- There are 24 bottles of water in a case.

HELP PLEASE! Can you please explain so I can understand how it was completed?

nlexa [21]

Answer:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

Step-by-step explanation:

Hello!

We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.

We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:

The radial coordinate which is often denoted by r.

The angular coordinate by θ.

So we need to find r and θ. So we know that:

$r=\sqrt{x^{2}+y^{2}}$ (1)

x = rcos(θ) (2)

x = rsin(θ) (3)

From the statement we know that (x, y) = (3, -3).

Using the equation (1) we find that:

$r=\sqrt{x^{2}+y^{2}}=\sqrt{3^{2}+(-3)^{2}} = 3\sqrt{2}$

Using the equations (2) and (3) we find that:

3 = rcos(θ)

-3 = rsin(θ)

Solving the system of equations:

θ= -45

Then:

r = 3\sqrt{2}[/tex]

θ= -45 or 315

Notice that there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.

So, the solution is:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

4 0

3 years ago

What is the equation of the axis of symmetry for the parabola y equals start fraction one over three end fraction left parenthes

wariber [46]

The correct axis of symmetry is x = -1.

Explanation:

Our equation is
$y=\frac{1}{3}(x+1)^2-3$ .

This is in vertex form, which is
y = a(x-h)² + k, where (h, k) is the vertex.

In our equation, h corresponds with -1 and k corresponds with -3, making the vertex (-1, -3).

The axis of symmetry is the x-coordinate of the vertex; this makes the axis of symmetry for this equation x = -1.

6 0

3 years ago

The number of major earthquakes in a year is approximately normally distributed with a mean of 20.8 and a standard deviation of

SCORPION-xisa [38]

Answer:

a) 51.60% probability that in a given year there will be less than 21 earthquakes.

b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 20.8, \sigma = 4.5$