all rotations of}\ 2\pi \ (360^o)$

$\text{In radians:}\ t = \dfrac{2\pi}{3} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{3} + 2\pi n$

In degrees: t = 120° + 360n and 300° + 360n

4 0

2 years ago

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperso

serg [7]

Using variable concepts, of dependent and independent variables, it is found that the dependent variable is the amount of sales dollars earned.

<h3>What is the relation between a function and the dependent and independent variables?</h3>

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, <u>x is the independent variable and y is the dependent variable</u>.

That is, the input of the function is the independent variable and the output is the dependent variable.

In this problem, the manager believes that the amount of sales dollars earned is a function of the number of contacts that the salesperson makes, hence:

The number of contacts is the independent variable.

The amount of sales dollars earned is the dependent variable.

More can be learned about dependent and independent variables at brainly.com/question/1429012

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6 0

1 year ago

An island is 3 kilometers due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 13 k

spin [16.1K]

Answer:

The visitor should run 13 km due west from the tent

Step-by-step explanation:

Here we have;

Location of island = 3 km North of point on shoreline

Location of tent = 13 km East of point on shoreline

Running speed of visitor = 8 km/h

Swimming speed = 1 km/h

Distance of island from tent = $\sqrt{3^{2} + 13^{2} } = 13.34 km$

Since, time = distance/speed, it will take 13.34/1 hours or 13.34 hours to swim directly to the island.

However if the visitor first runs to the closest point on the shoreline to the island, then swims across to the island, it will take;

13/8 Hr + 3/1 hr = 37/8 hours or 4.625 hours only.

Therefore, to minimize the time it takes to reach the island, the visitor has to run 13 km west of the tent to first get to the closest point of the shoreline to the island before swimming across to the island.

3 0

2 years ago

Read 2 more answers

What are the solutions to the equation? 4x^3=36x

deff fn [24]

I hope this helps you