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:
H) 24
Step-by-step explanation:
24 is the only number that is divisible by 3.
CHECK:
3 x 8 : 4 x 8
24:32✔
(<em>You</em><em> </em><em>can</em><em> </em><em>try</em><em> </em><em>dividing</em><em> </em><em>'</em><em>3</em><em>'</em><em> </em><em>by</em><em> </em><em>the</em><em> </em><em>other</em><em> </em><em>numbers</em><em> </em><em>to</em><em> </em><em>also</em><em> </em><em>check</em><em> </em><em>your</em><em> </em><em>answer</em>)
Hope this helped ^^
A, D, E and F are all true statements.
When looking for congruence in these type of problems, you have to look for the order of the letters in the original listing. Since they are listed LMN and PQR, this means we have to focus on the placement of those letters. Since L is the first listed in the sequence, it is congruent with P, which is also listed first. M is congruent with Q since they are both in the middle, and N and R are congruent since they are both at the end.
Now to find true statements, you need to make sure everything matches up in the statement.
Let's take A for instance. It states that MN = QR. Now we know M is in the middle and N is at the end. Since Q is in the middle and R is at the end, they match and are therefore true.
Answer: 13
Step-by-step explanation: i googled it
