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2 years ago

if you use synthetic division for this polynomial: 3x^5-12x^4+12x^3+30x^2-39x-42. What would the answer be?

Mathematics

1 answer:

kaheart [24]2 years ago

8 0

Answer : x^5 - 4x^4 +4x^3 + 10x^2 - 13x - 14

Explanation :

(3x^5-12x^4+12x^3+30x^2-39x-42)/3 = x^5 - 4x^4 +4x^3 + 10x^2 - 13x - 14

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Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$

Doing the operations inside of the brackets the derivatives are:

1 ) $(\frac{d((1/2)t^2)}{dt} )^2= t^2$

2) $\frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1$

Entering these values of the integral is

$r(t)= \int\limits^{16}_{0} \sqrt{t^2 +2t+1} dt$

It is possible to factorize the quadratic function and the integral can reduced as,

$r(t)= \int\limits^{16}_{0} (t+1) dt= \frac{t^2}{2} + t$

Thus, evaluate from 0 to 16

$\frac{16^2}{2} + 16$

The value is $r= 144 units$

5 0

3 years ago

Which stateless nation lives on territory that is part of Iran, Iraq, and Turkey? A. the Kurds B. the Palestinians C. the Basque

OLEGan [10]

A) The Kurds are a stateless nation which lives on territory that is part of Iran, Iraq and Turkey.

The Kurds have ethnically diverse origins and are often classified as Iranian, because of their linguistically close language to Farsi. There are around thirty-seven million Kurds living around the world.

9 0

3 years ago

Read 2 more answers

Simplify the following expressions using Order of Operations. 4+ 8 = 2 + 6 x 2

Hunter-Best [27]

Answer:

12 ≠ 14

Step-by-step explanation:

(4+8)=2+(6x2)

12 = 2 + 12

12 ≠ 14.

So the equation is false.

4 0

3 years ago

A quick quiz consists of a multiple-choice question with 4 possible answers followed by a multiple-choice question with 3 possib

olga55 [171]

Answer:

0.0825

Step-by-step explanation:

1/4x1/3=0.0825

7 0

3 years ago

PLEASE PLEASE HELP <3

anzhelika [568]

Answer:

Step-by-step explanation:

∠ AFD = ∠ AFB + ∠ BFC + ∠ CFD

The 3 angles form a straight angle and sum to 180°, that is

4x + 5 + 6x + 3 + 5x + 7 = 180, that is

15x + 15 = 180 ( subtract 15 from both sides )

15x = 165 ( divide both sides by 15 )

x = 11

∠ CFD = 5x + 7 = 5(11) + 7 = 55 + 7 = 62°, thus

∠ AFE = ∠ CFD = 62° ( vertical angles are congruent )

3 0

3 years ago