sum of the 5th and 10th terms of an arithmetic sequence which are equal to the 20th term (80). find the 30th term
1 answer:
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Answer:
<em>It will take 12 hours to fill the tank</em>
Step-by-step explanation:
Proportions
Tap A fills a tank in 4 hours. It means each hour it fills 1/4 of the tank.
Tap B fills the tank in 3 hours. Each hour it fills 1/3 of the tank.
Tap C empties the tank when full in 2 hours. Each hour it empties 1/2 of the tank.
Each hour, the tank gets filled by:
Since the tank fills 1/12 of its capacity in one hour, it follows that it will take 12 hours to fill the tank
Answer:
Step-by-step explanation:
If you plot the directrix and the focus, you can see that the focus is to the left of the directrix. Since a parabola ALWAYS wraps itself around the focus, our parabola opens sideways, to the left to be specific. The formula for the parabola that opens to the left is
We will solve this for x at the end. The negative is out front because it opens to the left. If it opened to the right, it would be positive.
The vertex of a parabola is exactly halfway between the focus and the directrix, so our vertex coordinates h and k are (3, 6). P is defined as the distance between the vertex and the directrix, or the vertex and the focus. Since the vertex is directly between both the directrix and the focus, each distance is the same. P = 1. Filling in what we have now:
which simplifies to
Now we will solve it for x.
and
so
Answer:
y = -2x - 7
Step-by-step explanation:
x - 2y = 6
-2y = -x + 6
Divide the whole equation by (-2)
slope = 1/2
Slope of the line perpendicular to this line = -1/m = -1 ÷ (1/2)
(-3, - 1)
y -y1 = m(x -x1)
y - [-1] = -2(x - [-3])
y + 1 = -2(x + 3)
y + 1= x* (-2) + 3*(-2)
y + 1 = -2x - 6
y = -2x - 6 - 1
y = -2x - 7