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andreyandreev [35.5K]
2 years ago
6

Write the equation if this line below​

Mathematics
1 answer:
Alexxandr [17]2 years ago
8 0

Answer:

Step-by-step explanation:

The first step to finding the equation of this line we must find two points that are on this line.

Two points on the lines are (0,3) and (1,0).

Now we must find the slope:

   slope = \frac{y2-y1}{x2-x1}  = \frac{3 - 0}{0-1} =-3

Now after finding the slope which is -3, now let us put it into the point-slope form using the point (0,3) which is also on the line. You could also use (1,0) in this case, but I am using (0,3).

y-3 = -3(x-0)\\y=-3x +3

Thus the equation is y=-3x +3

Hope that helps!

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2nd term:48.75

3rd term:49.6875

4th term:49.921875

B) Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)

Step-by-step explanation:

We are given;

h₀ = Initial height of the ball = 30

r = Rebound fraction = 0.25

a) The arithmetic sequence of bouncing balls is given by the following;

Sₙ=h₀+2h₀(r¹+r²+r³+r⁴.........rⁿ)

The first term of the sequence is;

S₁ = h₀ + 2h₀r¹

S₁ = 30 + (2 × 30 × 0.25)

S₁ = 45

The second term of the sequence is;

S₂ = h₀ + 2h₀(r¹+r²)

S₂ = 30 + (2 × 30 × (0.25 + 0.25²)) = 48.75

The third term of the sequence is;

S₃ = h₀ + 2h₀(r¹ + r² + r³) = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³)) = 49.6875

S₄ = h₀ + 2h₀(r¹ + r² + r³ + r⁴)

S₄ = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³ + 0.25⁴)) = 49.921875

B) The general expression for the nth term of the sequence is;

Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)

4 0
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