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I am Lyosha [343]
3 years ago
6

Find the approximate perimeter of AABC plotted below. A(2,7) C(6,7) B(-4,-3)

Mathematics
1 answer:
sergij07 [2.7K]3 years ago
8 0

Answer:

29.8 units

Step-by-step explanation:

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If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?​
Oduvanchick [21]

\large\underline{\sf{Solution-}}

<u>Given:</u>

\rm \longmapsto x = a \sin \alpha  \cos \beta

\rm \longmapsto y = b \sin \alpha  \sin \beta

\rm \longmapsto z = c\cos \alpha

Therefore:

\rm \longmapsto \dfrac{x}{a}  = \sin \alpha  \cos \beta

\rm \longmapsto \dfrac{y}{b}  = \sin \alpha  \sin \beta

\rm \longmapsto \dfrac{z}{c} = \cos \alpha

Now:

\rm =  \dfrac{ {x}^{2} }{ {a}^{2}} +  \dfrac{ {y}^{2} }{ {b}^{2} } +  \dfrac{ {z}^{2} }{ {c}^{2} }

\rm =  { \sin}^{2} \alpha  \cos^{2}  \beta   +  { \sin}^{2} \alpha  \sin^{2} \beta  +  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha  (\cos^{2}  \beta   +  \sin^{2} \beta  )+  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha \cdot1+  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha + { \cos}^{2} \alpha

\rm = 1

<u>Therefore:</u>

\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} +  \dfrac{ {y}^{2} }{ {b}^{2} } +  \dfrac{ {z}^{2} }{ {c}^{2} }  = 1

5 0
3 years ago
Find the equation of a line that goes through the points (-3,5) and (5,-11)
Rasek [7]

(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-11}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}}\implies \cfrac{-16}{5+3}\implies \cfrac{-16}{8}\implies -2

\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-2}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-5-2(x+3)\implies y-5=-2x-6\implies y=-2x-1

3 0
2 years ago
Multiply -10(-7x² + 5x)​
tatiyna

Answer: 70x^2 -50x

Step-by-step explanation:

^ means exponent

7 0
2 years ago
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three points are plotted in the coordinate plane which table of X and Y values corresponds to these points​
weeeeeb [17]

Answer:

Where is the table?

Step-by-step explanation:

4 0
2 years ago
Evaluate the expression when b=2<br> 12-b
exis [7]

Answer:

10 \huge\checkmark

Step-by-step explanation:

Hi there, hope you are having a nice day!

All we should do is plug in the value of b:

12-2

10 (Answer)

Hope you find it helpful.

Feel free to ask if you have any questions.

\bf{-MistySparkles^**^*

7 0
2 years ago
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