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Contact [7]
3 years ago
12

DAY 2 please help i dont get it

Mathematics
1 answer:
MrRa [10]3 years ago
3 0
G because she need to sell 20 vases because the cost is 450 and if you divide it by 23 for the price the vases will be sold for it comes to 19.57 and you can't sell .57 of a vase you have to round up to make more than the money spent
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Prove each of the following statements below using one of the proof techniques and state the proof strategy you use.
pochemuha

Answer:

See below

Step-by-step explanation:

a) Direct proof: Let m be an odd integer and n be an even integer. Then, there exist integers k,j such that m=2k+1 and n=2j. Then mn=(2k+1)(2j)=2r, where r=j(2k+1) is an integer. Thus, mn is even.

b) Proof by counterpositive: Suppose that m is not even and n is not even. Then m is odd and n is odd, that is, m=2k+1 and n=2j+1 for some integers k,j. Thus, mn=4kj+2k+2j+1=2(kj+k+j)+1=2r+1, where r=kj+k+j is an integer. Hence mn is odd, i.e, mn is not even. We have proven the counterpositive.

c) Proof by contradiction: suppose that rp is NOT irrational, then rp=m/n for some integers m,n, n≠. Since r is a non zero rational number, r=a/b for some non-zero integers a,b. Then p=rp/r=rp(b/a)=(m/n)(b/a)=mb/na. Now n,a are non zero integers, thus na is a non zero integer. Additionally, mb is an integer. Therefore p is rational which is contradicts that p is irrational. Hence np is irrational.

d) Proof by cases: We can verify this directly with all the possible orderings for a,b,c. There are six cases:

a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥b≥a, c≥a≥b

Writing the details for each one is a bit long. I will give you an example for one case: suppose that c≥b≥a then max(a, max(b,c))=max(a,c)=c. On the other hand, max(max(a, b),c)=max(b,c)=c, hence the statement is true in this case.

e) Direct proof: write a=m/n and b=p/q, with m,q integers and n,q nonnegative integers. Then ab=mp/nq. mp is an integer, and nq is a non negative integer. Hence ab is rational.

f) Direct proof. By part c), √2/n is irrational for all natural numbers n. Furthermore, a is rational, then a+√2/n is irrational. Take n large enough in such a way that b-a>√2/n (b-a>0 so it is possible). Then a+√2/n is between a and b.

g) Direct proof: write m+n=2k and n+p=2j for some integers k,j. Add these equations to get m+2n+p=2k+2j. Then m+p=2k+2j-2n=2(k+j-n)=2s for some integer s=k+j-n. Thus m+p is even.

7 0
3 years ago
What's the product of 12.34•0•74.91 ?
Eduardwww [97]
Because there is a zero in the expression 12.34 * 0 * 74.91 the product is 0.
4 0
3 years ago
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Can you help me on this one? I kinda forgot this whole unit Lowkey so can you explain it as if there were someone who never lear
DIA [1.3K]

Answer:

here’s something that will help

answer is at the bottom if needed

Step-by-step explanation:

8 0
3 years ago
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Suppose that the function f ( x ) = 2x + 12 represents the cost to rent x movies amonth from an internet movie club. Makayla now
Dafna11 [192]
x=7\ \ \ \ \Rightarrow\ \ \ f(x)=2\cdot7+12=14+12=26\ [\$]\\\\\$26-\$10= \$16\\\\Ans.\ Makayla\ need\ \ \ \$16.
3 0
3 years ago
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Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure m^2-n^2 and 2mn
My name is Ann [436]
\bf c^2=a^2+b^2\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
------\\
a=m^2-n^2\\
b=2mn
\end{cases}\\\\\\ c^2=(m^2-n^2)^2+(\underline{2mn})^2
\\\\\\
c^2=m^4-2m^2n^2+n^4+\underline{2^2m^2n^2}
\\\\\\
c^2=m^4-2m^2n^2+n^4+{4m^2n^2}
\\\\\\
c^2=m^4+2m^2n^2+n^4\impliedby \textit{perfect square trinomial}
\\\\\\
c^2=(m^2+n^2)^2\implies c=\sqrt{(m^2+n^2)^2}\implies c=m^2+n^2
7 0
3 years ago
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