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3 years ago

Which of the following is equivalent to the complex number -8(7i - 3i^2)

Mathematics

1 answer:

Leni [432]3 years ago

7 0

Answer: B) -56i - 24

This is the same as -24 - 56i

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Explanation:

The 'i' refers to the imaginary number $\sqrt{-1}$

In other words, $i = \sqrt{-1}$

Squaring both sides gets us $i^2 = -1$

So,

$x = -8(7i - 3i^2)\\\\x = -8(7i - 3(-1))\\\\x = -8(7i + 3)\\\\x = -8(7i) -8(3)\\\\x = -56i -24 \ \ \text{ .... Answer: Choice B}\\\\x = -24 - 56i\\\\$

The result is in the form a+bi where a = -24 is the real part and b = -56 is the imaginary part.

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An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft 3 . Find the d

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Answer:

The dimensions of the box that minimize the materials used is $6\times 3\times 2\ ft$

Step-by-step explanation:

Given : An open top box is to be built with a rectangular base whose length is twice its width and with a volume of 36 ft³.

To find : The dimensions of the box that minimize the materials used ?

Solution :

An open top box is to be built with a rectangular base whose length is twice its width.

Here, width = w

Length = 2w

Height = h

The volume of the box V=36 ft³

i.e. $w\times 2w\times h=36$

$h=\frac{18}{w^2}$

The equation form when top is open,

$f(w)=2w^2+2wh+2(2w)h$

Substitute the value of h,

$f(w)=2w^2+2w(\frac{18}{w^2})+2(2w)(\frac{18}{w^2})$

$f(w)=2w^2+\frac{36}{w}+\frac{72}{w}$

$f(w)=2w^2+\frac{108}{w}$

Derivate w.r.t 'w',

$f'(w)=4w-\frac{108}{w^2}$

For critical point put it to zero,

$4w-\frac{108}{w^2}=0$

$4w=\frac{108}{w^2}$

$w^3=27$

$w^3=3^3$

$w=3$

Derivate the function again w.r.t 'w',

$f''(w)=4+\frac{216}{w^3}$

For w=3, $f''(3)=4+\frac{216}{3^3}=12 >0$

So, it is minimum at w=3.

Now, the dimensions of the box is

Width = 3 ft.

Length = 2(3)= 6 ft

Height = $\frac{18}{3^2}=2\ ft$

Therefore, the dimensions of the box that minimize the materials used is $6\times 3\times 2\ ft$

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Answer:

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Jung has a total of 92 coins in his coin collection. This is 8 more then 3 times the number of quarters in the collection. How m

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Answer:

proof:

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Which of the following is equivalent to the complex number -8(7i - 3i^2)￼

Which of the following is equivalent to the complex number -8(7i - 3i^2)