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2 years ago

9

Which of the following statements will be true about the product of 6 and 1=? The product vál be greater than 6. The produci vil

l be equal to 6. The product will be less than 6

1 answer:

devlian [24]2 years ago

6 0

Since it said product then that means multiplication so 6 times 1 is 6 that means the product will be equal to 6

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Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

Molodets [167]

Notice that

$(n+1)^4-n^4=4n^3+6n^2+4n+1$

so that

$\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

We have

$\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)$

$\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1$

so that

$\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

You might already know that

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

so from these formulas we get

$\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n$

$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

2 years ago

Exam study guide I got six more help me as fast as yall can please

Ad libitum [116K]

Answer:

area of triangle is 18.3, area of circle is 113.097

Step-by-step explanation:

4 0

2 years ago

The polynomial 2x3y4-7x2y3 is what degree? 6 5 7 9

podryga [215]

Answer:

7

Step-by-step explanation:

To find the degree of a polynomial you must find the term with the highest degree.

First, you must identify each term in the polynomial. In this problem there are two terms 2x^3 y^4, and -7x^2 y^3.

If there are multiple variables in the terms, like in this equation, you will add the exponents within the term.

For the term 2x^3 y^4 you will add the exponents 3 and 4 (3+4=7). The sum of the exponents is 7 meaning this term has a degree of 7.

For the term -7x^2 y^3 you will add the exponents 2 and 3 (2+3=5). This term has a degree of 5.

Since the highest degree term is 7, the degree of polynomial is 7.

8 0

2 years ago

SOLUTION TO 2X=3=X-4

OlgaM077 [116]

Answer:so 2x square+5x-12

Step-by-step explanation:

look carefully

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2 years ago

Calculate the answer to the correct number of significant digits. (91.01)(10.7)

aalyn [17]

Answer:

974

Step-by-step explanation:

(91.01)*(10.7)

91.01*(10.7)

91.01*10.7

973.80700

974

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2 years ago