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3 years ago

Can someone please help?

Mathematics

2 answers:

elixir [45]3 years ago

8 0

X = -7 x = 0 and x = 7

Murljashka [212]3 years ago

4 0

Answer:

x= -9, x=9

Step-by-step explanation:

hope i helped if i did it wrong lmk i can try doing it better

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

4 years ago

Find the measure of the each angle indicated. HELP

Paraphin [41]

Answer:

(n-2)180 (this is the equation to find the sum of interior angles)

(4-2) 180 (plug in the amount of angles in the polygon and then solve)

2* 180

360

360 - 115 -100- 73= 72 (360 is the sum of all angles for this polygon. so subtract the known angles to find the unknown one)

measure of angle B is 72 degrees

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The first day Rita participates in a biathlon, she jogs at a rate of 6 miles/hour and bikes at a rate of 10 miles/hour. She cove

mafiozo [28]

Answer: she biked 0.8 hour each day

Step-by-step explanation:

Let x represent the number of hours that she jogged on both days.

Let y represent the number of hours that she biked on both days.

Distance = speed × time

On the first day, she jogs at a rate of 6 miles/hour and bikes at a rate of 10 miles/hour. She covers a total of 26 miles that day. This is expressed as

6x + 10y = 26- - - - - - - - - - - - - - - 1

The second day, she continues to jog at a rate of 6 miles/hour, but a hamstring pull slows her biking rate to 5 miles/hour. The second day she covers a total of 22 miles. This means that

6x + 5y = 22- - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

5y = 4

y = 4/5 = 0.8

Substituting y = 0.8 into equation 1, it becomes

6x + 10(0.8) = 26

6x + 8 = 26

6x = 26 - 8 = 18

x = 18/6

x = 3

8 0

3 years ago

Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Dale drove h

matrenka [14]

If you let X = the distance in miles from Dales's house, and understand rate = distance/ time, the rate going to mountains = x/7, and back from mountains is x/5. If dale was 18mph fast going home, the equation would be...
(coming home rate) = (going to mountain rate) + 18 which is
x/5 = x/7 + 18. Then solve for X.
Use the least common denominator = 35 so multiply everything by 35 and you get...

7x = 5x+630
simplify...
2x = 630, then
x = 315 .
Dale live 315 miles away from the mountains.

4 0

4 years ago

The law of cosine is A squared + B squared -2abcosC. find he value of 2abcosC

Gnoma [55]

D I think but not 100% sure

8 0

4 years ago

Can someone please help? ​

Can someone please help?