If a system of linear equations has one solution, what is an importan

trapecia [35]

It is E. 25:10 simplifies to 5:2.

7 0

2 years ago

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

Sav [38]

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

6 0

2 years ago

Evaluate rs+14s when <br> R=6 <br> S=1/4

krok68 [10]

Answer:

5

Step-by-step explanation:

plug in the values for r and s and solve.

(6)(1/4)+14(1/4)

(3/2)+(7/2)

(10/2)

5

3 0

3 years ago

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let X represent the amount of time till the next student will arriv ein the library partking lot at the university. If we know t

AlekseyPX

Answer:

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Mean of 4 minutes

This means that $m = 4, \mu = \frac{1}{4} = 0.25$

Find the probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot:

This is:

$P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2)$

In which

$P(X \leq 132) = 1 - e^{-0.25*132} = 1$

$P(X \leq 2) = 1 - e^{-0.25*2} = 0.393469$

$P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2) = 1 - 0.393469 = 0.606531$

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

4 0

2 years ago

What is the circumference of a circle with a radius of eight inches

stira [4]

Answer:

50.24 inches

$\:$

Step-by-step explanation:

It is given that, the radius of a circle is 8 inches and we are to find the circumference of the circle.

$\:$

To find the circumference of the circle we must know this formula first :

$\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Circumference_{(circle)}= 2 \pi r}}}}}} \: \: \bigstar \\ \\$

Where

r is the radius of the circle.

We'll take the value of π as 3.14

Now substituting the values in the formula :

$\\{ \longrightarrow \qquad{ {{\sf{{ \: Circumference_{(circle)}= 2 \times 3.14 \times 8}}}}}} \: \: \\ \\$

${ \longrightarrow \qquad{ {{\sf{{ \: Circumference_{(circle)}= 3.14 \times 16}}}}}} \: \: \\ \\$

${ \longrightarrow \qquad{ { \pmb{\frak{{ \: Circumference_{(circle)}= 50.24}}}}}} \: \: \\ \\$

Therefore,

The circumference of the circle is 50.24 inches

7 0

2 years ago

Read 2 more answers