Rhombus ABCD, with side length 6, is rolled to form a cylinder of volume 6 by taping side AB to side DC. What is sin(angle ABC)?
1 answer:
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So for this function we will be using the quadratic formula, which is , to solve. a = x^2 coefficient, b = x coefficient, and c = constant. Using our equation, we can solve for the zeros (x-intercepts) as such:
In short, your x-intercepts (rounded to the hundredths) are (1.92,0) and (-3.92,0).
Answer:
Proofs are in the explantion.
Step-by-step explanation:
We are given the following:
1) for integer
.
1) for integer
.
a)
Proof:
We want to show .
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(a+c)-(b+d)=rn. If we do that we would have shown that .
kn+mn = (a-b)+(c-d)
(k+m)n = a-b+ c-d
(k+m)n = (a+c)+(-b-d)
(k+m)n = (a+c)-(b+d)
k+m is is just an integer
So we found integer r such that (a+c)-(b+d)=rn.
Therefore, .
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b) Proof:
We want to show .
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(ac)-(bd)=tn. If we do that we would have shown that .
If a-b=kn, then a=b+kn.
If c-d=mn, then c=d+mn.
ac-bd = (b+kn)(d+mn)-bd
= bd+bmn+dkn+kmn^2-bd
= bmn+dkn+kmn^2
= n(bm+dk+kmn)
So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.
Therefore, .
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