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3 years ago

The figure above is a regular octagon with radii and a apothem drawn what is m<1

Mathematics

1 answer:

Nezavi [6.7K]3 years ago

5 0

<1 looks like a triangle so imma go wit a triangle

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Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago

In your own words make a conjecture about the relation

damaskus [11]

Step-by-step explanation:

The congruent angles of the isocels triangle's opposite sides's are congruent.

3 0

2 years ago

Simple interest I in dollars is calculated using the formula I=prt, where p represents the principal, or amount in dollars tha

Sergeeva-Olga [200]

and we do this one the same way as the other.

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$540\\ P=\textit{original amount deposited}\dotfill & \$4800\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years \end{cases} \\\\\\ 540=(4800)(0.045)t\implies \cfrac{540}{(4800)(0.045)}=t\implies 2.5=t$

8 0

3 years ago

Read 2 more answers

At what interest rate must you invest $4500 to have $7,000 after 6 years, if the interest is compounded quarterly?

labwork [276]

Answer:

The amount is $8358.7 and the interest is $3858.7.

Step-by-step explanation:

Explanation

STEP 1: To find amount we use formula:

A=P(1+rn)n⋅t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

P=$4500 , r=7% , n=2 and t=9 years

After plugging the given information we have

AAAA=4500(1+0.072)2⋅9=4500⋅1.03518=4500⋅1.857489=8358.7

STEP 2: To find interest we use formula A=P+I, since A=8358.7 and P = 4500 we have:

A8358.7II=P+I=4500+I=8358.7−4500=3858.7

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3 years ago

An ice hockey team is considering changing their team name and mascot and would like to measure city support for the change. Whi

Triss [41]

Answer:

Step-by-step explanation:

because there only allowing the first 50 to register that would be a contest

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3 years ago

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