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3 years ago

3. Which polynomial is equal to

Mathematics

1 answer:

Nataly_w [17]3 years ago

5 0

Which polynomial is equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x)?

<h3><u><em>Answer:</em></u></h3>

The polynomial equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x) is $x^3 + 2x^2 + x + 3$

<h3><u><em>Solution:</em></u></h3>

Given that two polynomials are: $(-3x^2 + 2x - 3)$ and $(x^3 - x^2 + 3x)$

We have to find the result when $(-3x^2 + 2x - 3)$ is subtracted from $(x^3 - x^2 + 3x)$

In basic arithmetic operations,

when "a" is subtracted from "b" , the result is b - a

Similarly,

When $(-3x^2 + 2x - 3)$ is subtracted from $(x^3 - x^2 + 3x)$ , the result is:

$\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)$

Let us solve the above expression

<em><u>There are two simple rules to remember: </u></em>

When you multiply a negative number by a positive number then the product is always negative.

When you multiply two negative numbers or two positive numbers then the product is always positive.

So the above expression becomes:

$\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3$

Removing the brackets we get,

$\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3$

Combining the like terms,

$\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3$

$\rightarrow x^3 + 2x^2 + x + 3$

Thus the resulting polynomial is found

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A mass of 1 g is set in motion from its equilibrium position with an initial velocity of 6in/sec, with no damping and a spring c

yan [13]

a) $y(t)=0.0016 sin(94.9t)$ [m]

b) 0.033 s

c) -0.152 m/s

Step-by-step explanation:

The force acting on the mass-spring system is (restoring force)

$F=-ky$

where

k = 9 is the spring constant

y is the displacement

Also, from Newton's second law of motion, we know that

$F=my''$

where

m = 1 g = 0.001 kg is the mass

y'' is the acceleration

Combining the two equations,

$my''=-ky$

This is a second order differential equation; the solution for y(t) is

$y(t)=A sin(\omega t-\phi)$

where

A is the amplitude of motion

$\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{9}{0.001}}=94.9 rad/s$ is the angular frequency

The spring starts its motion from its equilibrium position, this means that y=0 when t=0; therefore, the phase shift must be

$\phi=0$

So the displacement is

$y(t)=A sin(\omega t)$

The velocity of the spring is equal to the derivative of the displacement:

$v(t)=y'(t)=\omega A cos(\omega t)$

We know that at t = 0, the initial velocity is 6 in/s; since 1 in = 2.54 cm = 0.0254 m,

$v_0=6(0.0254)=0.152 m/s$

And since at t = 0, $cos(\omega t)=1$

Then we have:

$v_0=\omega A$

From which we find the amplitude:

$A=\frac{v_0}{\omega}=\frac{0.152}{94.9}=0.0016 m$

So the solution for the displacement is

$y(t)=0.0016 sin(94.9t)$ [m]

Here we want to find the time t at which the mass returns to equilibrium, so the time t at which

$y=0$

This means that

$sin(\omega t)=0$

We know already that the first time at which this occurs is

t = 0

Which is the beginning of the motion.

The next occurence of y = 0 is instead when

$\omega t = \pi$

which means:

$t=\frac{\pi}{\omega}=\frac{\pi}{94.9}=0.033 s$

As said in part a), the velocity of the mass-spring system at time t is given by the derivative of the displacement, so

$v(t)=\omega A cos(\omega t)$

where we have

$\omega=94.9 rad/s$ is the angular frequency

$A=0.0016 m$ is the amplitude of motion

t is the time

Here we want to find the velocity of the mass when the time is that calculated in part b):

t = 0.033 s

Substituting into the equation, we find:

$v(0.033)=(94.9)(0.0016)cos(94.9\cdot 0.033)=-0.152 m/s$

4 0

3 years ago

Who can pls follow me on rblx im trying to get 100 followers pls follow me tysm if you will :D

gladu [14]

I can my user is hxe_toxic

4 0

3 years ago

The temperature in degrees Celsius can be expressed by the function C(f)=59(f−32)C(f)=59(f−32) where f is the temperature in deg

Fiesta28 [93]

$\dfrac{5}{9}\cdot (55-32)=\dfrac{5}{9}\cdot 23=\dfrac{115}{9}\approx 13^\circ C$

4 0

3 years ago

Please try to help if you can.

PolarNik [594]

The equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

<h3>The sinusoidal function</h3>

The minimum and the maximum of the function are

Minimum = -1
Maximum = -5

The amplitude (A) is calculated as:

A = 0.5 * (Maximum - Minimum)

So, we have:

A = 0.5 * (-5 + 1)

A = -2

The vertical shift (d) is calculated as:

d = 0.5 * (Maximum + Minimum)

So, we have:

d = 0.5 * (-5 - 1)

d = -3

The period (P) is calculated as:

P = 2π/B

From the graph,

B = 1

So, we have:

P = 2π/1

P = 2π

So, the amplitude is -2 and the period is 2π.

<h3>The equation of the sine function</h3>

In (a), we have:

A = -2

B = 1

d = -3

A sine function is represented as:

y = A sin(Bx + C) + D

So, we have:

y = -2sin(x + C) - 3

The graph passes through the point (0, -5)

So, we have

-5 = -2sin(0 + C) - 3

Solve for C, we have

C = 1.5

So, we have:

y = -2sin(x + 1.5) - 3

Hence, the equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

Read more about sinusoidal function at

brainly.com/question/10700288

#SPJ1

7 0

1 year ago

Find the value of x.<br> (7x - 3)

Musya8 [376]

Answer:

Infinity Many

Step-by-step explanation:

x can pretty much be any number possible. It will just equal something different every time.

8 0

3 years ago