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3 years ago

BRAINLIEST for the correct answer!

Mathematics

1 answer:

Vladimir [108]3 years ago

4 0

Answer:

answer is A

Step-by-step explanation:

(3 $x^{2}$ +5x+1) ( $x^{2}$ −2x+4)

=(3 $x^{2}$ +5x+1)( $x^{2}$ +−2x+4)

=(3 $x^{2}$ )( $x^{2}$ )+(3 $x^{2}$ )(−2x)+(3 $x^{2}$ )(4)+(5x)( $x^{2}$ )+(5x)(−2x)+(5x)(4)+(1)( $x^{2}$ )+(1)(−2x)+(1)(4)

=3 $x^{4}$ −6 $x^{3}$ +12 $x^{2}$ +5 $x^{3}$ −10 $x^{2}$ +20x+ $x^{2}$ −2x+4

=3 $x^{4}$ − $x^{3}$ + 3 $x^{2}$ + 18x +4

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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

What are the domain and range of g(x)= √x-3?

Vera_Pavlovna [14]

Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

5 0

1 year ago

Diane keeps her ribbons in a drawer. She has 3 white ribbons, 6 pink ribbons, 2 yellow ribbons, and 7 blue ribbons. Without look

Akimi4 [234]

Answer:

1/3

Step-by-step explanation:

She has 18 ribbons in total and she has 6 pink ribbons so she has a 6/18 chance or 1/3 chance of pulling a pink ribbon

6 0

2 years ago

The approximate time between two high tides or<br> two low tides is?

NeX [460]

Answer:

It's (very roughly) 12 hours from one high tide to the next, and of course the same for low tides. That's because the tides produced when the Moon is directly overhead or in the opposite direction are the same. Same with two low tides, since there are two tides a day (both low and high).

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3 years ago

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Joyce old 218 cupcakes of lemonade at his lemonade stand. What is 218 rounded to the nearest tens

MAXImum [283]

220

from 218 the 1 is in the tens column. this is the figure that needs to be rounded.

using the following rule

If the digit after the 1 is ≥ 5 then round 1 up to 2

If the digit after the 1 is < 5 then the 1 remains as 1

here the digit after the 1 is 8 so the 1 in the ten's column becomes 2 and the 8 is replaced by 0

218 ≈ 220 ( to the nearest ten )

7 0

3 years ago