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4 years ago

What is the value of x

Mathematics

2 answers:

morpeh [17]4 years ago

7 0

using the formula of C^2 = A^2 + B^2

10^2= 6^2 + B^2

100 = 36 + B^2

100 - 36 = B^2

64 = B^2

Square Root of 64 = 8

value of x = 8

SVEN [57.7K]4 years ago

4 0

Using the pythagorean theorem, the value of x would be eight. The equation of Pythagorean is

a^2 + b^2 = c^2

(C is the hypotenuse. Hypotenuse being the length of 10) Applying the lengths leaves us with the equation

36 + x^2 = 100.

You then subtract 36 from 100 to get X alone on the opposite side of the equation.

X^2 = 64

Lastly, you take the square root of 64. Therefore, the final answer will be eight.

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∫<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2019%7D%7Bx%5E%7B2%7D%2B9%20%7D" id="TexFormula1" title="\frac{x+2019}{x^{2}+9

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$\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx$

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$\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)$

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$\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C$

Then

$\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}$

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3 years ago

What is the value of x ​

What is the value of x