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2 years ago

Solve the following quadratic equations:2x² - 4x - 9 = 0 x₊ = 1 + √22/2Answersx_ = 1 - √22/2

Physics

1 answer:

Pavel [41]2 years ago

6 0

The root quadratic equation of $2x^{2} - 4x - 9 = 0$ is $x=\frac{2+\sqrt{22}}{2},\:x=\frac{2-\sqrt{22}}{2}$

What is the formula used to calculate the quadratic equation?

To solve the quadratic equation use the formula of $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Find the quadratic equation by using the formula ?

On comparing with $2x^{2} - 4x - 9 = 0$

We get , $a=2 , b=-4 , c=-9$

$D=b^{2} +7\\\\\\=(-4)^{2} +7*2*(-9)\\\\=-16-126\\\\=110$

By using the formula,

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X==\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\c* \:2\left(-9\right)}}{2\c* \:2}\\\\\sqrt{\left(-4\right)^2-4\cdot \:2\left(-9\right)}\\\\$

Apply rule,

$-(-a)=a\\\\=\sqrt{\left(-4\right)^2+4\cdot \:2\cdot \:9}\\\\$

Apply exponent rule,

$(-a)^{n} =a^{n}$ if n is even

$(-4)^{2} =4^{2}$

$\sqrt{4^2+4\cdot \:2\cdot \:9}$

Multiply the numbers :

$4*2*9=72\\\\\sqrt{4^2+4\cdot \:2\cdot \:9}\\\\4^{2} =16\\\\=\sqrt{16+72}\\\\$

Add the number $=\sqrt{88}$

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Answer: v= 1.23 m/s θ = 75.3º

Explanation:

First of all, we define the direction in which both fruits are tossed as the x axis, so all initial momenta have horizontal components only.

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Replacing by the values of m1, m₂, vi₁, vi₂, and vf₂, we can calculate the value of the angle θ, that the apple forms with the horizontal, as follows:

(1) -0.13 Kg. 1.05 m/s + 0.15 Kg. 1.18 m/s = 0.13. vf . cos θ

(2) 0.15 Kg. 1.03 m/s = 0.13 vf. sin θ

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3 years ago

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4 years ago

In 2017, the company SpaceX became the first private company to send supplies to the International Space Station with a reusable

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Assumption: air resistance on the rocket is negligible. Take $g = \rm 9.81\; m \cdot s^{-2}$ .

Explanation:

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$\displaystyle \text{Acceleration} = \frac{\text{Net Force}}{\text{Mass}}$ .

Note that in this case, the uppercase letter $\rm M$ in the units stands for "mega-", which is the same as $10^6$ times the unit that follows. For example, $\rm 1\; Mg = 10^6\; g$ , while $\rm 1\; MN = 10^6\; N$ .

Convert the mass of the rocket and the thrust of its engines to SI standard units:

The standard unit for mass is kilograms: $\displaystyle m = \rm 552\; Mg = 552 \times 10^6\; g \times \frac{1\; \rm kg}{10^3\; g} = 552 \times 10^3 \; kg$ .
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At launch, the velocity of the rocket would be pretty low. Hence, compared to thrust and weight, the air resistance on the rocket would be pretty negligible. The two main forces that contribute to the net force of the rocket would be:

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Weight (downwards due to gravity.)

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The magnitude of the net force on the rocket would be

$\begin{aligned}&\text{Thrust} - \text{Weight} \\ &= 7.61 \times 10^6\; \rm N - 5.41412\times 10^6\; N \\ &\approx 2.19 \times 10^6\; \rm N\end{aligned}$ .

Apply the formula $\displaystyle \text{Acceleration} = \frac{\text{Net Force}}{\text{Mass}}$ to find the net force on the rocket. To make sure that the output (acceleration) is in SI units (meters-per-second,) make sure that the inputs (net force and mass) are also in SI units (Newtons for net force and kilograms for mass.)

$\begin{aligned}\displaystyle &\text{Acceleration} \\ &= \frac{\text{Net Force}}{\text{Mass}} \\ &= \frac{2.19 \times 10^6\; \rm N}{552 \times 10^3\; \rm kg} \\ &\approx \rm 3.98\; \rm m \cdot s^{-2}\end{aligned}$ .

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