3/(<em>x</em> ² - 1) = 3/((<em>x</em> - 1) (<em>x</em> + 1)) = <em>a</em>/(<em>x</em> - 1) + <em>b</em>/(<em>x</em> + 1)
==> 3 = <em>a</em> (<em>x</em> + 1) + <em>b</em> (<em>x</em> - 1)
==> 3 = (<em>a</em> + <em>b</em>) <em>x</em> + <em>a</em> - <em>b</em>
==> <em>a</em> + <em>b</em> = 3 and <em>a</em> - <em>b</em> = 0
==> <em>a</em> = <em>b</em>
==> <em>a</em> + <em>b</em> = 2<em>a</em> = 3 ==> <em>a</em> = 2/3 and <em>b</em> = 2/3
So you have
3/(<em>x</em> ² - 1) = 2/(3(<em>x</em> - 1)) + 2/(3(<em>x</em> + 1))
Answer:
c) parabola and circle: 0, 1, 2, 3, 4 times
d) parabola and hyperbola: 1, 2, 3 times
Step-by-step explanation:
c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.
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d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.
If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.
Answer:
5494
Step-by-step explanation:
Assuming all members of each set registered, the total number is ...
2(2697) +3(29) +4(2) +5(1) = 5494
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Since you're concerned with order of operations, perhaps you want to see the working out.
= 5394 + 87 +8 +5 . . . . perform all the multiplications
= 5481 +8 +5 . . . . . . . . . perform addition left to right
= 5489 +5
= 5494
Answer:
14 percent
Step-by-step explanation:
books/ total * 100 = percent
378/2700 * 100
.14 * 100
14 percent
Answer:
Sue will have 6 full cartons.
Step-by-step explanation:
1 dozen = 12
75/ 12= 6
6 X 12 = 72