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3 years ago

What is the Square root of -48, please show steps

1 answer:

8 0

Hey hey
Ok so if you don’t know imaginary numbers ( i) it is no real solution

But....
If you use imaginary numbers then there will be a solution

Ok so all negatives in a square root is equal to i so we are going to take out i so it is just the square root of 48 which is 4 square root 3 i. Hope that helps

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field biologist collects 220 butterflies and moths. He collects 4 butterflies for every moth. How many butterflies and how many

ki77a [65]

Answer:

The number of butterflies he collects = 176

The number of moth he collects = 44

Step-by-step explanation:

This question has to do with ratio.

We are told in the question that:He collects 4 butterflies for every moth.

Hence, the ratio of

Butterflies : Moth

4 : 1

Sum of the proportion = 4 + 1 = 5

We are also told he has a total of 220 butterflies and moths.

Hence:

The number of butterflies he collects is calculated as

4/5 × 220 = 176 butterflies

The number of moth that he collects =

1/5 × 220 = 44 moth

3 0

3 years ago

Read 2 more answers

Can someone help me with this and show the step to solving it

anyanavicka [17]

Answer:x = 9/16

Step-by-step explanation:

2x + 3 = 6x - 4

First you gotta get rid of the divided by 3

2x / 3 = 2/3x and 3 / 3 = 1

Now you have

2/3x + 1 = 6x - 4

Second you have to get rid of the 2/3x on the left side

2/3x + 1 = 6x - 4

-2/3x -2/3x

1 = 5 1/3x - 4

Third you have to get rid of the -4

1 = 5 1/3x - 4

-4 -4

-3 = 5 1/3x

Fourth you have to divide by 5 1/3

-3 = 5 1/3x

/ 5 1/3 / 5 1/3

x = 9/16

3 0

3 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$