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Lerok [7]
3 years ago
14

In the interval 0º < x < 360°, find the values of x for which tan x= -0.6745

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
7 0
Tan(θ) = 3 tan(θ), 0° ≤ θ ≤ 360°

Solve for θ to the nearest degree.

tan(θ) = 3 tan(θ)

Subtract tan(θ) from both sides:

0 = 2 tan(θ)

Divide by 2 both sides:

tan(θ) = 0

If (x,y) is a point on the terminal ray of θ,

then tan(θ) = y/x = 0, and y = 0.

y = 0 ==> θ = 0°, 180°, or 360° in the interval 0° ≤ θ ≤ 360°.
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Step-by-step explanation:

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A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hot dogs and 13 dozen
kicyunya [14]

Answer:

1 hot dog costs $0.75

1 bratwurst costs $1.35

Step-by-step explanation:

Let x and y be the price per dozen of hot dogs and bratwursts respectively.

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8x + 13y = 282.60

The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of ​$333.00

10x + 15y = 333

and we have the linear system

<em>8x + 13y = 282.60 </em>

<em>10x + 15y = 333 </em>

which can be written in matrix form as

\bf \left(\begin{array}{cc}8&13\\10&15\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}282.60\\333\end{array}\right)

The solution would be given by

\bf \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}8&13\\10&15\end{array}\right)^{-1}\left(\begin{array}{c}282.60\\333\end{array}\right)

We have  

\bf \left(\begin{array}{cc}8&13\\10&15\end{array}\right)^{-1}=\left(\begin{array}{cc}-3/2&13/10\\1&-4/5\end{array}\right)

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\bf \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}-3/2&13/10\\1&-4/5\end{array}\right)\left(\begin{array}{c}282.60\\333\end{array}\right)=\left(\begin{array}{c}9\\ 16.2\end{array}\right)

Now,

if a dozen hot dogs cost $9, 1 hot dog costs 9/12 = $0.75

if a dozen bratwursts cost $16.2, 1 bratwurst costs 16.2/12 = $1.35

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