Answer:
1. push 2. machine 3. gravity 4. balance 5. energy. 6 force 7. pull 8. friction 9. newtons 10. inertia
Step-by-step explanation:
Answer: if there had been no current, the rate would have been 4 km/hr.
The rate of the current is 1.5km/hr
Step-by-step explanation:
Let x represent the speed of the boat in still water.
Let y represent the speed of the current.
Impeded by the current the outing club took 4 hours and 24 minutes(4 + 24/60 = 4.4 hours) to paddle 11 km up the exeter river to their campsite last weekend. This means that the total speed with which they travelled is (x - y) km/h
Distance = speed × time. Therefore
11 = 4.4(x - y)
Dividing through by 4.4, it becomes
2.5 = x - y - - - - - - - - - - -1
The next day the same current was with them and it took only 2 hours to make the return trip to campus. This means that the total speed with which they travelled is (x + y) km/h. The distance travelled is
11 = 2(x + y)
Dividing through by 2, it becomes
5.5 = x + y - - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
8 = 2x
x = 8/2 = 4
Substituting x = 4 into equation 1, it becomes
2.5 = 4 - y
y = 4 - 2.5
y = 1.5
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>
By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
- a - Length of the major semiaxis.
- b - Length of the minor semiaxis.
Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
To learn more on ellipses: brainly.com/question/14281133
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