All categories

3 years ago

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Mathematics

2 answers:

Doss [256]3 years ago

7 0

By graphing the given equation

r = 4 - 3 sin θ

We find that the graph is symmetric about the y-axis
The graph of the given equation is attached below
------------------------------------------------------------------------------
Some information about the given equation:
the given equation is like the form of the Cardioid

A curve that is somewhat heart shaped. A cardioid can be drawn by tracing the path of a point on a circle as the circle rolls around a fixed circle of the same radius. The equation is usually written in polar coordinates.
Equations of Cardioid:

r = a ± a cos θ (horizontal) or r = a ± a sin θ (vertical)

MrMuchimi3 years ago

3 0

The graph is symmetric about y-axis only

You might be interested in

$22,000 divided by 18%

slavikrds [6]

18% = 18/100 = 0,18

22000/0,18 = 22000/(18/100) = (22000 . 100)/18 = 1100000/9 = 122222,2222...

So $22,000 divided by 18% is equal to $122.222,22

6 0

3 years ago

Read 2 more answers

For the straight line defined by the points (4, 59) and (6, 83), determine the slope and y-intercept. do not round the answers.

amid [387]

Slope=(59-83)/(4-6)=12
equation of the line:
(y-59)/(x-4)=12
y-59=12x-48
y=12x+11
put x=0, y=11
so the y-intercept is 11

6 0

3 years ago

Total donations at the firemans ball failed to reach $940

kumpel [21]

That sucks they should've worked harder

8 0

3 years ago

Find all the complex roots. Write the answer in exponential form.

dezoksy [38]

We have to calculate the fourth roots of this complex number:

$z=9+9\sqrt[]{3}i$

We start by writing this number in exponential form:

$\begin{gathered} r=\sqrt[]{9^2+(9\sqrt[]{3})^2} \\ r=\sqrt[]{81+81\cdot3} \\ r=\sqrt[]{81+243} \\ r=\sqrt[]{324} \\ r=18 \end{gathered}$ $\theta=\arctan (\frac{9\sqrt[]{3}}{9})=\arctan (\sqrt[]{3})=\frac{\pi}{3}$

Then, the exponential form is:

$z=18e^{\frac{\pi}{3}i}$

The formula for the roots of a complex number can be written (in polar form) as:

$z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1$

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

$r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}$

NOTE: It can not be simplified anymore, so we will leave it like this.

Then, we calculate the arguments of the trigonometric functions:

$\frac{\theta+2\pi k}{n}=\frac{\frac{\pi}{2}+2\pi k}{4}=\frac{\pi}{8}+\frac{\pi}{2}k=\pi(\frac{1}{8}+\frac{k}{2})$

We can now calculate for each value of k:

$\begin{gathered} k=0\colon \\ z_0=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{0}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{0}{2}))) \\ z_0=\sqrt[4]{18}\cdot(\cos (\frac{\pi}{8})+i\cdot\sin (\frac{\pi}{8}) \\ z_0=\sqrt[4]{18}\cdot e^{i\frac{\pi}{8}} \end{gathered}$ $\begin{gathered} k=1\colon \\ z_1=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{1}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{1}{2}))) \\ z_1=\sqrt[4]{18}\cdot(\cos (\frac{5\pi}{8})+i\cdot\sin (\frac{5\pi}{8})) \\ z_1=\sqrt[4]{18}e^{i\frac{5\pi}{8}} \end{gathered}$ $\begin{gathered} k=2\colon \\ z_2=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{2}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{2}{2}))) \\ z_2=\sqrt[4]{18}\cdot(\cos (\frac{9\pi}{8})+i\cdot\sin (\frac{9\pi}{8})) \\ z_2=\sqrt[4]{18}e^{i\frac{9\pi}{8}} \end{gathered}$ $\begin{gathered} k=3\colon \\ z_3=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{3}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{3}{2}))) \\ z_3=\sqrt[4]{18}\cdot(\cos (\frac{13\pi}{8})+i\cdot\sin (\frac{13\pi}{8})) \\ z_3=\sqrt[4]{18}e^{i\frac{13\pi}{8}} \end{gathered}$

Answer:

The four roots in exponential form are

z0 = 18^(1/4)*e^(i*π/8)

z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

5 0

1 year ago

Please help ASAP !! :)

Mila [183]

Answer:

temperature is decreasing as time passes
x-axis
hot drink temperature (°C)

Step-by-step explanation:

1. Each value of temperature is lower than the one previous, so we can say the temperature is decreasing. We also notice that the rate of decrease is getting smaller, possibly because the temperature is approaching a horizontal asymptote.

2. The horizontal axis, where temperature is plotted, is conventionally called the x-axis.

3. The label on the vertical axis is "temperature" and the graph title is "cooling a hot drink ...", so we presume the dependent variable is the temperature of a hot drink.

7 0

4 years ago