Marcus states that the polynomial expression 3x3 – 4x2y + y2 + 2 is in standard form. Ariel states that it should be y2 – 4x2y + 3x3 +2. Explain which student is correct and why.

Answers

Answer 1

Answer:

The standard form of a polynomial is: $P(x) = ax^n + bx^(n-1) + cx^(n-2) + .... + d$ where the exponent of the variable decrease to 0.

Marcus and Ariel are both correct.

Given that:

$M \to Marcus$

$A \to Ariel$

So, we have:

$M = 3x^3 - 4x^2y + y^2 + 2$

$A = y^2 - 4x^2y + 3x^3 + 2$

For Marcus polynomial

$M = 3x^3 - 4x^2y + y^2 + 2$

The variable is x and the degree of the polynomial is 3.

Marcus' representation is correct

For Ariel polynomial

$A = y^2 - 4x^2y + 3x^3 + 2$

The variable is y and the degree of the polynomial is 2.

Ariel' representation is also correct

Hence, we can conclude that Marcus and Ariel are correct with their representation of polynomial

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Answers

Answer:

3002

Step-by-step explanation:

i hope i helped

A.3(f) The line graphed on the grid represents the first of two equations in a system of linear equations.20
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48
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If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?

Answers

I don’t any idea for this

Which interval for the graphed function has a local minimum of 0?

Answers

Answer: your answer would be [2, 4]

Step-by-step explanation:

tell me if im wrong please

The following is a list of 5 measurements. 20,10,13,11,20 Suppose that these 5 measurements are respectively labeled.

Answers

Answer:

1190

Step-by-step explanation:

Here, you need to add the squares of the measurements.

20² + 10² + 13² + 11² + 20² =

= 400 + 100 + 169 + 121 + 400

= 1190

yeah it would be 1190

Use the binomial theorem to expand the expression :(3x + y)^5 and simplify.
(b) find the middle term in the expansion of
(1/x+√x)^4 and simplify your unswer.
(c) determine the coefficient of x^11 in the expansion of (x^2 +1/x)^10, simplify your answer.

Answers

Answer:

a) $(3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5$ .

b) The middle term in the expansion is $(6)/(x)$ .

c) The coefficient of $x^(11)$ is 120.

Step-by-step explanation:

Remember that the binomial theorem say that $(x+y)^n=\sum_(k=0)^(n) \binom{n}{k}x^(n-k)y^(k)$

a) $(3x+y)^5=\sum_(k=0)^5\binom{5}{k}3^(n-k)x^(n-k)y^k$

Expanding we have that

$\binom{5}{0}3^5x^5+\binom{5}{1}3^4x^4y+\binom{5}{2}3^3x^3y^2+\binom{5}{3}3^2x^2y^3+\binom{5}{4}3xy^4+\binom{5}{5}y^5$

symplifying,

$(3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5$ .

b) The middle term in the expansion of $((1)/(x) +√(x))^4=\sum_(k=0)^(4)\binom{4}{k}(1)/(x^(4-k))x^{(k)/(2)}$ correspond to k=2. Then $\binom{4}{2}(1)/(x^2)x^{(2)/(2)}=(6)/(x)$ .

c) $(x^2+(1)/(x))^(10)=\sum_(k=0)^(10)\binom{10}{k}x^(2(10-k))(1)/(x^k)=\sum_(k=0)^(10)\binom{10}{k}x^(20-2k)(1)/(x^k)=\sum_(k=0)^(10)\binom{10}{k}x^(20-3k)$

Since we need that 11=20-3k, then k=3.

Then the coefficient of $x^(11)$ is $\binom{10}{3}=120$

The profit on a teddy bear can be found by using the function P(x) = - 2x2 + 35x - 99 where x is the price of the bear.Calculate the price that maximizes profit.

Answers

Answer:

x=8.75

Step-by-step explanation:

The price x that maximizes profit is the maximum value of the function, and the maximum value of the function is located at a point where the first derivative of the function is equal to zero. The first derivative is:

$P(x) = - 2x^2+35x-99\nP'(x)=-2(2)x^((2-1))+35(1)-0\nP'(x)=-4x+35$

Using P'(x)=0:

$0=-4x+35\n4x=35\nx=35/4\nx=8.75$

The minimum value of the function is also at a point where the first derivative of the function is equal to zero. To differentiate if x=8. is a minimum or a maximum obtain the second derivative and evaluate it at x=8.75 if the value P''(x)>0 x is minimum and if P''(x)<0 x is a maximum.

$P'(x)=-4x+35\nP''(x)=-4(1)\nP''(x)=-4$

Evaluating at x=8.75:

$P''(8.75)=-4$

Therefore, x=8.75 is the maximum value of the function and it is the price that maximizes profit.

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