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)
You're basically doing 890 divided by 1, so the answer would be 800.. 800 ones.
The volume that could belong to a cube with a side length that is an integer is 64 cubic inches.
Answer:
The new car costs more
Old car = $5062.125
New car = $7161.357
Step-by-step explanation:
Manny drives an average of 110 miles per week with his old car. The old car gets 16 miles per gallon. The cost per gallon is $2.65 repair and Maintainance costs an average of $740 per year.
For the old car, to find the amount spent on the car we have
110/16 * 2.65 = $18.21875 / week
There are 52 weeks in a year. We have
10.21875*52 = $ 947.375
947.375 + 740
= $1687.375
= 1687.357 * 3
= $5062.125
The new car cost $6500 over a three year loan process.
The car gets 28 miles per gallon. It requires a maintenance f $10 per month. For the new car to find the amount, we have
110*28 * 2.65 *52 = $541.357
541.357 + 10(12) + 6500
= $7161.357
