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3 years ago

Simplify 8i^6+6i^5-5i^3-3i^2-7i-9 A) -14+4i B) -4+4i C) -10i D) -14-18i

Mathematics

2 answers:

kipiarov [429]3 years ago

7 0

The answer is A) -14 + 4i. God bless!

poizon [28]3 years ago

7 0

Answer:

The simplified form of complex expression is -14+4i

A is correct.

Step-by-step explanation:

Given: $8i^6+6i^5-5i^3-3i^2-7i-9$

As we know, $i^2=-1$

$i^6=-1$

$i^5=i$

Put the value and simplify i

$\Rightarrow 8(-1)+6(i)-5(-i)-3(-1)-7i-9$

$\Rightarrow -8+6i+5i+3-7i-9$ 3

Combine the like term and simplify it

$\Rightarrow (-8+3-9)+(6i+5i-7i)$

$\Rightarrow -14+4i$

Hence, The simplified form of complex expression is -14+4i

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A manufacturing process makes rods that vary slightly in length but follow a normal distribution with mean length 25 cm and stan

Galina-37 [17]

Answer:

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = 0.1251

Step-by-step explanation:

Step(i):-

Given mean of the Population = 25cm

Given standard deviation of the Population = 2.60

Let 'x' be the random variable in normal distribution

Given x=22

$Z = \frac{x-mean }{S.D} = \frac{22-25}{2.60} = -1.15$

Step(ii):-

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = P( Z<-1.15)

= 1-P(Z>1.15)

= 1-( 0.5+A(1.15)

= 0.5 - A(1.15)

= 0.5 - 0.3749

= 0.1251

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = 0.1251

7 0

3 years ago

Witch fraction has the same value as 2 3/3

saul85 [17]

Answer: Technically, it would be 9/3, but you can simplify that to 3.

3 0

3 years ago

Read 2 more answers

3^2 ÷ 3^-1 explain the steps

Ksenya-84 [330]

First you would need to Simplify {3}^{2}32 to 99

Next you would need to : Use Negative Power Rule =9÷31

then you would need to use a ÷ b/c = a * c/b and get 9*3

And you will lastly get 27

7 0

3 years ago

5% of what number is 85?

Semmy [17]

5% = 0.5

0.5n = 85

Divide by 0.5

0.5n = 85
/0.5 /0.5

n = 170.

The number is 170.

8 0

4 years ago

3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall

Katen [24]

Answer:

The volume of the toy is $V=5.23\ ft^3$

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

$V=\frac{2}{3}\pi r^{3}$

In this problem, the wide of the toy is equal to the diameter of the hemisphere

$D=2\ ft$

$r=2/2=1\ ft$ ----> the radius is half the diameter

substitute

$V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3$

step 2

Find the volume of the cone

The volume of the cone is given by

$V=\frac{1}{3}\pi r^{2}h$

we know that

The radius of the cone is the same that the radius of the hemisphere

$r=1\ ft$

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

$h=4-1=3\ ft$

substitute the given values

$V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3$

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

$V=(\frac{2}{3} \pi+\pi)\ ft^3$

$V=(\frac{5}{3}\pi)\ ft^3$

assume

$\pi=3.14$

$V=\frac{5}{3}(3.14)=5.23\ ft^3$

5 0

4 years ago