Answer:
15 hip hop performances
12 ballet performances
Step-by-step explanation:
5:4 (multiply by 3)
15:12
Answer:
y=3/4x-3
Step-by-step explanation:
Okay so to be parallel to an equation of another line, the line must have the same slope but a different y-intercept. First, you need to find the slope of the equation -3x+4y=4. The equation must be in y=mx+b format, so you first move -3x to the right by adding it on both sides, leaving you with 4y=3x+4. Next, you divide 4y by 4 in order to isolate y and do that on the other side. Now, you have y=3/4x+1.
To find the equation of the new line, you must put the point and slope into point slope form: y-y1=m(x-x1). In the point (4, 0), 4 would be x1 and 0 would be y1. so, the new equation is y-0=3/4 (x-4). now, distrubute the 3/4, leaving you with y=3/4x-3. This is correct since the slope remains the same in both equations with a different y-intercept. To check deeper, you could place point (4, 0) on a graph and then rise 3, run 4 until you get the line :) hope this helps
Answer:
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Step-by-step explanation:
Arc length of a parametric curve is:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
x = t + cos t, dx/dt = 1 − sin t
y = t − sin t, dy/dt = 1 − cos t
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Or, if you wish to simplify:
L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt
L = ∫₀²ᵖⁱ √(3 − 2 sin t − 2 cos t) dt
Answer:
√2' = t
Step-by-step explanation:
1 1/2s = 3/5t^2 + 1/3u^2; substitute known values
1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify
42 = 3 • t^2 ÷ 5 + 1/3 • 36
42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality
42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify
30 = 3t^2 ÷ 5; apply property of multiplication of equality
30 • 5 = 3t^2 ÷ 5 • 5; simplify
6 = 3t^2; apply property of division of equality
6 ÷ 3 = 3t^2 ÷ 3; simplify
2 = t^2
√2' = t
