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3 years ago

What is the maximum number of terms a fourth-degree polynomial function in standard form can have?

1 answer:

3 0

A polynomial of four terms is sometimes called a quadrinomial, but there's really no need for such words.
Likewise, what is a 4th degree polynomial? Fourth degree polynomials are also known as quartic polynomials. Quartics have these characteristics: Zero to four roots. One, two or three extrema. Zero, one or two inflection points.
The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Zero Polynomial. The constant polynomial. whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. The zero polynomial is the additive identity of the additive group of polynomials.

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a 28 ft. ladder leaning against a vertical wall makes an angel of 80 degrees with the ground. How far from the base of the wall

worty [1.4K]

Answer:

The ladder is 4.86 foot from the base of the wall .

Step-by-step explanation:

Given as :

The length of the ladder = 28 ft

The ladder makes angle of 80° with the ground

Let The distance of the ladder from the foot of the wall = x ft

Now, From Triangle BAC

Cos angle = $\dfrac{\textrm Base}{\textrm Hypotenuse}$

I.e Cos 80° = $\dfrac{\textrm BA}{\textrm AC}$

Or, 0.1736 = $\dfrac{\textrm x}{\textrm 28}$

Or, x = 0.1736 × 28

∴ x = 4.86 foot

So, The distance of ladder from wall base = x = 4.86 foot

Hence The ladder is 4.86 foot from the base of the wall . Answer

3 0

3 years ago

Differential equations by separation of variables

MissTica

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

Below is the solution:

xdy/dx = 4y
xdy = 4ydx 
∫ dy/y =∫ 4dx/x 
ln(y) = 4ln(x) + C 
y = e^[4ln(x)] e^C 
y = e^[ln(x)^4] e^C 
y = Cx^4 answer

5 0

3 years ago

Solve the following equation. Show your work. 7x + 14 = 7(x+2)

Mama L [17]

7(x+2)= 7x + 14
7x + 14 = 7x + 14

8 0

3 years ago

Read 2 more answers

Find the value of x 6x + 12 3x - 3

Shalnov [3]

Answer:

19°

Step-by-step explanation:

Concept Used :-

The measure of a straight line is 180°. So the sum of angles on a straight line is 180° .

Using this ,

$\bf\implies 6x + 12 + 3x - 3 = 180\\\\\bf\implies 9x + 9 = 180\\\\\bf\implies 9x = 180-9 \\\\\bf\implies x =\dfrac{171}{9} \\\\\bf\implies\boxed{\red{\bf x = 19 }}$

<h3>Hence the value of x is 19°</h3>

3 0

3 years ago

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January

Blababa [14]

Answer:

a) 27.89% probability that two have ever boycotted goods for ethical reasons

b) 41.81% probability that at least two respondents have boycotted goods for ethical reasons

c) 41.16% probability that between 3 and 6 have boycotted goods for ethical reasons

d) The expected number is 2.3 and the standard deviation is 1.33.

Step-by-step explanation:

We use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

23% of the respondents have boycotted goods for ethical reasons.

This means that $p = 0.23$

a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

This is P(X = 2) when n = 6. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{6,2}.(0.23)^{2}.(0.77)^{4} = 0.2789$

27.89% probability that two have ever boycotted goods for ethical reasons

b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

Either less than two have, or at least two. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{6,0}.(0.23)^{0}.(0.77)^{6} = 0.2084$

$P(X = 1) = C_{6,1}.(0.23)^{1}.(0.77)^{5} = 0.3735$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.2084 + 0.3735 = 0.5819$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5819 = 0.4181$

41.81% probability that at least two respondents have boycotted goods for ethical reasons

c) In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?

Now n = 10.

$P(3 \leq X \leq 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

$P(X = 3) = C_{10,3}.(0.23)^{3}.(0.77)^{7} = 0.2343$

$P(X = 4) = C_{10,4}.(0.23)^{4}.(0.77)^{6} = 0.1225$

$P(X = 5) = C_{10,5}.(0.23)^{5}.(0.77)^{5} = 0.0439$

$P(X = 6) = C_{10,6}.(0.23)^{6}.(0.77)^{4} = 0.0109$

$P(3 \leq X \leq 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.2343 + 0.1225 + 0.0439 + 0.0109 = 0.4116$

41.16% probability that between 3 and 6 have boycotted goods for ethical reasons

d) In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

$E(X) = np = 10*0.23 = 2.3$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.23*0.77} = 1.33$

The expected number is 2.3 and the standard deviation is 1.33.

5 0

3 years ago