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irina [24]
3 years ago
9

The following equation is often referred to as Euler's Formula; e^pii+1=0 Use what you know about complex numbers to show that t

his equation is true. In other words, show that e^pii+1=0 __ If someone could please help me understand the proof and the answer to this ill give you brainliest!! thank you
Mathematics
1 answer:
Sav [38]3 years ago
6 0

Answer:

\large \boxed{e^{i\pi}+1=0}

Step-by-step explanation:

Hello, please consider the following.

For any x real number,

e^{ix}=cos(x)+i\cdot sin(x)\text{, right? So}\\\\e^{i\pi}=cos(\pi)+i\cdot sin(\pi)\\\\e^{i\pi}=-1+i\cdot 0=-1\\\\\text{ We add 1 to both sides of the equation.}\\\\\large \boxed{e^{i\pi}+1=0}\\

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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What is 7.13×10 to the fifth power in standard form
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713000 is your answer
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A rectangular piece of wood is 12 centimeters longer than it is wide. A strip 1 centimeter wide is cut off all around. This decr
denis-greek [22]

Answer:

Length 37 cm, width 25 cm.

Step-by-step explanation:

Let the original dimensions be length x and width x - 12 cms.

The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.

So , from the areas, we have:

x(x - 12) - (x - 2)(x - 14) = 120

x^2 - 12x  - (x^2 - 16x + 28) = 120

-12x + 16x - 28 = 120

4x = 148

x = 37 cms

So the length was 37 cm and the width was 37-12 = 25 cm.

7 0
3 years ago
Find the value of 7x^2+2x when x=3
frozen [14]

Answer:

69

Step-by-step explanation:

so x2 will give you 9 times 7 which is 63. add it to 2 times 3 which is 63 + 6 will give you 69.

8 0
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A person making $500 a week receives a 12% raise, which is an increase in their salary. Find the person’s new weekly salary.
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5 0
2 years ago
For the problem, use the discriminant to determine the number of real solutions for the equation. Then, find the solutions and c
Ksivusya [100]

Answer:

Discriminant = 55.2 > 0 -> 2 real solutions

Solutions: t1 = -1.1663 s and t2 = 0.35 s

The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.

So the solution is t2 = 0.35 s

Step-by-step explanation:

To find the time when the ball will reach the height of 2 meters, we just need to use the value of h = 2 in the equation given. So, we have that:

−4.9t^2 − 4t + 4 = 2

−4.9t^2 − 4t + 2 = 0

For this equation, we have the constants a = -4.9, b = -4 and c = 2. So the discriminant Delta is:

Delta = b^2 - 4ac = 16 + 39.2 = 55.2

sqrt(Delta) = 7.4297

As Delta > 0, we have 2 real solutions

t1 = (-b + sqrt(Delta)) / 2a = (4 + 7.4297) / (-9.8)  = -1.1663 s

t2 = (-b - sqrt(Delta)) / 2a = (4 - 7.4297) / (-9.8)  = 0.35 s

Number of real solutions: 2

Solutions: t1 = -1.1663 s and t2 = 0.35 s

The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.

So the solution is t2 = 0.35 s

8 0
3 years ago
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