Answer:
Speed of boat in still water = 64 km/hr
Speed of the current = 11 km/hr
Step-by-step explanation:
Let the speed of motorboat in still water = x km/hr
Let the speed of current = y km/hr
Motorboat travels 371 km in 7 hours going upstream.
Speed of motorboat while going upstream = speed of motorboat in still water - speed of current = (x-y)
=> ![\[x-y = \frac{371}{7}\]](https://tex.z-dn.net/?f=%5C%5Bx-y%20%3D%20%5Cfrac%7B371%7D%7B7%7D%5C%5D)
=> ![\[x-y = 53\]](https://tex.z-dn.net/?f=%5C%5Bx-y%20%3D%2053%5C%5D)
------------------------------(1)
Motorboat travels 525 km in 7 hours going downstream.
Speed of motorboat while going downstream = speed of motorboat in still water + speed of current = (x+y)
=> ![\[x+y = \frac{525}{7}\]](https://tex.z-dn.net/?f=%5C%5Bx%2By%20%3D%20%5Cfrac%7B525%7D%7B7%7D%5C%5D)
=> ![\[x+y = 75\]](https://tex.z-dn.net/?f=%5C%5Bx%2By%20%3D%2075%5C%5D)
-----------------------------(2)
Solving for x and y from (1) and (2):
Adding (1) and (2):
2x = 128
=> x = 64
Substituting the value of x in (1), y = 11
Step-by-step explanation:
Option D is the correct answer because we will cross multiply
4/6 = 9/x
4x = 54
X = 27/2
Answer:
See below
Step-by-step explanation:
<em>Vector argument</em>
Vector DF is (5, -4) - (5, 5) = (0, -9).
Vector EG is (2, 2) - (8, 2) = (-6, 0).
The dot-product of these two vector is (0, -9)•(-6, 0) = 0·(-6) + (-9)·0 = 0.
When the dot-product of two vectors is zero, those vectors are at right-angles to each other. Therefore diagaonal DF ⊥ diagonal EG.
_____
<em>Alternate argument</em>
The x-coordinates of points D and F are the same, so diagonal DF is a vertical line. The y-coordinates of points E and G are the same, so diagonal EG is a horizontal line. Vertical lines are perpendicular to horizontal lines, so DF ⊥ EG.
Answer:
No.
Step-by-step explanation:
The numbers aren't going up at a constant rate. Say each lap costs 2 dollars. On lap 4, you have paid 8 dollars total. On lap 9, you have paid 18 dollars total. But the 10th lap is free, which means you pay 0 dollars. In order for this pattern to be constant, you would need to pay 20 dollars, but instead you pay 0.
