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)
4(2x-5)+7(x+2)
bracket means multiplying
do 4(2x+5) first
4*2x=8x
4*-5=-20
7*x=7x
7*2=14
8x-20+7x+14
do the x first
8x+7x=15x
-20+14=-6
answers: 15x-6 or -6+15x
an eight pack because you get more water and its cheaper that way
I hope this helps you
42=1.42
42= 2.3.7
42= 6.7
Answer:
28
Step-by-step explanation:
probability of getting blue ball is 4/9
total cases = 72
i.e number of blue ball 32
number of red vall is 40
so extra 28 is added
