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Gre4nikov [31]
3 years ago
5

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=

Mathematics
1 answer:
lys-0071 [83]3 years ago
7 0

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}

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1/2 (-2-1) +6(5) +6(8) + (3) - (-4)6-(-1)6-5(0) -8(-5) =<br> 150.
alina1380 [7]
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5 0
3 years ago
The Carson family sent 500 text messages last month. Mrs. Carson sent 15 text messages; Mr. Carson sent 1; Cathi sent 104; and B
Llana [10]

Answer:

76%

Step-by-step explanation:

pls mark brainliest!

3 0
3 years ago
angel's dad bought a television for her completing all of her digital learning day lesson. he want to warp the gift. the box mea
atroni [7]

Answer: 13 sheets of paper

Step-by-step explanation:

We are given the dimensions of the box and the wrap paper:

Box:

(56 in)(8 in)(36 in)

Warp paper:

(26 in)(17 in)

Now we need to find the surface area of the box and the area of the wrap paper:

Box:

surface_{1}=(56 in)(8 in)(2)=896 in^{2}

surface_{2}=(8 in)(36 in)(2)=576 in^{2}

surface_{3}=(56 in)(36 in)(2)=4032 in^{2}

surface-area=896 in^{2}+576 in^{2}+4032 in^{2}=5504 in^{2}

Warp paper:

area=(26 in)(17 in)=442 in^{2}

Dividing the area of the box by the area of the paper:

\frac{surface-area}{area}=\frac{5504 in^{2}}{442 in^{2}}=12.45 \approx 13

This means Angel's dad needs to purchase 13 sheets of wrapping paper.

4 0
3 years ago
Sara has 24 sweets
Tresset [83]
<h2>Hello!</h2>

The answer is:

The expression for the number of sweets that Sara and Tim have now, are:

Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

<h2>Why?</h2>

To write the expressions for the number of sweets that Sara and Tim have now, we need to follow the next steps:

Sara starts with 24 sweets and Tim starts with 24 sweets

Sara=24 Sweets\\Tim=24 Sweets

Then, Sara gives Tim x Sweets

Sara=(24-x)Sweets\\Tim=(24+x)Sweets

Then. Sara eats 7 of her Sweets

Sara=(24-x-7) Sweets\\Sara=(17-x )Sweets\\Tim=(24+x) Sweets

Then, Tim eats half of his sweets

Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

So, the expression for the number of sweets that Sara and Tim have now, are:

Sara=(17-x) Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

Have a nice day!

8 0
3 years ago
The parents club wants to sell buttons to raise money for the local community center sports program. The buttons cost 60 cents e
astraxan [27]

Their profit made will be 4,420

This is because 0.60 x 1300 is 780

And the amount they will make by selling is $5200, because 1300 x 4

So we will do 5200 - 780, and that is the profit made- $4,420

3 0
3 years ago
Read 2 more answers
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