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3 years ago

What is leading coefficient of the function f(x) = 3x5 + 6x4 − x − 3?

Mathematics

2 answers:

Crazy boy [7]3 years ago

6 0

Answer:

(A) 3

Step-by-step explanation:

The given function is:

$f(x)=3x^5+6x^4-x-3$

Now, The leading term is the term containing the highest power of the variable and the leading coefficient is the coefficient of the leading term.

Thus, The leading term of the given function is $3x^5$ , therefore the leading coefficient is the coefficient of this leading term that is 3.

Hence,, option A is correct.

Morgarella [4.7K]3 years ago

3 0

F(x) = 3x⁵ + 6x⁴ - x - 3

The coefficient of a function f(x) is the number that multiplies the x with the highest exponent., that is 3. Answer a)

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ivann1987 [24]

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3 years ago

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Step-by-step explanation:

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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

You schedule production of communications chips. After the chips are produced, they go to the QC department, where each chip mus

Irina-Kira [14]

The best batch size is 1053.

Since 5% have failed, this means 95% have passed the test.

95% = 95/100 = 0.95

We can set up an equation to answer this:
0.95x = 1000

Divide both sides by 0.95:
0.95x/0.95 = 1000/0.95
x = 1052.6 ≈ 1053

7 0

3 years ago

Please help Explanation will be appreciated thanks,

Genrish500 [490]

Answer: A; 6.3%

Step-by-step explanation:

Problem 1

For the first problem, we first want to find y so that we can plug it into the expression.

We can use elimination method for the system of equations to solve.

3x+3y=21

3x-y=5

We subtract both equations to eliminate x.

4y=16 [divide both sides by 4]

y=4

Now that we know y, we can plug it into the expression.

$\frac{4}{2} -3$ [divide]

$2-3$ [subtract]

$-1$

We know that the answer is A.

--------------------------------------------------------------------------------------------------------

Problem 2

For the second problem, we need to know how to calculate percent error. The formula for precent error is $\frac{|measured-exact|}{exact} *100%$ . We know that the exact value is 80 because the buyer was supposed to given 80. 75 is the measured value because that was what the buyer was given.

$\frac{|75-80|}{80} *100%$ [subtract]

$\frac{|-5|}{80} *100%$ [solve absolue value]

$\frac{5}{80} *100%$ [divide]

$0.0625*100%$ [multiply]

$6.25$

Since the problem said to round to one decimal place, we know that the answer is 6.3%.

4 0

3 years ago