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4 years ago

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

Physics

1 answer:

lora16 [44]4 years ago

3 0

<h3>Solution:</h3>

firstly solve parenthesis bracket ( )

-4×3 + 4×5x ≥ -6x + 9

-12 + 20x ≥ -6x + 9

Add 12 on both sides

-12 + 12 + 20x ≥ -6x + 9 + 12

20x ≥ -6x + 21

Add 6x on both sides

6x+ 20x ≥ -6x + 6x + 21

26x ≥ 21

divide both side by 26

26 x/26 ≥21/26

x ≥21/26

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A baseball with a mass of 0.15 kilograms collides with a bat at a speed of 40 meters/second. The duration of the collision is 8.

Vedmedyk [2.9K]

Answer: 1687.5 N

Explanation:

From the second law of motion given by Newton, Force is the rate change of momentum.

$F = \frac{dp}{dt}=\frac {m dv}{dt} = \frac{m (v_f-v_i)}{dt}$

Mass of the baseball, m = 0.15 kg

Initial velocity, $v_i=-40 m/s$ (negative because direction of initial velocity is opposite to the final velocity)

Final velocity, $v_f=50 m/s$

The duration of collision, $dt= 8.0 \times 10^{-3} s$

Force, $F = \frac{0.15 kg (50-(-40) m/s)}{8.0 \times 10^{-3} s}=1687.5 N$

Hence, the value of force is 1687.5 N.

8 0

3 years ago

Which has more kinetic energy, a 4.0 kg bowling ball moving at 1.0 m/s or a 1.0 kg

jolli1 [7]

Answer:

The kinetic energy of bocce ball is more.

Explanation:

Given that,

Mass of a bowling ball, m₁ = 4 kg

Speed of the bowling ball, v₁ = 1 m/s

Mass of bocce ball, m₂ = 1 kg

Speed of bocce ball, v₂ = 4 m/s

We need to say which has more kinetic energy.

The kinetic energy of an object is given by :

$E=\dfrac{1}{2}mv^2$

Kinetic energy of the bowling ball,

$E_1=\dfrac{1}{2}m_1v_1^2\\\\E_1=\dfrac{1}{2}\times 4\times (1)^2\\\\E_1=2\ J$

The kinetic energy of the bocce ball,

$E_2=\dfrac{1}{2}m_2v_2^2\\\\E_2=\dfrac{1}{2}\times 1\times (4)^2\\\\E_2=8\ J$

So, the kinetic energy of bocce ball is more than that of bowling ball.

5 0

3 years ago

Referring to the graph below of data describing a cart pulled across a level surface. When a 4 N force pulls on the cart, the ca

LenKa [72]

Answer:gjv

Explanation:

4 0

3 years ago

Read 2 more answers

Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm

mario62 [17]

Answer:

A) if each astronaut breathes about 500 cm³, the total volume of air breathed in a year is 14716.8m³.

B) The Diameter of this spherical space station should be 30.4m

Explanation:

The breathing frequency (according to Rochester encyclopedia) is about 12-16 breath per minute. if we take the mean value (14 breath per minute), we can estimate the total breaths of a person along a year:

$f_b=14\frac{br}{min} \cdot \frac{60min}{1hr} \frac{24hr}{1day}\frac{365day}{1year}=29433600\frac{br}{year}$

If we multiply this for the number of people in the station and the volume each breath needs, we obtain the volume breathed in a year.

The volume of a sphere is:

$V_{sph}=\frac{4\pi}{3}r^3$

So the diameter is:

$D=2r=2\sqrt[3]{\frac{3V_{sph}}{4\pi}} =30.4m$

6 0

3 years ago

What's the formula for efficiency?

Neko [114]

Answer:

r=P/C, where P is the amount of useful output ("product") produced per the amount C ("cost") of resources consumed.

Explanation:

Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output ("product") produced per the amount C ("cost") of resources consumed.

3 0

3 years ago