Answer:
Plot the line y = 2x - 3 and the portion above the line will satisfy the inequality.
Use the power rule for differentiation:
You can use this formula if you remember that a root is just a rational exponential:
![\sqrt[4]\ln(x) = (\ln(x))^{\frac{1}{4}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%5Cln%28x%29%20%3D%20%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20)
So, remembering that the derivative of the logarithm is 1/x, you have
Which you can rewrite as
![\dfrac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x} =\dfrac{1}{4}(\ln(x))^{\frac{-3}{4}}\dfrac{1}{x} =\dfrac{1}{4}\dfrac{1}{\sqrt[4]{\ln(x))^3}}\dfrac{1}{x} = \dfrac{1}{4x\sqrt[4]{\ln(x))^3}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B1%7D%7B4%7D-1%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%5Cdfrac%7B1%7D%7B4%7D%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B-3%7D%7B4%7D%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%5Cdfrac%7B1%7D%7B4%7D%5Cdfrac%7B1%7D%7B%5Csqrt%5B4%5D%7B%5Cln%28x%29%29%5E3%7D%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%20%5Cdfrac%7B1%7D%7B4x%5Csqrt%5B4%5D%7B%5Cln%28x%29%29%5E3%7D%7D%20)
Answer:
x² + (y+3)² = 4²
Step-by-step explanation:
A close look at the diagram reveals that the center of this circle is (0, -3) and that the radius is 4 units.
Starting from the general equation of a circle, (x - h)² + (y - k)² = r²
and substituting the givens (h = 0, k = -3, r = 4), we get:
x² + (y+3)² = 4². This is Answer B.
Answer: pi
Step-by-step explanation:
Formula for circumference = 2 x pi x radius
Formula for diameter = 2 x radius
Plug in 6.25 for radius
Circumference = 2 x pi x 6.25
Diameter = 2 x 6.25
Find ratio by diving Circumference over Diameter:
(2 x pi x 6.25) / (2 x 6.25)
Simplify: answer is pi
could also be 3.14
Step-by-step explanation:
Substitute 3 and 4 into the expression:
3(3)²+24(4)
Work it out:
3(3)²+24(4)=123
