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yoyo1542
28.09.2020 •
Mathematics
Question 1:
Your goal this year is to earn a B or better in Algebra
class. If you do, your parents said they would give you
$200. Write an inequality to represent the grades you
can earn and receive money from your parents for it.
Then explain the graph for the inequality. Hint:
Remember you cannot earn higher than a 100 in any
class.
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Ответ:
The hyperbolas in increasing order of the horizontal widths of their asymptote rectangles are:
(x-4)^2/2^2-(y+2)^2/5^2=1
↓
(y+5)^2/2^2-(x+4)^2/3^2=1
↓
(x+7)^2/4^2-(y-9)^2/9^2=1
↓
(y-11)^2/7^2-(x-2)^2/6^2=1
↓
(x-6)^2/8^2-(y+1)^2/3^2=1
↓
(y+1)^2/2^2-(x-1)^2/9^2=1
↓
(y-1)^2/5^2-(x-7)^2/12^2=1
Step-by-step explanation:
1. (y-11)^2/7^2-(x-2)^2/6^2=1
Vertical hyperbola
Horizontal width of its asymptote rectangle is 2b
b^2=6^2→b=6
2b=2(6)→2b=12
2. (y-1)^2/5^2-(x-7)^2/12^2=1
Vertical hyperbola
Horizontal width of its asymptote rectangle is 2b
b^2=12^2→b=12
2b=2(12)→2b=24
3. (x-6)^2/8^2-(y+1)^2/3^2=1
Horizontal hyperbola
Horizontal width of its asymptote rectangle is 2a
a^2=8^2→a=8
2a=2(8)→2a=16
4. (x-4)^2/2^2-(y+2)^2/5^2=1
Horizontal hyperbola
Horizontal width of its asymptote rectangle is 2a
a^2=2^2→a=2
2a=2(2)→2a=4
5. (y+5)^2/2^2-(x+4)^2/3^2=1
Vertical hyperbola
Horizontal width of its asymptote rectangle is 2b
b^2=3^2→b=3
2b=2(3)→2b=6
6. (y+1)^2/2^2-(x-1)^2/9^2=1
Vertical hyperbola
Horizontal width of its asymptote rectangle is 2b
b^2=9^2→b=9
2b=2(9)→2b=18
7. (x+7)^2/4^2-(y-9)^2/9^2=1
Horizontal hyperbola
Horizontal width of its asymptote rectangle is 2a
a^2=4^2→a=4
2a=2(4)→2a=8