Step-by-step explanation:
the derivative of an inverse function is
1/f'(f^-1(x))
f'(x) = -6x²
f^-1(7) is solving the original function equation for x under the knowledge that y = 7
7 = 5 - 2x³
2 = -2x³
-1 = x³
=>
x = -1
f'(-1) = -6×(-1)² = -6×1 = -6
so,
(f^-1)'(7) = -1/6
Answer:
x= 3.5
Step-by-step explanation:
2x + 3 = 10 (-3)
2x = 7 (divide by 2 )
x = 3.5
Answer:
a = 40
Step-by-step explanation:
This is a multi-step equation using the distributive property and rational coefficents (fractions). The first step is to complete the distributive property on both sides of the equation and multiply each term in the expression in parenthesis by the constant on the outside. (3/4 x 2a) - (3/4 x 6) +1/2 = (2/5 x 3a) + (2/5 x 20). When we multiply and simplify, we get 3/2a - 9/2 + 1/2 = 6/5a + 8. Next step is to combine like terms: 3/2a - 8/2 = 6/5a +8. We then need to isolate the variable by using inverse operations: 3/10a = 12, then solve for 'a' by multiplying both sides by the reciprocal (10/3) to get a = 40.
P=a+b+c. Sub in what we know: 29=a+a+(a+5). Combine like terms: 29=3a+5. Subtract 5 from both sides: 24=3a. Divide by 3: 8=a. Short sides: A=8m, b=8m, long side: c=13m. :)
