Answer:
8
Step-by-step explanation:
The absolute value of |-8| is 8. |8| = 8.
8 is bigger than 3
Answer:
Depends on the type of rope but I would say feet
Step-by-step explanation:
Answer:
1) We know that e is an irrational number, so we usually can find it by computational methods.
![e = \lim_{n \to \infty} (1 + \frac{1}{n})^n](https://tex.z-dn.net/?f=e%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%281%20%2B%20%5Cfrac%7B1%7D%7Bn%7D%29%5En)
and we know that e accurate to 10 decimal points is:
e = 2.7182818285
2) Now we want to write the properties of the exponential and logarithmic functions.
We will write first the exponential property, and then the correspondent one for the logarithmic function.
(e^a)*(e^b) = e^(a + b)
The equivalent Ln property is:
Ln(a) + Ln(b) = Ln(a*b)
(e^a)/(e^b) = e^(a - b)
The eqivalent Ln property is:
Ln(a) - Ln(b) = Ln(a/b)
(e^a)^b = e^(a*b)
The equivalent Ln property is:
Ln(a^b) = b*Ln(a)
Answer:
![\large\boxed{x=2\sqrt{181}\approx26.91}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%3D2%5Csqrt%7B181%7D%5Capprox26.91%7D)
Step-by-step explanation:
If AB is a tangent of a circle, then the angle B is right angle. Therefore the triangle ABC is a rigth triangle.
BC and x are the radius of a circle. Therefore BC = x.
Use the Pythagorean theorem:
![BC^2+BA^2=AC^2](https://tex.z-dn.net/?f=BC%5E2%2BBA%5E2%3DAC%5E2)
We have
![BC=x,\ BA=80,\ AC=82](https://tex.z-dn.net/?f=BC%3Dx%2C%5C%20BA%3D80%2C%5C%20AC%3D82)
Substitute:
![x^2+80^2=82^2](https://tex.z-dn.net/?f=x%5E2%2B80%5E2%3D82%5E2)
<em>subtract 6400 from both sides</em>
![x^2=724\to x=\sqrt{724}\\\\x=\sqrt{4\cdot181}\\\\x=\sqrt4\cdot\sqrt{181}\\\\x=2\sqrt{181}](https://tex.z-dn.net/?f=x%5E2%3D724%5Cto%20x%3D%5Csqrt%7B724%7D%5C%5C%5C%5Cx%3D%5Csqrt%7B4%5Ccdot181%7D%5C%5C%5C%5Cx%3D%5Csqrt4%5Ccdot%5Csqrt%7B181%7D%5C%5C%5C%5Cx%3D2%5Csqrt%7B181%7D)