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2 years ago

State the degree and dominant term of this polynomial

Mathematics

1 answer:

artcher [175]2 years ago

4 0

The degree of the polynomial f(x) = 2x(x - 3)³(x + 1)(4x - 2) is 6, and the dominant term is - 216x²

<h3>The degree of the polynomial?</h3>

The polynomial function is given as:

f(x) = 2x(x - 3)³(x + 1)(4x - 2)

To determine the degree, we simply add the multiplicities.

So, we have:

Degree = 1 + 3 + 1 + 1

Evaluate

Degree = 6

Hence, the degree of the polynomial is 6

<h3>The dominant term of the polynomial</h3>

We have:

f(x) = 2x(x - 3)³(x + 1)(4x - 2)

Expand

f(x) = 8x⁶ - 68x⁵ + 176x⁴ - 72x³ - 216x² + 108x

The term with the highest absolute value is - 216x²

Hence, the dominant term is - 216x²

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Darren is painting a wooden block as part of his art project The block is a rectangular prism that is 12cm long by 9 cm wide by

Ksenya-84 [330]

Answer:

<h3>The surface area in square meters that Darren has to paint is $426cm^2$ </h3><h3>∴ $A=426cm^2$ </h3>

Step-by-step explanation:

Given that Darren is painting a wooden block is a rectangular prism

Its length is 12 cm ,width is 9 cm and height is 5 cm

<h3>To find the surface area in square meters that Darren has to paint :</h3>

Let l be the length, w be the width and h be the height

Then l=12 cm , w=9 cm and h=5 cm

The formula for the Surface area is

A=2(lw+wh+hl) square units

Substitute the values in formula we get,

A=2(12(9)+9(5)+5(12))

=2(108+45+60)

=2(213)

=426

<h3>∴ $A=426cm^2$ </h3><h3>∴ the surface area in square meters that Darren has to paint is $426cm^2$ </h3>

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3 years ago

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3 years ago

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Colt1911 [192]

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3 years ago

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7 0

3 years ago

Read 2 more answers

The population of rabbits on an island is growing exponentially. In the year 1994, the population of rabbits was 9600, and by 20

drek231 [11]

Answer:

49243

Step-by-step explanation:

Given that the population of rabbits on an island is growing exponentially.

Let the population, $P=P_0e^{bt}$

where, $P_0$ and b are constants, t=(Current year -1994) is the time in years from 1994.

In 1994, t=0, the population of rabbit, P=9600, so

$9600=P_0e^{b\times 0}$

So, $P_0=9600$

and in 2000, t=2000-1994=6 years and population of the rabbit, P=18400

$18400=9600 \times e^{b\times 6} \\\\\frac{18400}{9600}=e^{b\times 6} \\\\$

$\ln(23/12}=6b \\\\$

$b = \frac{\ln{1.92}}{6} \\\\$

b=0.109

On putting the value of P_0 and b, the population of the rabbit after t years from 1994 is

$P=9600 \times e^{0.109\times t}$

In 2009, t= 2009-1994=15 years,

So, the population of the rabbit in 2009

$P=9600 \times e^{0.109\times 15}=49243$

Hence, the population of the rabbit in 2009 is 49243.

7 0

3 years ago