Alan

The mass is not needed here.

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You need to supply the length of the pendulum and state if there is any damping, and if there is an initial velocity.

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Force is mass times acceleration.  You have given the weight of the truck, not its mass, so you would need to find its mass by dividing this number by the acceleration of gravity (g = 9.8 m/s²) then multiply the result by 3.5m/s²

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$$\frac{x^r-1}{x-1}=x^{r-1}+x^{r-2}+...+x^{r-r}$$

There are r terms so when x = 1 we have r as the value of the sum, and hence of the limit of (x^r - 1)/(x - 1) as x→1

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You can clear the comnplex number from the denominator by multiplying both top and bottom by the complex conjugate of the number on the bottom.  Using your example we have

$$\frac{4i}{-3+6i}$$

The complex conjugate of -3 + 6i is -3 - 6i, so

$$\frac{4i}{-3+6i}=\frac{4i(-3-6i)}{(-3+6i)(-3-6i)}$$

Now the denominator can be expressed as the difference of two squares:  (-3)² - (6i)² = 9 - 36i² = 9 + 36 = 45

and the numerator becomes -3*4i - 6i*4i = -12i -24i² = -12i +24 (or 24 - 12i)

Hence:

$$\frac{4i}{-3+6i}=\frac{24-12i}{45}$$

or $$\frac{4i}{-3+6i}=\frac{8-4i}{15} = \frac{8}{15}-\frac{4i}{15}$$

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I guess this is a binary number.  To find its decimal equivalent do the following:

1*2⁷ + 0*2⁶ + 0*2⁵ +0*2⁴ + 0*2³ + 1*2² + 0*2¹ + 0*2⁰ = 132

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Let y = x^1/3, then your equation becomes 

7y - 1/y² = 0  (I've assumed your equation is meant to be 7x^1/3 - x^-2/3 = 0)

Multiply through by y²

7y³ - 1 = 0

so

y³ = 1/7

But y³ = x so x = 1/7

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This is an identity.

LHS

1 - csc(x)*sin³(x) → 1 - sin³(x)/sin(x) → 1- sin²(x) → cos²(x)

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