15 points: a motorboat traveling downstream covers the distance between port m and port n in 6 hours. once, the motorboat stopped 40 km before reaching n, turned around, and returned to m. this took the motorboat 9 hours. find the speed of the motorboat in still water if the speed of the current is 2 km/hour.

S=18

Step-by-step explanation:

D = distance between M and N  

S = speed of the boat  

S + 2 = speed down streem  

S - 2 = speed upstream  

T = time on the downstream leg until the boat made its turn  

9-T= time on the upstream leg  

6(S + 2) = D  

T (S + 2) = D - 40  

(9-T)(S-2) = D - 40  

now we have 3 equations and 3 uknowns  

lets multply everything out  

6S + 12 = D  

ST + 2T = D - 40  

9S - 18 - ST + 2T = D - 40  

add the second 2 together to get rid of the ST term  

9S - 18 + 4T = 2D - 80  

and lest subtract them from one annother  

2ST - 9S + 18 = 0  

if we can find T in terms of S we will have a quadratic equation, and will be able to use the quadratic formula / factor

9S - 18 + 4T = 2(6S + 12) - 80  

9S - 18 + 4T = 12 S + 24 - 80  

4T = 3S - 38  

T = 0.75 S - 9.5  

2S(0.75 S - 9.5) - 9S + 18 = 0  

1.5 S^2 - 28 S + 18 = 0  

S = 18, 2/3  

now it doesn't make sense for S to equal -2/3 as it suggests the boat moves backward when it is going up stream. (and that it travels downstream for negative time)  

S = 18

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: