Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
Answer:
B
Step-by-step explanation:
6 times 50 = 300
6 times 2 = 12
300 + 12 = 312
6 times 52 = 312
Answer: 5503680
Step-by-step explanation:
The coach wants 2 senior out of 36 so he have
C₃₆,₂ = 36!/( 36 - 2 )! = 36*35*34!/34! = 36 * 35 = 1260
possibilities
Now he also wants 3 juniors out of 14
C₁₄,₃ = 14!/ (14- 3)! = 14*13*12*11!/11! = 14*13*12 = 2184
Now for each pair of senior (from 1260 outcomes) coach has 2184 possiblities therefore
Coach has
2184 * 1260 = 2751840 possibilities to choose from
Again as there are 2 senior to choose for captain we have to multiply by 2 to get the total ways the team could be
2751840*2 = 5503680
Answer:
64m^3
Step-by-step explanation:
The volume of a cube formula is side^3.
Using that formula, we get 64 meters cubed as the answer.
The formula for the volume of cylinder is pi*r^2*h.
What is the radius and what is the height?
Answer:
I think it is 7.6
the square root of 58 is 7.6
7.6 x2 = y y/2= 7.6 again
