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marin [14]
1 year ago
13

Which equation can be used to solve for x in the triangle below?

Mathematics
1 answer:
belka [17]1 year ago
4 0

Using the cosine rule, the equation to use to solve for x is: x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41)) ≈ 3.1 cm.

<h3>How to Use the Cosines Rule to Solve a Triangle?</h3>

The cosine rule is given as, c = √(a² + b² − 2ab × cos(C))

Given the following:

  • c = x = ?
  • a = 4.0 cm
  • b = 4.7 cm
  • C = 41°

Plug in the values:

x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41))

x ≈ 3.1 cm

Learn more about the cosine rule on:

brainly.com/question/23720007

#SPJ1

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Trevor is swimming laps to raise money for the local food bank. He earns $1.85 per lap and has already swum 23 laps.
Studentka2010 [4]

Answer: L greater than 31

Step-by-step explanation:

Trevor is swimming laps to raise at over 100 dollars for the local food bank. He earns $1.85 per lap and has already swum 23 laps.

This means that the total amount that he has raised is number of laps that he has swum × the amount he earns per lap. Therefore,

Amount that he has already raised

= 1.85 × 23 = $42.55

100 - 42.55 = 57.45

He still needs to raise an amount greater than $57.45

To raise this amount, he needs to swim more laps. Number of laps that he needs to swim will be

57.45/1.85 = 31.05

Approximately 31 laps

Let the number of laps that he needs to swim be L

The inequality to show how many more laps Trevor needs to swim in order to raise more than $100 will be

L greater than 31

4 0
3 years ago
Convert from rectangular to polar coordinates:Note: Choose r and θ such that r is non-negative and 0 ≤ θ &lt; 2πa. (6,0)b. (9,9/
Anuta_ua [19.1K]

Answer:

The polar coordinates are as follow:

a. (6,2π)

b. (18, π/3)

c. (2√2 , 3π/4)

d. (2, 5π /6)

Step-by-step explanation:

To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .

To calculate r, we use Pythagorean theorem:

r = \sqrt{ x^{2} +y^{2} } ---- (1)

To calculate the θ, first we will find out the θ '  using the inverse of cosine as it is easy to calculate.

So,    θ '  = cos ⁻¹  (x/r)

If  y  ≥  0  then  θ  =  ∅

If  y  <  0  then  θ  =  2 π  −  ∅

For a. (6,0)

Sol:

Using the formula in equation (1). we get the value of r as:

r = \sqrt{6^{2} + 0^{2}  }

r = 6

And ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (6/6)

∅  =cos ⁻¹   (1) = 2π

As If  y  ≥  0  then  θ  =  ∅

So ∅ = 2π

The polar coordinates are (6,2π)

For a. (9,9/\sqrt{3})

Sol:

r = 9 + 3(3) = 18

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (9/18)

∅ = cos ⁻¹   (1/2) = π/3

As  If  y  ≥  0  then  θ  =  ∅

then θ  = π/3

The polar coordinates are (18, π/3)

For (-2,2)

Sol:

r =√( (-2)²+(2)² )

r = 2 √2

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (-2/ 2 √2)

∅ = 3π/4

As  If  y  ≥  0  then  θ  =  ∅

then   θ  = 3π/4

The polar coordinates are (2√2 , 3π/4)

For (-√3, 1)

Sol:

r = √ ((-√3)² + 1²)

r = 2

and ∅  = cos ⁻¹  (x/r)

∅  = cos ⁻¹ ( -√3/2)

∅  = 5π /6

As  If  y  ≥  0  then  θ  =  ∅

So  θ  = 5π /6

The polar coordinates are (2, 5π /6)

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