Answer:
P = 10x³ + 4x² + 8x + 6
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L+W) = 2((x³ +2x² -6x +12) +(4x³ +10x -9))
= 2(5x³ +2x² +4x +3) . . . . collect terms inside parentheses
P = 10x³ +4x² +8x +6
The approximate mass of the spherical weight is 51 pounds
To answer the question, we need to know what the mass of the sphere is
<h3>Mass of the sphere</h3>
The mass of the sphere m = ρV where
- ρ = density of steel = 0.284 lb/in³ and
- V = volume of sphere = 4πr³/3 where
- r = radius of sphere = 3.5 in
So, m = ρV
= ρ4πr³/3
Substituting the values of the variables into the equation, we have
m = ρ4πr³/3
= 0.284 lb/in³ × 4π(3.5 in)³/3
= 0.284 lb/in³ × 4π × 42.875 in³/3
= 48.706π lb/3
= 153.014 lb/3
= 51 lb
The approximate mass of the spherical weight is 51 pounds
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ANSWER
A) -1
EXPLANATION
The average rate of change of the given quadratic function on the interval 0 ≤ x ≤4 is the slope of the secant line connecting the points (0,f(0)) and (4,f(4)).
That is the average rate of change is:

From the graph, f(0) is 0 and f(4) is -4.
We plug in these values to obtain;

This simplifies to;


Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1
Answer:
36 minutes past 1, or 1:36
Step-by-step explanation:
A watch normally has an hour hand that does one revolution in 12 hours.
It takes 1 hour to go from the 1 o'clock position to the 2 o'clock position.
Since 1 hour equals 60 minutes, it takes 60 minutes to go from the 1 o'clock position to the 2 o'clock position.
The hour hand is 3/5 of the way from 1 to 2, so the number of minutes past 1 o'clock is 3/5 of 60 minutes.
3/5 of 60 minutes =
= 3/5 * 60 minutes
= 3/5 * 60/1 minutes
= 180/5 minutes
= 36 minutes
The time is 36 minutes past 1, or 1:36
Answer:
21
Step-by-step explanation:
27÷3 is 9 and 21÷3 is 7