Let x be rate of boat in still water
let y be rate of current
we use this equation to relate quantities:
distance = speed · time
we have two unknowns so we might need to create a system of equationss
upstream:
speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)
time = 3 hours
distance = 144 km
downstream:
speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)
time = 2 hours
distance = 144 km (same distance upstream and downstream)
using distance = speed times time
for upstream
144 = 3(x-y)
144 = 3x - 3y
for downstream
144 = 2(x+y)
72 = x + y
system of eqns:
144 = 3x - 3y
72 = x + y
solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x
144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h
Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h
rate of boat in still water is 60 km/h
rate of the current is 12 km/h
Answer:
10 seconds
Step-by-step explanation:
using the formula we can see that since 30 seconds have passed we divide this by 3 to get 10.
Therefore the answer is 10 seconds
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For the given function, we have:
Domain: (-∞, ∞)
Range: [-2, ∞)
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How to find the domain and range of the given function?</h3>
Remember that for a function the domain is the set of the possible inputs while the range is the set of the outputs.
On the graph, we can see a quadratic equation, remember that for every polynomial the domain is the set of all the real values, the same is for this case, so we conclude that the domain is:
D: (-∞, ∞)
The range will be the set of all values larger than the minimum of the parabola, which is at the vertex.
On the graph, we can see that the minimum is y = -2, then the range is:
R: [-2, ∞)
If you want to learn more about range and domains:
brainly.com/question/10197594
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Answer:
angleQ+angleR is 180degrees because of the properties of isoceles trapezoid. So, if you set equation and solve, you'll get the fact that x is 12, and angleR is 130degrees, and angleQ is 50degrees. According to the properties of isoceles trapezoid, angleQ is the same as angleT. So, angleT is 50degrees
