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11111nata11111 [884]
2 years ago
9

Show that the following rectangular form x^2+y^2=2xy can be expressed as 1 = sin(2) in polar form.

Mathematics
1 answer:
lara [203]2 years ago
7 0

Answer:

Step-by-step explanation:

substitute x = r*cos(θ), y = r*sin(θ) ==> r²(cos²(θ) + sin²(θ)) = 2r²cos(θ)sin(θ). Cancel the r² on both sides. On the left, use pythagorean identity cos²(θ) + sin²(θ) = 1. On the right apply double angle identity sin(2θ) = 2cos(θ)sin(θ).

This yields 1=sin(2θ). (I assume you meant to type sin(2θ) on the right hand side of the equation).

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if a pound of grapes cost $0.14 in 1960 and the price of grapes increased at the same rate as the CPI from 1960 to 1980 by appro
masya89 [10]

The CPI increased from 29.6 to 82.4.  

The rate of increase, is:

82.4/29.6 = 2.78

Now multiply this rate to the $0.14 price of grapes from 1960.

$0.14 x 2.78 = $0.39

Now to get the amount of increase subtract the new price from the original price:

$0.39 - $0.14 = $0.25 increase.

5 0
3 years ago
In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the
earnstyle [38]

Answer:

(a) The probability that at least one of these components will need repair within 1 year is 0.0278.

(b) The probability that exactly one of these component will need repair within 1 year is 0.0277.

Step-by-step explanation:

Denote the events as follows:

<em>A</em> = video components need repair within 1 year

<em>B</em> = electronic components need repair within 1 year

<em>C</em> = audio components need repair within 1 year

The information provided is:

P (A) = 0.02

P (B) = 0.007

P (C) = 0.001

The events <em>A</em>, <em>B</em> and <em>C</em> are independent.

(a)

Compute the probability that at least one of these components will need repair within 1 year as follows:

P (At least 1 component needs repair)

= 1 - P (No component needs repair)

=1-P(A^{c}\cap B^{c}\cap C^{c})\\=1-[P(A^{c})\times P(B^{c})\times P(C^{c})]\\=1-[(1-0.02)\times (1-0.007)\times (1-0.001)]\\=1-0.97216686\\=0.02783314\\\approx 0.0278

Thus, the probability that at least one of these components will need repair within 1 year is 0.0278.

(b)

Compute the probability that exactly one of these component will need repair within 1 year as follows:

P (Exactly 1 component needs repair)

= P (A or B or C)

=P(A\cap B^{c}\cap C^{c})+P(A^{c}\cap B\cap C^{c})+P(A^{c}\cap B^{c}\cap C)\\=[0.02\times (1-0.007)\times (1-0.001)]+[(1-0.02)\times 0.007\times (1-0.001)]\\+[(1-0.02)\times (1-0.007)\times 0.001]\\=0.02766642\\\approx 0.0277

Thus, the probability that exactly one of these component will need repair within 1 year is 0.0277.

7 0
2 years ago
X + y = -15<br> rewrite in y=mx+b
diamong [38]

Answer:

y = -x - 15

Step-by-step explanation:

x + y = -15

-x        -x

y = -x - 15

:3

5 0
2 years ago
Question 15
borishaifa [10]
A is the answer I think
3 0
2 years ago
Read 2 more answers
I need help solving this question with explaining please <br> ANSWER ASAP!!!!!!!!!
andrew11 [14]

x = 85 degrees and

y = 45 degrees.

Step-by-step explanation:

Step 1:

The angle for a straight line is 180°. The sum of the angles in a triangle is 180°. These two statements are required to solve this problem.

The angles of x° and 95° are on a single straight line.

So x^{\circ} + 95^{\circ} = 180^{\circ}.

x^{\circ} = 180^{\circ} - 95^{\circ} = 85^{\circ} .

So the angle of x is 85°.

Step 2:

The sum of the angles in a triangle is 180°.

So 50^{\circ} + x^{\circ} + y^{\circ} =180^{\circ}.

50^{\circ} + 85^{\circ} + y^{\circ} =180^{\circ}.

y^{\circ} =180^{\circ} - 135^{\circ}, y = 45 ^{\circ}.

So the angle of y is 45°.

6 0
3 years ago
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