Solve a + b + c = 55, b+c= 13, and a + c = 45 for c.

The angle between the complex numbers 2+2i and -7

anygoal [31]

Answer:Consider the right triangle formed by the complex number in the Argand-Gauss plane and it's projections on the axis. – José Siqueira Nov 12 '13 at 17:21

In particular what is the definition of sine of theta in terms of the known sides of the above mentioned right triangle? – Adam Nov 12 '13 at 17:27

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3 Answers

1

Consider the following Argand-diagram

enter image description here

The y-axis is the imaginary axis and the x-axis is the real one. The complex number in question is

x+yi

To figure out θ, consider the right-triangle formed by the two-coordinates on the plane (illustrated in red). Let θ be the angle formed with the real axis.

tanθ=yx

⟹tan−1(yx)

The hypotenuse of the triangle will be

x2+y2−−−−−−√

Therefore,

Step-by-step explanation:

5 0

3 years ago

a company decided to increase the size of the box for the packaging of their alcohol products. the length of the original packag

Igoryamba

Answer:

The answer is below

Step-by-step explanation:

a company decided to increase the size of the box for the packaging of their alcohol products. the length of the original packaging box was 40 cm longer than its width and the height 12 cm, volume was at most 4800 cm3. Suppose the length of the new packaging box is still 40cm longer than its width and the height is 12cm, what mathematical statement would represent the volume of the new packaging box?

Solution:

Let the width of the box be x cm.

The length of the box is 40 cm longer than the width, therefore the length of the box = x + 40

The height of the box = 12 cm

The volume of the box can be gotten from the formula:

Volume = length × width × height

Substituting:

Volume = (x + 40) × (x) × 12

Volume = 12x(x + 40)

Therefore the volume of the new box is 12x(x + 40)

8 0

3 years ago

Please solve 5/5 ÷ 1/2 =

Gala2k [10]

5/5 ÷ 1/2 =
5/5 is the same as 1 so 1/2 of 1 = 1/2

5 0

3 years ago

One person can do a certain job in 15 minutes and another person can do the same job in 30 minutes. How many minutes will it tak

Flauer [41]

Hello! Your answer is B, 10 minutes.

Say the x = minutes taken to do the job. You can set up an equation like this to solve this.

$\frac{1}{15} x + \frac{1}{30} x = 1$

This is representative of the situation. The fractions each represent how much each person does in a minute, and when they're multiplied by x, that's how much of the project they get done based off of the minutes they work together on the job. Add the two together, and you get how much of the project is finished in x amount of time. Set it equal to 1, as you are looking for 100% completion.

Once you have this equation, find a common denominator, add, and solve.

$\frac{1}{15} x + \frac{1}{30} x = 1$

$\frac{2}{30} x + \frac{1}{30} x = 1$

$\frac{3}{30}x = 1$

$\frac{1}{10}x = 1$

$x = 10$

Therefore, it will take them 10 minutes to do the job together.

Hope this helps!

8 0

3 years ago

Liana can see that the measure of Angle L and Angle M form a straight line. Since Liana knows that a straight line has an angle

cricket20 [7]

Answer:

150 degrees

Step-by-step explanation:

Let's start off by looking at what we are working with in this specific problem:

We can see that we are looking at 2 angles, angle L and angle M, that add up to a total of 180 degrees (aka a straight line)

Now that we know that, we also have to keep is mind that angle L + angle M = 180 degrees.

Now that we've got all of that out of the way, let's set up a simple algebraic equation:

angle L + angle M = 180

We also know that angle L is 30 degrees so let's add it into the equation we have just created:

30 + angle M = 180

We now know that 30 plus angle M (whatever it might be) is equal to 180 so in order to solve this problem we have to do some simple subtraction.

180 - 30 = angle M

Now we are left with:

150 degrees = angle M

4 0

3 years ago