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<h2>Answer:</h2>
55°
<h2> Step-by-step explanation:</h2>To solve this, follow these steps:
i. <em>Make a sketch of the problem</em>.
The sketch has been attached to this response.
ii. <em>Label the sketch properly</em>
As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).
iii. <em>Solve using the tangent trigonometric ratio</em>
With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being 5 units and 7 units respectively.
Using the tangent formula,
tan θ = opposite / adjacent
tan θ = 7 / 5
θ = tan⁻¹ (7/5)
θ = tan⁻¹ (1.4)
θ = 54.46
θ = 55° to the nearest integer.
Therefore, the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°
Answer: Simple interest rate = 3%.
Step-by-step explanation: We are given invested amount = $5000.
Number of years of investment = 4 years.
Interest earned = $600.
Simple interest formula.
I = P R T.
Where I is the earned interest, P is the invested amount , R is the rate of interest and T is the time in years.
Plugging values in formula, we get
600 = 5000 × R × 4
600 = 20000R.
Dividing both sides by 20000, we get
0.03 = R.
Multiplying by 100 to convert it in percentage, we get
0.03 × 100 = R
R = 3 %.