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3 years ago

Prove the identity.

Mathematics

1 answer:

Delvig [45]3 years ago

5 0

Answer:

D. Pythagorean

Step-by-step explanation:

Given the identity

cos²x - sin²x = 2 cos²x - 1.

To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.

Starting from the left hand side

cos²x - sin²x ... 1

According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:

x = rcostheta

y = rsintheta

Substituting into the Pythagoras firnuka we have

(rcostheta)²+(rsintheta)² = r²

r²cos²theta+r²sin²theta = r²

r²(cos²theta+sin²theta) = r²

(cos²theta+sin²theta) = 1

sin²theta = 1 - cos²theta

sin²x = 1-cos²x ... 2

Substituting equation 2 into 1 we have;

= cos²x-(1-cos²x)

= cos²x-1+cos²x

= 2cos²x-1 (RHS)

This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM

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The UAE Hope Probe is between 22,000 Km and 44,000 KM away from mars. This means its between _____________m and ______________m.

Marina86 [1]

Answer:

This means it is between 22000000 m and 44000000 m.

Step-by-step explanation:

From the question, the UAE Hope Pobe is between 22 000 km and 44 000 km away from Mars.

Since,

1 000 m = 1 km

Then,

22 000 km = 22 000 x 1000 m

= 22000000 m

also,

44000 km = 44000 x 1000 m

= 44000000 m

Therefore, the Probe is between 22000000 m and 44000000 m.

6 0

2 years ago

How do you write 20 in exponential form

seropon [69]

Answer:

2 to the power of 2 times 5 to the power of 1

= 20

Step-by-step explanation:

6 0

2 years ago

Can someone please explain how the answer is D

Kitty [74]

Step-by-step explanation:

Because the length of ST is calculated using pythagorean theorem:

${c}^{2} = {a}^{2} + {b}^{2}$

Where the square of the hypotenuse is equal to the sum of squares of the other two sides of a right triangle. In this case, the hypotenuse is ST and the other two sides are distances between S and T over the X and Y axis. Those are easily calculated:

$x = |sx - tx| \\ y = |sy - ty|$

Where x is the distance between S and T over X axis and Y distance over Y axis, sx and tx are X coordinates of S and T, sy and ty are Y coordinates of S and T.

Using that formula, you get that y = 17 and x = 8.

Back to the pythagorean theorem, if we put those number in the formula of the pythagorean theorem, we get something like this:

${c}^{2} = {x}^{2} + {y}^{2} \\ {c}^{2} = {8}^{2} + {17}^{2} = 64 + 289 \\ {c}^{2} = 353 \\ c = \sqrt{353}$

And finally, the correct answer is in fact 353.

3 0

2 years ago

A sample of n = 5 scores has a mean of m = 8. one new score is added to the sample and the new mean is calculated to be m = 9. w

Yuri [45]

If the 5 scores have a mean of 8, then their total sum would be 8*5 = 40

Now if one score if added (let's call this score x), there are 6 scores and the mean changes to 9, thus:
(40 + x)/6 = 9
40 + x = 54
x = 14

6 0

2 years ago

Read 2 more answers

Look at this I really need help with this

Anettt [7]

$y = 7500 {(.97)}^{0} \\ = 7500(1) \\ = 7500$
D

6 0

2 years ago