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Ne4ueva [31]
3 years ago
15

(y^4 – y^3 + 2y^2 + y – 1) ÷ (y^3 + 1) DO NOT INCLUDE PARENTHESES IN YOUR ANSWER

Mathematics
1 answer:
jarptica [38.1K]3 years ago
8 0
Use long division.

                                     y - 1
         -------------------------------
y³+1  | y⁴  - y³  + 2y²  + y  - 1
          y⁴                    + y
         -------------------------------
               - y³  + 2y²         - 1
               - y³                    - 1
              ---------------------------
                         2y²

Answer:  y - 1 + 2y2 ÷ y³+1

Note:  
The correct answer should be written with parenthesis, as y - 1 + y²/(y³+1) in order to avoid ambiguity. 
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What is the value of the expression 6/7 divided by 3/4
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2 ounces.

EXPLANATION:

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3 0
2 years ago
Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.
siniylev [52]

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

\displaystyle S = \frac{n}{2}\left(a + x_n\right)

Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>x</em>_<em>n</em> is the last term.

We know that the initial term <em>a</em> is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find <em>n</em>.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

x_n=a+d(n-1)

Since the initial term is 13 and the common difference is 7:

x_n=13+7(n-1)

Substitute:

\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)

We are given that the initial term is 13 and the sum is 2613. Substitute:

\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))

Solve for <em>n</em>. Multiply both sides by two and combine like terms:

5226 = n(26+7(n-1))

Distribute:

5226 = n (26+7n-7)

Simplify:

5226 = 7n^2+19n

Isolate the equation:

7n^2+19n-5226=0

We can use the quadratic formula:

\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

In this case, <em>a</em> = 7, <em>b</em> = 19, and <em>c</em> = -5226. Substitute:

\displaystyle x  =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}

Evaluate:

\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}

Evaluate for each case:

\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

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2 years ago
the triangular prism below has equilateral bases with sides of 4 in and a height of 4.5 in and rectangular sides measuring by 4
Ksju [112]

Answer:

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Step-by-step explanation:

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