Name the vertex

Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y=1(−sin θ)x + (cos θ)y = 0x=y=

lys-0071 [83]

Answer:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

Step-by-step explanation:

The given system of linear equations is:

$(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0$

We have to solve the equations for the values of $x, y$ .

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by $sin\theta$ and second equation by $cos\theta$

Now, the equations become:

$(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)$

Now, let us add (1) and (2):

$(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta$

Using the equation:

$(-sin\theta)x+(cos\theta)y=0$

Putting value of $y$ :

$\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta$

So, the answer to the system of linear equations is:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

7 0

3 years ago

If the average speed of a garden snail is 0.025 miles per hour and one inch is approximately 2.54 centimeters, how many minutes

BaLLatris [955]

Snail takes 1.5 minutes to travel around one meter

<u>Solution:</u>

Given, the average speed of a garden snail is 0.025 miles per hour

And one inch is approximately 2.54 centimeters,

We have to find how many minutes would it take a garden snail to travel one meter?

Now, let us convert the speed in miles per hour to meters per minute

Then, speed = 0.025 miles per hour

= 0.025 x 1 mile / 1 hour

= 0.025 x 1609.34 meters / 60 minutes

= 0.025 x 1609.34 / 60 meters per minute

$\begin{array}{l}{=\frac{0.025 \times 1609.34}{60} \text { meters per minute }} \\\\ {=\frac{40.2335}{60} \text { meters per minute }}\end{array}$

= 0.670 meters per minute.

Now, 0.670 meters ⇒ 1 minute

Then, 1 meter ⇒ n minutes

So, by criss cross method

n x 0.67 = 1 x 1

n = 1.4912

Hence, snail takes 1.5 minutes approximately to travel 1 meter.

3 0

3 years ago

Read 2 more answers

Help plss grade 3 math

abruzzese [7]

Answer:

I thought is should only take pic of 1 question

Step-by-step explanation:

Rick Astley,Donald trump,Obama,China has conora

7 0

3 years ago

Find the smallest of two consecutive even integers if the square is 10 more than the larger

djverab [1.8K]

I think your answers are 4 and 6

7 0

3 years ago

I don't understand this

Anton [14]

Answer: (2,1)

Step-by-step explanation:

The two equations given are:

y = 3 -x

y = x - 1

The question is asking to determine the point of intersection for two linear functions aka two lines.

Step #1: Both functions must be in slope intercept form which is y = mx+b. In this case, this step can be skipped because both functions are in slope form. At an intersection, x and y must have the same value for each equation. This means that the equations are equal to each other. Therefore, we can set both equations equal to each other to solve for x.

Add x to both sides to get 2x - 1 = 3
Add 1 to both sides to get 2x = 4
Divide both sides by 2 to get x = 2

Step #2: We found the x-coordinate, but we need to find the y-coordinate. We know that the x-coordinate is 2, so substitute the number 2 into any of the given equations. So, either into y = 3 - x or y = x - 1.

The point of intersection is (2,1).

Hope this helps ^_^

3 0

3 years ago