The perimeter is:
P = 2x + 2y = 80
The area is:
A = x * y
The area as a function of a variable is:
A (x) = x * (40-x)
Rewriting we have:
A (x) = 40x-x ^ 2
We derive the function:
A '(x) = 40-2x
We equal zero and clear x:
40-2x = 0
2x = 40
x = 40/2
x = 20 feet
The other dimension is:
y = 40 - x
y = 40 - 20
y = 20 feet
The area will be:
A = x * y
A = 20 * 20
A = 400 feet ^ 2
Answer:
The dimensions are:
x = 20 feet
y = 20 feet
The area is:
A = 400 feet ^ 2
Answer:
22 inch is the diameter because d =2r
Answer:
The mass of the radioactive sample after 40 minutes is 12.8 g.
Step-by-step explanation:
The mass of the sample can be found by using the exponential decay equation:

Where:
N(t): is the amount of the sample at time t =?
N₀: is the initial quantity of the sample = 120 g
t = 40 min
λ: is the decay constant = 0.056 min⁻¹
Hence, the mass of the sample after 40 min is:

Therefore, the mass of the radioactive sample after 40 minutes is 12.8 g.
I hope it helps you!
Answer:
circle= 5, triangle= 3
Step-by-step explanation:
Please see attached picture for full solution.
Answer:
A'(-3,0), B'(0,-3) and C'(4,7)
Step-by-step explanation:
We are given that the vertices of triangle are A(0,-3), B(3,0) and C(-7,4).
We have to find the coordinates of the image of triangle under a rotation of 90° clockwise about the origin.
90° clockwise about the origin
Rule:
Using the rule
The coordinates of A'

The coordinates of B'

The coordinates of C'

Hence, the vertices of image of triangle is given by
A'(-3,0), B'(0,-3) and C'(4,7)