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Rama09 [41]
3 years ago
5

R=8cos(theta)-10sin(theta) to cartesian coordinates

Mathematics
1 answer:
dsp733 years ago
8 0
Convert polar equation (R, Ф):

(1) R= 8cos Ф - 10sin Ф into Cartesian (x , y)
We know that:
x = R.cos Ф  → cos Ф = x/R , and
y = R.sin Ф →  sin Ф = y/R
and that x² +y² = R²

Replace in 
R= 8cos Ф - 10sin Ф , cos Ф and sin Ф by the related x and y:

R = 8(x/R) - 10(y/R)
Multiply both sides by R:

R² = 8R(x/R) - 10R(y/r) ↔ R² = 8x - 10y , but we have also R² = x² + y². hence: 8x -10y = x² + y²
OR x² + y² - 8x + 10y = 0
We can continue in completing th squares of (x² - 8x + ?) and (y² +10y + ?)

(x² - 8x + ?) = (x - 4)² - 16

and  (y² +10y + ?) = (y +5)² - 25
Final Equation:
(x - 4)² - 16 + (y +5)² - 25 →→→(x - 4)² + (y +5)² = 41 
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In the given question , we have a function given , which is

y= 13(0.5^x)

And we need to find the value of y when x=5.

So we substitute 5 for x and solve for y, that is

y=13(0.5^5) = 0.40625

And on rounding to the nearest tenths, we will get

y=0.4

So when x=5, y=0.4

7 0
3 years ago
Rebecca is at the zoo with her family. She sees 3 times as many elephants as cheetahs. There are 4 cheetahs. How many animals di
Mekhanik [1.2K]
Hello!

There are 4 cheetahs. There are 3 times as many elephants than cheetahs. Multiply:

4 • 3 = 12

12 + 4 = 16

Rebecca saw 16 animals at the zoo.

I really hope you found this helpful! :)
4 0
3 years ago
The distance between the pair of points (3,5) and (11,11)
statuscvo [17]

Formula: d = √(x2-x1)²+(y2-y1)²

d = √(11-3)²+(11-5)²

d = √8²+6²

d = √64+36

d = √100

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Best of Luck!

5 0
3 years ago
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Pick 2 coordinates:

I choose first & last one (0,15) & (8-9)

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Change in x is 8

(0 - 8) = - 8

24/-8 = - 3

So, slope = - 3

Hope this helps!

8 0
2 years ago
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Answer:

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Step-by-step explanation:

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