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3 years ago

Translate equation into a sentence. 2/5v + 3/4 = 2/3x

Mathematics

1 answer:

tatyana61 [14]3 years ago

8 0

Answer:

Two fifths v plus three fourths equals two thirds x

Step-by-step explanation:

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Lesson: 1.08Given this function: f(x) = 4 cos(TTX) + 1Find the following and be sure to show work for period, maximum, and minim

Ber [7]

The given function is

$f(x)=4\cos \text{(}\pi x)+1$

The general form of the cosine function is

$y=a\cos (bx+c)+d$

a is the amplitude

2pi/b is the period

c is the phase shift

d is the vertical shift

By comparing the two functions

a = 4

b = pi

c = 0

d = 1

Then its period is

$\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}$

The equation of the midline is

$y_{ml}=\frac{y_{\max }+y_{\min }}{2}$

Since the maximum is at the greatest value of cos, which is 1, then

$\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}$

Since the minimum is at the smallest value of cos, which is -1, then

$\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}$

Then substitute them in the equation of the midline

$\begin{gathered} y_{ml}=\frac{5+(-3)}{2} \\ y_{ml}=\frac{2}{2} \\ y_{ml}=1 \end{gathered}$

The answers are:

Period = 2

Equation of the midline is y = 1

Maximum = 5

Minimum = -3

3 0

1 year ago

Solve the equation in the interval 0 to 2pi.

galben [10]

Answer:

You don't need to single out $\cos \theta$ to solve this question.

To solve:

$\begin{aligned}3 \cos 4 \theta & = -2\\\\\cos 4 \theta & = -\dfrac{2}{3}\\\\4 \theta & = \cos^{-1}\left( -\dfrac{2}{3\right)}\\\\\implies 4 \theta & =2.30053... \pm 2 \pi n, -2.30053...\pm 2 \pi n\\\\\theta & =\dfrac{2.30053...}{4} \pm \dfrac{\pi n}{2}, -\dfrac{2.30053...}{4}\pm \dfrac{\pi n}{2}\end{aligned}$