"If you have 2 pieces of spaghetti that have lengths 4 cm and 10 cm, what could be the possible length of a third piece of spagh
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Answer:
a) see below
b) 32 minutes after turn-on
c) 52 minutes after turn-on
d) 20 minutes
e) 6856.6 ft²
Step-by-step explanation:
a) We have elected to put the origin at the point where the hose crosses the south edge of the sidewalk. Units are feet. Then the sprinkler starts at (0, -100). After 1 hour, 3600 seconds, the sprinkler is 1800 inches, or 150 ft north of where it started, so stops at (0, 50).
The lines forming the sidewalk boundaries are y=0 and y=10.
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b) Water will first strike the sidewalk when the sprinkler is 20 feet south of it, or 80 feet north of where it started. The sprinkler travels that distance in ...
(80 ft)(12 in/ft)/(1/2 in/s)(1 min/(60 s)) = 32 min . . . time to start sprinkling sidewalk
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c) The sprinkler has to travel to a point 130 ft north of its starting position for the water to fall north of the sidewalk. That distance is traveled in ...
(130 ft)(2/5 min/ft) = 52 min . . . time until end of sprinkling sidewalk
Note that we have combined the scale factors in the expression of part b into one scale factor of (2/5 min/ft).
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d) The difference of times in parts b and c is the time water falls on the sidewalk: 20 minutes.
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e) In one hour, the sprinkler travels a distance of ...
(60 min)(5/2 ft/min) = 150 ft
Of that distance, 10 feet is sidewalk. So, the sprinkler covers an area of grass that is a 140 ft by 40 ft rectangle and a circle of 20 ft radius. The total area of that is ...
A = LW + πr² = (140 ft)(40 ft) +π(20 ft)² = (14+π)(400) ft² ≈ 6856.6 ft²
The area of grass watered in 1 hour is about 6856.6 ft².
Answer:
A ( t ) = -4t + 51
B ( t ) = -2t + 29
t < 11 hours ... [ 0 , 11 ]
Step-by-step explanation:
Given:-
- The height of snowman A, Ao = 51 in
- The height of snowman B, Bo = 29 in
Solution:-
- The day Mason made two snowmans ( A and B ) with their respective heights ( A(t) and B(t) ) will be considered as the initial value of the following ordinary differential equation.
- To construct two first order Linear ODEs we will consider the rate of change in heights of each snowman from the following day.
- The rate of change of snowman A's height ( A ) is:
- The rate of change of snowman B's height ( B ) is:
Where,
t: The time in hours from the start of melting process.
- We will separate the variables and integrate both of the ODEs as follows:
- Evaluate the constant of integration ( c ) for each solution to ODE using the initial values given: A ( 0 ) = Ao = 51 in and B ( 0 ) = Bo = 29 in:
- The solution to the differential equations are as follows:
A ( t ) = -4t + 51
B ( t ) = -2t + 29
- To determine the time domain over which the snowman A height A ( t ) is greater than snowman B height B ( t ). We will set up an inequality as follows:
A ( t ) > B ( t )
-4t + 51 > -2t + 29
2t < 22
t < 11 hours
- The time domain over which snowman A' height is greater than snowman B' height is given by the following notation:
Answer: [ 0 , 11 ]