Answer:
49 cm²/s
Step-by-step explanation:
The problem statement tells you what to do.
Write an equation relating A, b, h:
A = bh . . . . . . the equation for the area of a rectangle
Differentiate with respect to t:
dA/dt = (db/dt)h + b(dh/dt) . . . . . . . product rule
To find the rate of change after 18 seconds, you need to know the dimensions b and h after 18 seconds. Since each dimension was increasing at the rate of 1 cm/s, it is 18 cm more than it was at the beginning:
At 18 seconds,
b = 6 cm + 18 cm = 24 cm;
h = 7 cm + 18 cm = 25 cm.
Of course, db/dt = dh/dt = 1 cm/s. Then the rate of change of area is ...
dA/dt = (1 cm/s)(25 cm) + (24 cm)(1 cm/s)
dA/dt = 49 cm²/s
_____
You could write a formula for the area as a function of time and differentiate that:
A = (6 +t)(7 +t) = 42 + 13t + t²
Then the derivative is ...
dA/dt = 13 +2t
and when t=18, this is ...
dA/dt = 13 + 2(18) = 49 . . . . cm²/s
Provided the 2% interest rate. The interest itself over a period of 4 years, compounds to $300. Thus, the total interest plus the cost of the fitness equipment would be a total of, $4,050.
(3^3)* (3^-3)= 3^0
Remember that if you have the same base, add the exponents.
3^0=1
5(1)=5
Final answer: 5
1.
The first transformation, the translation 4 units down, can be described with the following symbols:
(x, y) → (x, y-4).
as the points are shifted 4 units vertically, down. Thus the x-coordinates of the points do not change.
A'(1, 1) → A"(1, 1-4)=A"(1, -3).
B'(2, 3) → B"(2, 3-4)=B"(2, -1).
C'(5, 0) → C"(5, 0-4)=C"(5, -4).
2.
The second transformation can be described with:
(x, y) → (x, -y).
as a reflection with respect to the x-axis maps:
for example, (5, -7) to (5, 7), or (-3, -4) to (-3, 4)
thus, under this transformation A", B", C" are mapped to A', B' and C' as follows:
A"(1, -3)→A'(1, -(-3))=A'(1, 3)
B"(2, -1)→B'(2, -(-1))=B'(2, 1)
C"(5, -4)→C'(5, -(-4))=C'(5, 4)
Answer:
A'(1, 3), B'(2, 1), C'(5, 4)
