Answer:
f(x)=-18x^2
Step-by-step explanation:
Given:
1+Integral(f(t)/t^6, t=a..x)=6x^-3
Let's get rid of integral by differentiating both sides.
Using fundamental of calculus and power rule(integration):
0+f(x)/x^6=-18x^-4
Additive Identity property applied:
f(x)/x^6=-18x^-4
Multiply both sides by x^6:
f(x)=-18x^-4×x^6
Power rule (exponents) applied"
f(x)=-18x^2
Check:
1+Integral(-18t^2/t^6, t=a..x)=6x^-3
1+Integral(-18t^-4, t=a..x)=6x^-3
1+(-18t^-3/-3, t=a..x)=6x^-3
1+(6t^-3, t=a..x)=6x^-3
That looks great since those powers are the same on both side after integration.
Plug in limits:
1+(6x^-3-6a^-3)=6x^-3
We need 1-6a^-3=0 so that the equation holds true for all x.
Subtract 1 on both sides:
-6a^-3=-1
Divide both sides by-6:
a^-3=1/6
Raise both sides to -1/3 power:
a=(1/6)^(-1/3)
Negative exponent just refers to reciprocal of our base:
a=6^(1/3)
Answer:
Your correct and final answer is (9+x^6) (3+x^3) (3-x^3)
Hope this helps!!!
Answer:
A liter is 1000 mL so half of 1000 = 500
500 mL is the answer!Step-by-step explanation:
Both point (5,12) and (11,12) lie on the horizontal line y=12.
If these two points is a leg of the triangle, the other leg must be perpendicular to the horizontal line, that is, the other leg must be vertical, but passing through either (5,12) or (11,12), i.e. lies on either the vertical line x=5 or x=11.
There is only one point that passes through x=11, i.e. point A(11,4).
