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)
The length of the third side is 4 7step-by-step the explanation- the perimeter of a triangle is 16 to the square root of 7 feet.
Answer: Barbara did not include a variable in the term 
, which must represents the number of bottles of iced tea she needs to sell.
Step-by-step explanation:
Let be "x" the number of bottle of water Barbara needs to sell and "y" the number of bottle of iced tea she needs to sell.
She sells iced tea for $1.49 per bottle and water for $1.25 per bottle, so she can write the following equation in order to calculate the number of bottles she needs to sell to earn $100:
Since Barbara wrote this equation:
We can conclude that the error Barbara made in writing the equation was: She did not include a variable in the term , which must represents the number of bottles of iced tea she needs to sell.
The answer is D, 8$. One easy way to do it is to take 10% of 40, which is 4, and double it.
