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:
Step-by-step explanation:-8
Answer:
y = 
x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 7 ← is in slope- intercept form
with m =
Parallel lines have equal slopes, thus
y = x + c ← is the partial equation
To find c substitute (3, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 2 - 1 = - 3
y = x - 3 ← equation of line
Answer:
$740.00
Step-by-step explanation:
85% of x is 629
Translate into algebra. Use a decimal in place of the percent:
.85x = 629
Divide by .85
x = 740
This answer makes sense because the regular price should be a little higher than the sale price. If they are paying 85% they're only getting 15% off.
Check:
740×.85 = 629
Answer:
$150012.84 or $150013 rounded
The growth factor is 1.07
Step-by-step explanation:
First create the equation:
y=1.07x+150,000
Then substitute:
y=1.07(12)+150,000
Calculate:
y=150012.84
