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Arte-miy333 [17]
3 years ago
10

For the transformation to be reflection which statement mist be true

Mathematics
1 answer:
Fiesta28 [93]3 years ago
5 0

Are there any options?

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Does anyone know how to solve this?
dezoksy [38]

Answer:

NOO I DONOT NO IF U KNOW PLEASE SHARE ME

7 0
3 years ago
Find the imaginary part of\[(\cos12^\circ+i\sin12^\circ+\cos48^\circ+i\sin48^\circ)^6.\]
iren [92.7K]

Answer:

The imaginary part is 0

Step-by-step explanation:

The number given is:

x=(\cos(12)+i\sin(12)+ \cos(48)+ i\sin(48))^6

First, we can expand this power using the binomial theorem:

(a+b)^k=\sum_{j=0}^{k}\binom{k}{j}a^{k-j}b^{j}

After that, we can apply De Moivre's theorem to expand each summand:(\cos(a)+i\sin(a))^k=\cos(ka)+i\sin(ka)

The final step is to find the common factor of i in the last expansion. Now:

x^6=((\cos(12)+i\sin(12))+(\cos(48)+ i\sin(48)))^6

=\binom{6}{0}(\cos(12)+i\sin(12))^6(\cos(48)+ i\sin(48))^0+\binom{6}{1}(\cos(12)+i\sin(12))^5(\cos(48)+ i\sin(48))^1+\binom{6}{2}(\cos(12)+i\sin(12))^4(\cos(48)+ i\sin(48))^2+\binom{6}{3}(\cos(12)+i\sin(12))^3(\cos(48)+ i\sin(48))^3+\binom{6}{4}(\cos(12)+i\sin(12))^2(\cos(48)+ i\sin(48))^4+\binom{6}{5}(\cos(12)+i\sin(12))^1(\cos(48)+ i\sin(48))^5+\binom{6}{6}(\cos(12)+i\sin(12))^0(\cos(48)+ i\sin(48))^6

=(\cos(72)+i\sin(72))+6(\cos(60)+i\sin(60))(\cos(48)+ i\sin(48))+15(\cos(48)+i\sin(48))(\cos(96)+ i\sin(96))+20(\cos(36)+i\sin(36))(\cos(144)+ i\sin(144))+15(\cos(24)+i\sin(24))(\cos(192)+ i\sin(192))+6(\cos(12)+i\sin(12))(\cos(240)+ i\sin(240))+(\cos(288)+ i\sin(288))

The last part is to multiply these factors and extract the imaginary part. This computation gives:

Re x^6=\cos 72+6cos 60\cos 48-6\sin 60\sin 48+15\cos 96\cos 48-15\sin 96\sin 48+20\cos 36\cos 144-20\sin 36\sin 144+15\cos 24\cos 192-15\sin 24\sin 192+6\cos 12\cos 240-6\sin 12\sin 240+\cos 288

Im x^6=\sin 72+6cos 60\sin 48+6\sin 60\cos 48+15\cos 96\sin 48+15\sin 96\cos 48+20\cos 36\sin 144+20\sin 36\cos 144+15\cos 24\sin 192+15\sin 24\cos 192+6\cos 12\sin 240+6\sin 12\cos 240+\sin 288

(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)

A calculator simplifies the imaginary part Im(x⁶) to 0

4 0
3 years ago
PLS HELP ASAP I DONT HAVE TIME FOR THIS, IT ALSO DETECTS IF ITS RIGHT IR WRONG
Airida [17]

Answer:

A, or 50.24 ft.

Step-by-step explanation:

Doing the equation above, we know the radius of the circle, which is 8 ft.

8ft times 2 is 16ft.

16ft times pi gives us (rounded) 50.24 ft.

8 0
3 years ago
A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $10.20 per pound with a Terraza coffee b
padilas [110]

Answer:

Rift =37.92 pounds

Terraza=2.08 pounds

4 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=4x%20-%202%20%5Cleqslant%20-%2022" id="TexFormula1" title="4x - 2 \leqslant - 22" alt="4x - 2
Bad White [126]

Answer:

x ≤ -5

Step-by-step explanation:

4x-2 ≤-22

Add 2 to each side

4x-2+2 ≤-22+2

4x ≤ -20

Divide each side by 4

4x/4 ≤ -20/4

x ≤ -5

3 0
3 years ago
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