Math help please.. number 13

Mathematics

1 answer:

Lerok [7]3 years ago

4 0

Use the Law of Cosines here with angle A as your reference angle. It will be the one that the helicopter is at, the one we are looking for. If that angle is angle A, then the side across from it is a, measure of 11.4. Here's how the Law looks in our particular situation: $(11.4) ^{2}=(7.4) ^{2} +(8.5)^2-2(7.4)(8.5)cos(A)$ . Simplifying a bit we get 129.96 = 54.76 + 72.25 - 125.8cos(A) Combining like terms across the equals sign gives us 2.95 = -125.8 cosA. Doing the division we get -.0234499205 = cosA. Find the angle using the 2nd and cos buttons on your calculator. It's 91.34°, rounded to just 91°. Choice A

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Yanka [14]

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Step-by-step explanation:

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6 0

3 years ago

What are the types of roots of the equation below? - 81=0

Tju [1.3M]

Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0. This can be obtained by finding root of the equation using algebraic identity.

<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,

⇒ x⁴ - 81 = 0

⇒ (x² + 9)(x² - 9) = 0

(x² - 9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

⇒ [x² - 3x + 3x - 9][x² - 3xi + 3xi - 9i²] = 0

⇒ (x² +0x - 9)(x² +0xi - 9(- 1)) = 0

⇒ (x² - 9)(x² + 9) = 0

⇒ x⁴ - 9x² + 9x² - 81 = 0

⇒ x⁴ - 81 = 0

Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

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5 0

1 year ago

Point O is the incenter of ΔABC. What is mQBO? mQBO is ___ degrees.