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2 years ago

Need the answer to number 4

Mathematics

2 answers:

Dvinal [7]2 years ago

5 0

Answer:

$\sqrt{85}$ /2

Step-by-step explanation:

lets find hypotenuse( longest side) first

let other two samller sides be a and b and hypotenuse be c

pythagorsd theorem

a^2 + b^2 =c^2

9^2 + 2^2 =c^2

81 + 4=c^2

85 =c^2

$\sqrt{85}$ =c

take theta as reference angle

cosec theta=hypotenuse/opposite

= $\sqrt{85}$ / 2

Ymorist [56]2 years ago

5 0

Answer:

Answer is B. CSC ∅ = √85 /2

Step-by-step explanation:

CSC = 1 / Sin ∅

So first find Sin ∅ = 2 / √ 85 and then substitute in the formula

And oh, in case you're wondering, √ 85 is the hypotenuse side which you find like this:

√ 9² + 2²

√ 81 + 4

√ 85

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What complex number is represented by the polar coordinates (4, -pi/4)

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Answer:

$\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

$\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}$

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

$\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Hence, the complex number that has polar coordinate of (4,-45°) is $\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

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Answer:

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Step-by-step explanation:

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The number of accidents per week can be treated as a Poisson distribution.

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