Three vertices of a rectangle are given. Find the coordinates of the fourth vertex. (0,5),(5,0),(2,-3)

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! THIS IS NOT A TEST OR AN ASSESSMENT!! Please help me with these math questions

Art [367]

Answer:

See below

Step-by-step explanation:

3. What are two ways that a vector can be represented?

Considering a vector $\vec{v}$ in some vector space $\mathbb R^n$ we have

$\vec{v} = \langle a,b\rangle$

This is the component form. I don't like that way. It is probably used in high school, but

$\vec{v} = \begin{pmatrix} a\\ b\\ \end{pmatrix}$

is preferable because the inner product on $\mathbb R^n$ is defined to be

$\langle a,b\rangle := \sum_{i = 1}^n a_i b_i$

You can also write it using linear form such as $\vec{v} = 2i+2j$

4.

For this question, I think you meant

vectors

$\vec{u_1} = (-8, 12)$

$\vec{u_2} = (13, 15)$

Once

$\cos(\theta)=\dfrac{\vec{u_1} \cdot\vec{u_2}}{||\vec{u_1}||||\vec{u_2}||}$

Considering that the dot product is

$\vec{u_1}\cdot \vec{u_2} = (-8)\cdot 13 + 12\cdot 15 = -104+180= 76$

and the norm of $\vec{u_1}$ is $||\vec{u_1}|| = \sqrt{(-8)^2 + 12^2} = \sqrt{64 + 144}= \sqrt{208}$

and the norm of $\vec{u_2}$ is $||\vec{u_2}|| = \sqrt{13^2 + 15^2} = \sqrt{169 + 225}= \sqrt{394}$

Thus,

$\cos(\theta)=\dfrac{76}{\sqrt{208} \sqrt{394}} = \dfrac{19}{\sqrt{13}\sqrt{394}}=\dfrac{19}{\sqrt{5122}}$

$\therefore \theta = \arccos \left(\dfrac{19}{\sqrt{5122}} \right)$

3 0

2 years ago

Cami and Enrique's ages add up to 46. Cami is two years older than three times Enrique's age. How old are Cami and Enrique?

stira [4]

answer:

Cami is 35 and Enrique is 11

35 plus 11 = 46

3 0

2 years ago

Ronald picked many oranges from his trees. He squeezed out 256 fluid ounces of juice. How many half-gallon containers of juice w

Aneli [31]

It is pretty much About 4

7 0

2 years ago

Drag all of the division problems that have an estimated quotient of 12 into the box.

Mars2501 [29]

Answer:
Option 5 & 6

Step by Step Explanation:
8 / 0.95 = 8.4 ( wrong )
18 / 2.2 = 8.18 ( wrong )
47.6 / 3.9 = 16.41 ( wrong )
10.6 / 1.89 = 5.6 ( wrong )
71.9 / 6.5 = 11.061 ( correct )
123.4 / 9.2 = 13.41 ( correct )
157.4 / 16.4 = 9.59 ( wrong )

hope this helps! please give brainliest and thanks!!!

4 0

2 years ago

During which time period does Landon's elevation change the fastest? Explain how you know?

bogdanovich [222]

<h3>1. How many inches per minute does London's elevation change between 4 minutes and 8 minutes. </h3>

The question actually asks for the slope of the line that stands for the points $(4,3) \ and \ (8,6)$ why? because the questions tells us that London's elevation changes between 4 minutes and 8 minutes here. Hence, to find the slope of this line we have to use the following formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6) \\ \\ So: \\ \\ m=\frac{6-3}{8-4}=0.75in/min$

<em>So London's elevation changes 0.75 inches per minute</em>

<h3>2. During which time period does London's elevation change the fastest?</h3>

The greater the absolute value of the slope of the line the faster London's elevation changes. Since this is a Piecewise function, we must analyze each period.

FIRST:

→ Between 0 minutes and 4 minutes the function is constant, so there is no any change here.

→ Between 10 minutes and 14 minutes the function is constant, so there is no any change here.

→ Between 18 minutes and 22 minutes the function is constant, so there is no any change here.

So the solution is not in these parts of the function.

SECOND:

→ Between 4 minutes and 10 minutes the function has a positive slope, so there is change here.

In the previous item we calculated the slope between 4 and 8 minutes that is the same slope between 4 and 8 minutes and equals 0.75.

→ Between 14 minutes and 18 minutes the function has a positive slope, so there is change here.

Let's take two points here, say, $(16,5) \ and \ (18,3)$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(16,5) \\ P(x_{2},y_{2})=P(18,3) \\ \\ So: \\ \\ m=\frac{3-5}{18-16}=-1 in/min$

As you can see, the absolute value here is 1 that is greater than 0.75.

<em>In conclusion, London's elevation changes the fastest between 14 and 18 minutes</em>

7 0

2 years ago