Answer:
hope this can help you (^^)
The arch of the Gateshead Millennium Bridge forms a parabola with equation:
1 answer:
Answer:
about 106 meters
Step-by-step explanation:
The difference in x-values when y=0 is found by solving ...
0 = -0.016(x -52.5)² +45
-45 = -0.016(x -52.5)² . . . . . . subtract 45
45/0.016 = (x -52.5)² . . . . . . . divide by the coefficient of the squared term
±√2812.5 = x -52.5 . . . . . . . . take the square root
x = 52.5 ±√2812.5 . . . . . . . . .add 52.5. These are the x-values where y=0.
So, the difference in x-values at y=0 is ...
(52.5 +√( )) - (52.5 -√( )) = 2√2812.5 ≈ 106.07 . . . . meters
The width of the arch at ground level is about 106 meters.
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9514 1404 393
Answer:
1. asymptotes: x=-6, x=6, y=0; zero: x=0
2. 20 blue fish
Step-by-step explanation:
1. The vertical asymptotes are where the denominator is zero. It factors as (x-6)(x+6), so will have zeros at x=-6 and x=6.
The horizontal asymptote is at the limit when x goes to infinity. Here, the ratio of highest-degree terms is 6/x, so the value goes to zero as x gets large.
The zero is where the numerator is zero, at x=0.
In summary:
- vertical asymptotes: x = ±6
- horizontal asymptote: y = 0
- zero: (0, 0)
__
2. 60% are red, so 40% are blue. The difference in percentages is 60%-40% = 20%. The percentage of blue fish (40%) is twice the difference (=2×20%), so the number of blue fish is twice the difference in numbers.
blue fish = 2×10 = 20 fish
<em><u>Check</u></em>
There are then 20+10=30 red fish, so 20+30=50 fish total. Reds are 30/50 = 60% of the total.
<u><em>Additional comment</em></u>
I find it often works well to work with ratios, which I can often do in my head. Other folks like to see equations. Here, we could write equations like ...
r = 60%(r + b) . . . . reds are 60% of the total
r - b = 10 . . . . . . . . 10 more reds than blues
We want the value of b, so we can eliminate r by substituting for it:
r = 10 + b . . . . from the second equation above
(10 +b) = 0.60((10 +b) + b) . . . . substitute for r
10 +b = 6 + 1.2b . . . simplify
4 = 0.2b . . . . subtract b+6
20 = b . . . . . . multiply by 5 (there are 20 blue fish)
Answer:
Step-by-step explanation:
