Answer:
Step-by-step explanation:
So we have the function:
To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:
Add 9 to both sides:
Take the natural log of both sides:
The right side cancels:
Divide both sides by 6:
And we're done!
Answer:
b = a divided by 6
Step-by-step explanation:
Since a is equal to b times 6, you would have to divide a by 6 to find b
Answer:
86 units squared.
Step-by-step explanation:
If the perimeter is 30 and it is an equilateral triangle, the means each side of the triangle is equal so they must all be 10 units longs. Since the line XA is part of the quadrilateral, lines FL and XA of the rectangle must be 10 units long. But we still don't know the length of the sides. Within the box are two right triangles, FZX and ZLA. We know the the length of the hypotenuse which is 10 units, and the base which is 5 units. Then we use the Pythagorean Theorem so find the length of the sides. After we do that we get about 8.6. Now we can multiply the length and width to get an area of 86.
The partial fraction expansion takes the form
-6<em>x</em>/((<em>x</em> + 2) (<em>x</em> + 8)) = <em>a</em>/(<em>x</em> + 2) + <em>b</em>/(<em>x</em> + 8)
Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.
Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:
-6<em>x</em> = <em>a</em> (<em>x</em> + 8) + <em>b</em> (<em>x</em> + 2)
Expand the right side and collect terms by powers of <em>x</em> :
-6<em>x</em> = (<em>a</em> + <em>b</em>) <em>x</em> + (8<em>a</em> + 2<em>b</em>)
It follows that
<em>a</em> + <em>b</em> = -6 and 8<em>a</em> + 2<em>b</em> = 0
==> <em>a</em> = -2 and <em>b</em> = 8
So we end up with
-6<em>x</em>/((<em>x</em> + 2) (<em>x</em> + 8)) = -2/(<em>x</em> + 2) + 8/(<em>x</em> + 8)
