<span>x = child ticket price
y = adult ticket price
5x+3y=52 the cost accounting for the first group.
3x+2y=38 the cost accounting for the second group.
Child price: 5$
Adult price: 9$</span>
Answer:
M = 1/0.000121 = 8264.5 years
Step-by-step explanation:
M = − k ∫∞₀ teᵏᵗdt
To obtain this mean life, we'll use integration by parts to integrate the function ∫ teᵏᵗdt
∫udv = uv - ∫ vdu
u = t
du/dt = 1
du = dt
∫ dv = ∫ eᵏᵗdt
v = eᵏᵗ/k
∫udv = ∫ teᵏᵗdt
uv = teᵏᵗ/k
∫ vdu = eᵏᵗ/k
∫ teᵏᵗdt = (teᵏᵗ/k) - ∫eᵏᵗ/k
But, ∫eᵏᵗ/k = (1/k) ∫eᵏᵗ = (1/k²) eᵏᵗ = eᵏᵗ/k²
∫ teᵏᵗdt = (teᵏᵗ/k) - eᵏᵗ/k²
The rest of the calculation is done on paper in the image attached to this question
<span>it depends how the interest is calculated, but there's not much of a difference
assuming its continuously compouned, you use this formula: A(t)=Pe^(rt), where A is the final amount, P is the initial investment, r is the interest, and t is the time in years
you want to find t such that A(t)=18,600 so 18,600=1000e^(.0675t)
you need to use logarithm to figure it out, take the natural log of both sides
the following properties will come into use:
ln(a*b)=ln(a)+ln(b)
ln(a^b)=bln(a)
ln(e)=1
taking the natural log
ln(18,600)=ln(1000e^(.0675t))
ln(18,600)=ln(1000)+ln(e^.0675t)
ln(18600)=ln(1000) + .0675t
now solve for t: t= (ln(18600)-ln(1000))/.0675
t=43.31</span>
A ray in mathematics starts at a point and extends infinitely in one direction away from that point
it differes from a line because a line extend indefinitely in both directions
the sun ray starts from the sun and does not pass through the sun so it starts from a point (the sun's surface) and extends indefinitely into space unless it hits something (planets, black holes, endpoint)
