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Lesechka [4]
3 years ago
13

What is Constant Term? ​

Business
2 answers:
denpristay [2]3 years ago
5 0

Answer:

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial

   x 2 + 2 x + 3 ,   {\displaystyle x^{2}+2x+3,\ } x^{2}+2x+3,\

the 3 is a constant term.

After like terms are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial

   a x 2 + b x + c ,   {\displaystyle ax^{2}+bx+c,\ } ax^{2}+bx+c,\

where x is the variable, and has a constant term of c. If c = 0, then the constant term will not actually appear when the quadratic is written.

It is notable that a term that is constant, with a constant as a multiplicative coefficient added to it (although this expression could be more simply written as their product), still erm as a variable is still not present in the new term. Although the expression is modified, the term (and coefficient) itself classifies as constant. However, should this introduced coefficient contain a variable, wginal number has a constant meaning, this has no bearing if the new term stays constant as the introduced coefficient will always override the constant expression - for example, in ( x + 1 ) ( x − 2 ) {\displaystyle (x+1)(x-2)} (x+1)(x-2) when x is multiplied by 2, the result, 2x, is not constant; while 1 * -2 is -2 and still a constant.

Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of x0. In particular, the constant term will always be the lowest degree term of the polynomial. This also applies to multivariate polynomials. For example, the polynomial

   x 2 + 2 x y + y 2 − 2 x + 2 y − 4   {\displaystyle x^{2}+2xy+y^{2}-2x+2y-4\ } x^{2}+2xy+y^{2}-2x+2y-4\

has a constant term of −4, which can be considered to be the coefficient of x0y0, where the variables are eliminated by being exponentiated to 0 (any number exponentiated to 0 becomes 1). For any polynomial, the constant term can be obtained by substituting in 0 instead of each variable; thus, eliminating each variable. The concept of exponentiation to 0 can be extended to power series and other types of series, for example in this power series:

   a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ⋯ , {\a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cdots ,} a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cdots ,

a0 is the constant term. In general a constant term is one that does not involve any variables at all. However in expressions that involve terms with other types of factors than constants and powers of variables, the notion of constant term cannot be used in this sense, since that would lead to calling "4" the constant term of ( x − 3 ) 2 + 4 {\displaystyle (x-3)^{2}+4} (x-3)^{2}+4, whereas substituting 0 for x in this polynomial makes it evaluate to 13.

Explanation:

stich3 [128]3 years ago
5 0

Answer:

Constant Term  

The term in a simplified algebraic expression or equation which contains no variable(s). If there is no such term, the constant term is 0.

Explanation:

Example:   –5 p(x) 2x^{3} -4x^{2} +9x-5

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Entertainer's Aid plans five annual colossal concerts, each in a different nation's capital. The concerts will raise funds for a
Finger [1]

Answer: $5,569,758.43

Explanation:

First you need to find the present value of the Perpetuity at the end of the fifth year.

Present value of Perpetuity = Amount / Interest rate

= 3,000,000 / 9%

= $33,333,333.33

Given an interest rate of 9%, Entertainer's aid should deposit an amount per year that would lead to the endowment having $33,333,333.33 at the end of the fifth year.

Future value of annuity = Annuity * Future value of annuity interest factor, 9%, 5 years

33,333,333.33 = Annuity * 5.9847

Annuity = 33,333,333.33 / 5.9847

= $5,569,758.43

3 0
3 years ago
Lagle Corporation has provided the following information:
mezya [45]

Answer:

b.$20,550

Explanation:

The period costs are those costs which include costs  for a particular period. The calculation for these costs differ under the two methods  absorption and variable. Under absorption Costing the Period costs include Variable selling and administrative + Fixed selling and administrative expenses.

<u>Lagle Corporation</u>

<u>Absorption Costing</u>

Direct materials $ 4.75 * 7000= $ 33250

Direct labor $ 3.70  * 7000= $ 25900

Variable manufacturing overhead $ 1.45  * 7000= $ 10150

Fixed manufacturing overhead $ 18,200

Total Product costs $ 87,500

Sales commissions $ 1.70  * 7000=$ 11900

Variable administrative expense $ 0.55  * 7000= $ 3850

Fixed selling and administrative expense $ 4,800

Total Period Costs $ 20550

<u><em>Mostly Absorption costing is used for daily basis. Therefore Choice b is the best option</em></u><em>. </em>

Under variable costing the Period costs include Fixed manufacturing overheads + Fixed selling and administrative expenses.

<u>Lagle Corporation</u>

<em>Variable Costing</em>

Direct materials $ 4.75 * 7000= $ 33250

Direct labor $ 3.70  * 7000= $ 25900

Variable manufacturing overhead $ 1.45  * 7000= $ 10150

Sales commissions $ 1.70  * 7000=$ 11900

Variable administrative expense $ 0.55  * 7000= $ 3850

<em>Total Product costs $ 85,050</em>

Fixed selling and administrative expense $ 4,800

Fixed manufacturing overhead $ 18,200

<em>Total Period Costs $ 23000</em>

7 0
3 years ago
Set up an amortization schedule for a $25000 loan to be repaid in equal installment at the end of each 3 years. The interest rat
Lesechka [4]

Answer:

we must first determine the annual payment:

annual payment = present value / annuity factor

present value = $25,000

PV annuity factor, 10%, 3 periods = 2.4869

annual payment = $25,000 / 2.48685 = $10,052.87

year       payment     interest paid       principal paid       ending balance

1          $10,052.87      $2,500              $7,552.87             $17,447.13

2         $10,052.87      $1,744.71           $8,308.16              $9,138.97

3         $10,052.87      $913.90             $9,138.97              $0

in percentages:

year       payment     interest paid       principal paid    

1               100%            25%                        75%

2              100%        17.36%                   82.64%

3              100%         9.09%                   90.91%

4 0
3 years ago
Roselawn Company reported net sales of $90,000 and net income of $18,000 for the previous year ended December 31. The company re
gregori [183]

Answer:

The company’s profit margin for the current year ended December 31 (rounded to the nearest decimal point) is 20%

Explanation:

Use the following formula to calculate the Profit Margin

Profit Margin = \frac{Net Income}{Net Sales} X 100

Where

Net Income = $20,000

Net Sales = $100,000

Placing values in the formula

Profit Margin = \frac{20000}{100000} X 100

Profit Margin = 0.2 x 100

Profit Margin = 20%

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3 years ago
What is the best revision of sentence 6 to maintain a formal style? moreover, students will benefit from having the most current
leva [86]
The best option which contains a sentence with a perfect grammar structure is : M<span>oreover, students will benefit from having the most current information. This sentence in quite concise and includes only formal language. Formal style does not accept shortenings that you can see in the next option (info) and informal vocabulary (kids) that is placed in the third option.</span>
4 0
3 years ago
Read 2 more answers
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