All we need to do is use FOIL here to multiply these.
(3x + 2)(3x^2 + 4)
9x^3 + 12x + 6x^2 + 8
Simplify.
Rearrange terms.
9x^3 + 6x^2 + 12x + 8 is the expanded form of the original binomials.
10+20+23 is 53. A sales tax of 7.2% is $3.82. 53+3.82 is $56.82
This item can be answered through the concept of fundamental principles of counting. In the first of the four digits, there are 10 possible digits. The same with all the other 3 places or digits of the code. That is,
n = 10 x 10 x 10 x 10
Giving us the answer of 10,000. Thus, there are 10,000 possible keys for the keyless entry.
consider the motion of the ball along the vertical direction
v₀ = initial velocity in vertical direction = 0 m/s (since the ball was thrown horizontally)
a = acceleration = acceleration due to gravity = 9.8 m/s²
Y = vertical displacement = height of the cliff = 123 m
t = time of travel
Using the kinematics equation
Y = v₀ t + (0.5) a t²
inserting the values
135 = (0) t + (0.5) (9.8) t²
t = 5.25 sec
consider the motion of the ball along the horizontal direction
v'₀ = initial velocity in horizontal direction = 18 m/s
a' = acceleration = 0 m/s²
X = horizontal displacement = ?
t = time of travel = 5.25 sec
Using the kinematics equation
X = v'₀ t + (0.5) a' t²
inserting the values
X = (18) (5.25) + (0.5) (0) t²
X = 94.5 m
