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:
Relative Frequency Method
Step-by-step explanation:
If I carry out an experiment involving 25 throws of a coin and I obtain 13 Heads(H), the Relative Frequency of obtaining Heads will be 13/25.
Now if I intend to find out approximately how many Heads will
occur in 300 throws, I simply use the result or experimentation data that I have.
This is done below:
Relative Frequency of Obtaining a Head= 13/25 =0.52
Number of Heads obtained in 300 throws
= Relative Frequency X Number of Trials
=0.52 X 300
=156
This is an example of how relative frequency method works.
<h2>...571 is the correct answer!</h2><h3></h3><h3>This decimal is <u>repeating.</u></h3><h3>The pattern is 571428</h3><h3></h3><h3><em>Please let me know if I am wrong.</em></h3>
The picture is very blurry I can’t see , wish I could help doe !!! Can you still mark brainliest for effort of trying to help !?
