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3 years ago

What is the value of 15i/ 2 + i

Mathematics

2 answers:

Yuki888 [10]3 years ago

8 0

Answer:

The value of the given expression is $\frac{15i}{2+i}=3(2i+1)$

Step-by-step explanation:

Given : Expression $\frac{15i}{2+i}$

To find : The value of the given expression?

Solution :

We solve the expression by rationalizing,

$\frac{15i}{2+i}$

Rationalize by multiplying the Nr. and Dr. by 2-i

$=\frac{15i}{2+i}\times \frac{2-i}{2-i}$

$=\frac{15i(2-i)}{(2+i)(2-i)}$

Applying property, $(a+b)(a-b)=a^2-b^2$

$=\frac{30i-15i^2}{2^2-i^2}$

We know, $i^2=-1$

$=\frac{30i-15(-1)}{2^2-(-1)}$

$=\frac{30i+15}{4+1}$

$=\frac{30i+15}{5}$

Divide by 5,

$=6i+3$

$=3(2i+1)$

Therefore, The value of the given expression is $\frac{15i}{2+i}=3(2i+1)$

madreJ [45]3 years ago

5 0

the answer would be

3 + 6i

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What is sin 45°? O A. 1/2 12 1 OB. NI O C. 1 O D. O E. 1 3 O F. 13 ap.ex

andrew-mc [135]

1/√2

Step-by-step explanation:

Imagine a right-angled triangle, for e.g. Triangle ABC,

Where

B = 90°

Remember your Toa Cah Soh.

sin 45° = opposite / hypotenuse

If theta = 45°

Angles A and C = 45° (Sum of angles in a triangle equal = 180°)

Since theta are the same, we can also deduce that the length AB and BC are the same.

Take for example AB = BC = 1 = opposite

By the Pythagorean theorem,

AB² + BC² = AC²

1² + 1² = AC²

2 = AC²

AC = √2 = hypotenuse

Therefore:

sin 45° = opposite / hypotenuse

sin 45° = 1/√2

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3 years ago

What's the next common different of 35,32,29,26

Georgia [21]

23 since the pattern rules is that we subtract by 3 each time

3 0

3 years ago

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Show the work of 6.2 +3.4

Musya8 [376]

Answer:

9.6

Step-by-step explanation:

When we are adding decimals we try 2 add them like normal integers, but in the end we add the decimal in the same place as it was in the beginning

so 62+34=96 and there's a decimal in the tenths place so its 9.6

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3 years ago

Historically 80% of the monitors made by your company will pass your stringent quality control checks. 40 monitors have just com

madam [21]

Answer:

a) 10.75% probability that exactly 30 of them will pass the quality control checks.

b) Expected value is 32

Variance is 6.4

Step-by-step explanation:

For each monitor, there are only two possible outcomes. Either they will pass the quality checks, or they will not pass these checks. The probability of a monitor passing these checks is independent of other monitors. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

80% of the monitors made by your company will pass your stringent quality control checks.

This means that $p = 0.8$

40 monitors have just come off the assembly line.

This means that $n = 40$

a) What is the probability that exactly 30 of them will pass the quality control checks?

This is P(X = 30). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 30) = C_{40,30}.(0.8)^{30}.(0.2)^{10} = 0.1075$

10.75% probability that exactly 30 of them will pass the quality control checks.

b) What are the expected value and variance of the number of these monitors that will pass the quality control checks?

$E(X) = np = 40*0.8 = 32$

Expected value is 32

$V(X) = np(1-p) = 40*0.8*0.2 = 6.4$

Variance is 6.4

4 0

3 years ago

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and *blank*

prisoha [69]

Answer:

12 is the answer.

Step-by-step explanation:

The best way to get the roots of the equation is to factorize the equation but when the factors are not possible then we should apply the quadratic equations formula to get the value of x.

Now we will try to factorize

x² - 8x -48 = 0

Now we multiply coefficient of highest degree term and constant term

48×1 = 48 which may be factored in 12×4. 8×6, 24×2.

Now we will choose 12×4 out of three because the 12-4 = 8 which is the coefficient of x.

Now its simple.

x²-12x + 4x -48 = 0

x(x -12) + 4(x-12) = 0

(x +4)(x-12) = 0

Therefore roots are x + 4 = 0

x = -4

and x - 12 = 0

x = 12

So the answer is 12.

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3 years ago

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