Answer:
243
Step-by-step explanation:
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)
I think this is the Transitive postulate of equality.
Personally I can't see much point in giving labels to these equalities.
Answer:
We put the value of the x in the formula
f(6)=
Step-by-step explanation:
Than solve equation.
Answer: 17/60
Step-by-step explanation:
Change all of the fractions to have a common denominator:
LCM of 10, 12, 15 is 60
You get 12/60, 25/60, and 54/60.
54/60 is what he had at the start, and so you can just subtract what he gave away
54/60-12/60=42/60
42/60-25/60=17/60
17 is a prime number so you cannot simplify the fraction
