Comparision of volume of sphere and cube=0.98820059
coparision of surface area of sphere and cone=0.807582012
Look at the picture.
The base of the ladder is 6.47 feet from the house.
Your answer goes to 3995.100
Answer:
40°, 60°, and 80°
Step-by-step explanation:
We know that the sum of the angles of a triangle is equal to 180°.
We can use this equation to solve for these angles:
180 = 2x + 3x + 4x
180 = 9x
20 = x
Then substitute the solution in for x to solve for the angles:
2(20) = 40°
3(20) = 60°
4(20) = 80°
Therefore, the angles are 40°, 60°, and 80°.
Answer:
(f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
Step-by-step explanation:
The function f⁻¹(x) is the reflection of the function f(x) across the line y=x. Every point (a, b) that is on the graph of f(x) is reflected to be a point (b, a) on the graph of f⁻¹(x).
Any line with slope m reflected across the line y=x will have slope 1/m. (x and y are interchanged, so m=∆y/∆x becomes ∆x/∆y=1/m) Since f'(x) is the slope of the tangent line at (x, f(x)), 1/f'(x) will be the slope of the tangent line at (f(x), x).
Replacing x with f⁻¹(x) in the above relation, you get ...
... (f⁻¹)'(x) = 1/f'(f⁻¹(x)) will be the slope at (x, f⁻¹(x))
Putting your given values in this relation, you get
... (f⁻¹)'(b) = 1/f'(f⁻¹(b)) = 1/f'(a)
