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Margaret [11]
3 years ago
6

Please help and tell me how to do this 20 POINTS

Mathematics
2 answers:
OLga [1]3 years ago
7 0

Answer:

Q13.9

Q14. 200

Q15. -10

Q16. -300

Q17. -276

Q18. -66

Step-by-step explanation:

For Q13, 14, 15 and 16

For questions involving negative integers its good to reference a number line (see attached picture), if a number with a - (negative sign) in front of it is bigger, the number will be smaller! Having 5 less apples is more than having 10 less apple, eg. -5 is bigger than -10.

For Q17 and 18

An integer is a whole number, like 3, 4, -1, -6 and so on. For 17, death valley has an elevation BELOW sea level, meaning it is under the level of the sea. Therefore it is a negative value as it is LESS THAN the sea (you are deeper swimming below the ocean than floating above it)! For 18, the number is LESS THAN 0, check the attached picture! If something is BELOW 0 then it is negative.

svp [43]3 years ago
3 0
The answers are :
13) 9
14) 200
15) -10
16) -300

17) -276
18) -66
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3 years ago
Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.
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<u>ANSWER</u>

{r}^{2}  = 4  \cos2\theta

<u>EXPLANATION</u>

The Cartesian equation is

{( {x}^{2}  +  {y}^{2} )}^{2}  = 4( {x}^{2} -  {y}^{2}  )

We substitute

x = r \cos( \theta)

y = r \sin( \theta)

and

{x}^{2}  +  {y}^{2}  =  {r}^{2}

This implies that

{( {r}^{2} )}^{2}  = 4(( { r \cos\theta)  }^{2} -  {(r \sin\theta) }^{2}  )

Let us evaluate the exponents to get:

{r}^{4}  = 4({  {r}^{2} \cos^{2}\theta } -   {r}^{2}  \sin^{2}\theta)

Factor the RHS to get:

{r}^{4}  = 4{r}^{2} ({   \cos^{2}\theta } -   \sin^{2}\theta)

Divide through by r²

{r}^{2}  = 4 ({   \cos^{2}\theta } -   \sin^{2}\theta)

Apply the double angle identity

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The polar equation then becomes:

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7 0
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