Look at picture because I cannot put square roots in

galben [10]

These are two questions and two answers.

Question 1) Which of the following polar equations is equivalent to the parametric equations below?

 x=t²
y=2t

Answer: option A.) r = 4cot(theta)csc(theta)


Explanation:

1) Polar coordinates ⇒ x = r cosθ and y = r sinθ

2) replace x and y in the parametric equations:

r cosθ = t²
r sinθ = 2t

3) work r sinθ = 2t

r sinθ/2 = t
(r sinθ / 2)² = t²

4) equal both expressions for t²

r cos θ = (r sin θ / 2 )²

5) simplify

r cos θ = r² (sin θ)² / 4

4 = r (sinθ)² / cos θ

r = 4 cosθ / (sinθ)²

r = 4 cot θ csc θ ↔ which is the option A.

Question 2) Which polar equation is equivalent to the parametric equations below?

 x=sin(theta)cos(theta)+cos(theta)
y=sin^2(theta)+sin(theta)

Answer: option B) r = sinθ + 1

Explanation:

1) Polar coordinates ⇒ x = r cosθ, and y = r sinθ

2) replace x and y in the parametric equations:

a) r cosθ = sin(θ)cos(θ)+cos(θ)
 b) r sinθ =sin²(θ)+sin(θ)

3) work both equations

a) r cosθ = sin(θ)cos(θ)+cos(θ) ⇒ r cosθ = cosθ [ sin θ + 1] ⇒ r = sinθ + 1

 b) r sinθ =sin²(θ)+sin(θ) ⇒ r sinθ = sinθ [sinθ + 1] ⇒ r = sinθ + 1


Therefore, the answer is r = sinθ + 1 which is the option B.

6 0

3 years ago

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Explain the level of uncertainties involve in concept of probability. The next generation of miniaturized wireless capsules with

RUDIKE [14]

Answer:

a) the probability that Both motors will operate satisfactorily in the capsule 0.6222

b) the probability that One motor will operate satisfactorily and the other will not is 0.3556

Step-by-step explanation:

Given that;

total number of motors N = 10

number of motors will not operate satisfactory m = 2

number of motors randomly selected n = 2

let X be number of motors will that will not operate successfully

here, X≅Hyper geometric (x; N,n,m)

The probability mass function of x is;

P (X = x)= { m } {N - m }

{x } {n - x}

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

{ N }

{ n }

a)

the probability that both motors will operate satisfactorily in the capsule i.e no motor will not operate satisfactory

so

P(X= 0) = { 2 } { 10 - 2 }

{0 } { 2 - 0}

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

{ 10 }

{ 2 }

so

P (X = 0) = { 2 } { 8}

{ 0 } { 2 }

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

{ 10 }

{ 2 }

p(P= 0)=1×28 / 45 = 28/45 = 0.6222

Therefore the probability that Both motors will operate satisfactorily in the capsule 0.6222

b)

the probability that one motor will operate satisfactorily and the other will not.

P(X=1) = { 2 } { 10 - 2 }

{ 1 } { 2 - 1 }

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

{ 10 }

{ 2 }

so

P(X=1) = { 2 } { 8 }

{ 1 } { 1 }

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

{ 10 }

{ 2 }

P(X=1) = 2×8 / 45 = 16/45 = 0.3556

Therefore the probability that One motor will operate satisfactorily and the other will not is 0.3556

3 0

3 years ago

Solve 6-2x=3 (bensjdkmenskkw)

Kamila [148]

Answer:

answer: 4.5

Step-by-step explanation:

2x=3+6

2x=9

x=9/2

x=4.5

5 0

3 years ago

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What is the common difference between the terms in the following sequence?

Ipatiy [6.2K]

Answer:

-6

Step-by-step explanation:

17-6=11

11-6=5

5-6=-1

-1-6=-7

6 0

2 years ago

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Pls check the attachment :) f(x)=x^5-9x^3

Galina-37 [17]

Answer:

As x —> negative infinity, f(x) —> negative infinity

As x —> positive infinity, f(x) —> positive infinity.

Step-by-step explanation:

$y = {x}^{5} - 9 {x}^{3}$

An odd-degree function, meaning that the graph starts from negative infinity at x —> negative infinity and positive infinity at x —> positive infinity.

As x —> negative infinity, f(x) —> negative infinity

As x —> positive infinity, f(x) —> positive infinity.

An odd-degree function is an one-to-one function so whenever x approaches positive, f(x) will also approach positive.

5 0

3 years ago