All categories

3 years ago

Who else is in online school this semester. I live in ga btw.

Mathematics

2 answers:

natka813 [3]3 years ago

5 0

Answer:

Step-by-step explanation:

natima [27]3 years ago

3 0

Answer:

mee

Step-by-step explanation:

You might be interested in

There is a closed carton of eggs in Mai's refrigerator. The carton contains e eggs and it can hold 12 eggs. What does the inequa

LiRa [457]

Answer:

Step-by-step explanation:

8 0

3 years ago

Marisa bought three movies for $9.99 each into video games for $14.99 each the prices included tax she gave the cashier $70 how

Mrrafil [7]

Answer:

106.70 because you have to subtract 14.99 by 9.99 which is 106.00 and then add that to 70 and your answer is 106.70. by the way I am a kid and a fifth grader.

3 0

3 years ago

Join 78902567210 ... kmnj76 .............

erik [133]

Answer:

joining

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

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

the time it takes to lay a sidewalk of a certain type varies directly as the length and inversely as the # of men working. If ei

Lesechka [4]

If 8 men ----------------------------- >take 2 days to lay 100 feet

then
they can lay 50 feet in a day.
Each man lays 50/8 or 6.25 feet per day.

3 men can lay 3 * 6.25 = 18.75 feet per day. 

150/18.75 = 17.14 days.

the answer is 17.14 days.

4 0

4 years ago