4 years ago

What is value of sin2npi

1 answer:

7 0

$n=0\to\sin(2\cdot0\pi)=\sin0=0\\\\n=1\to\sin(2\cdot1\pi)=\sin2\pi=0\\\\n=2\to\sin(2\cdot2\pi)=\sin4\pi=0\\\vdots\\\sin2n\pi=0\ for\ n\in\mathbb{Z}$

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Integral pls i couldnt

olga nikolaevna [1]

Simplify the integrand:

$\dfrac{4x^4 + 3x^2 + 5x}{x^2} = 4x^2 + 3 + \dfrac5x$

Now integrate one term at a time.

$\displaystyle \int 4x^2 \, dx = \frac43 x^3 + C$

$\displaystyle \int 3 \, dx = 3x + C$

$\displaystyle \int \frac5x \, dx = 5 \ln|x| + C$

Putting everything together,

$\displaystyle \int \frac{4x^4 + 3x^2 + 5x}{x^2} \, dx = \int \left(4x^2 + 3 + \frac5x\right) \, dx = \boxed{\frac43 x^3 + 3x + 5 \ln|x| + C}$

5 0

2 years ago

A 96 foot tree casts a shadow that is 120 feet long. What is the angle of elevation of the sun? Round to the nearest degree.

zysi [14]

Answer:

$\alpha \approx 39^{\circ}$

Step-by-step explanation:

Let assume that tree grows perpendicular to surface. The statement is geometrically represented in the attachment included below, which resembles a right-angled triangle. Lastly, the angle of elevation of the sun is determined with the help of the following trigonometric relationship:

$\tan \alpha = \frac{96\,ft}{120\,ft}$