Answer:
You can do this without the calculator
115 grams
after 1 half-life = 115 / 2 = 57.5 grams
after 2 half-lives = 28.75 grams
after 3 half-lives = 14.375 grams
after 4 half-lives = 7.1875 grams
after 5 half-lives = 3.59375 grams
after 6 half-lives = 1.796875 grams
Step-by-step explanation:
Answer:
20m by 80m
Step-by-step explanation:
Let the dimension of the garden be x by y
The garden is fenced on three sides with a perimeter of 120m
Perimeter of the three sides = 2x+y
Therefore:
The Area of the garden = 
From the first equation, y=120-2x
Substitute y=120-2x into xy=1600
xy=1600
x(120-2x)=1600
Recall,
xy=1600
When x=20, 20y=1600===>y=80
When x=40, 40y=1600===>y=40
So we have the pair (20,80) and (40,40).
However since we are told that the garden is rectangular, we pick the dimension with unequal sides.
The dimension of the garden is 20m by 80m.
Answer: 101.6 ft/min
Step-by-step explanation:
let x be the horizontal distance to the dock. And the rope is attached to the boat 10 feet below the pulley
Using pythagorean theorem
x^2=R^2-10^2
where R is rope length to the pulley.
Differentiates with respect to time t
2x dx/dt=2RdR/dt
Xdx/dt = RdR/dt ...... (1)
If the boat be approaching the dock when 125 ft of rope is out
This is R = 125ft
Using pythagorean theorem again
X^2 = R^2 - 10^2
X^2 = 125^2 - 10^2
X^2 = 15525
X = 124.6 ft
The rate the boat be approaching the dock = dx/dt
While
the rope is pulled through the pulley at a rate of 20 ft/min = dR/dt
Solve for dx/dt when R is 125, x= 124.6 and dR/dt= 20ft/min
Substitute all in equation 1
124.6 dx/dt = 125 × 20
dx/dt = 2500/124.6
dx/dt = 101.6 ft/min
