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2 years ago

What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.

2 answers:

8 0

Sample Response/Explanation: I would use the square root property of equality. Because there is no x term, I would just add and divide to get x2 by itself. Then I would take the square root.

oksano4ka [1.4K]2 years ago

7 0

I would add 7 to get ...

... 2x² = 16

then divide by 2 to get

... x² = 8

Now, I would take the square root, recognizing that both positive and negative values will solve the problem.

... x = ±√8

The root can be simplified, so we have ...

... x = ±2√2

_____

The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.

... 2x² -16 = 0 . . . . subtract 9

... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula

... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result

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The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

iren [92.7K]

For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

$\dfrac{3\pi}2\approx5$

$\dfrac{5\pi}2\approx8$

$\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1$

$2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7$

$2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6$

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2 years ago

Steve and josephina run a total of 42 miles in a week. Steve ran six fewer miles than josephina. How many miles did josephina ru

Zielflug [23.3K]

Subtract 42 from 6 and you get 36

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2 years ago

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A company makes 150 bags.

irina [24]

35% chance because the company made 150 bags

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1 year ago

A ----------------------- chart would best describe the steps in the processing of a product.

BlackZzzverrR [31]

A: a flow chart would best describe the steps

4 0

2 years ago

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Which reaction describes a beta emission? 2659Fe→ 2759Co + −10e 88226Ra→ 86222Rn + 24He ��94239Pu + 24He→ 96242Cm + 01n

shepuryov [24]

Correct question:

Which reaction describes a beta emission? 2659Fe→ 2759Co + −10e, 88226Ra→ 86222Rn + 24He, 94239Pu + 24He→ 96242Cm + 01n, 54118Xe→ 53118I + +10e

Answer:

2659Fe→ 2759Co + 1e

Step-by-step explanation:

General equation for beta decay is given as;

$^A_zX -> \ ^A_{z+1}Y +\ ^0_{-1} \beta$

where;

A is the atomic mass of the element

z is atomic number of the element

X is the parent atom

Y is the daughter element

β is beta emission

In beta emission, there is loss of one electron and zero proton, the will cause the daughter element to gain on electron in order to balance the reaction.

Based on beta decay equation above, we select the reaction that describes beta emission.

2659Fe→ 2759Co + 1e

Here;

A = 59

z = 26

z + 1 = 27

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2 years ago

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