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)
2) C: 4+d
3) A: x-3
4) C: 5(1-f)
I know that this is a few weeks late...
but hope this helps!
14) 23.24778564
15) 38.01327111
The last one, I also need help
Answer:
15
Step-by-step explanation:
x = 2
-4x+8+2x+3 = ?
-4 (-2) + 8 + 2 (-2) + 3 =
= 8 + 8 - 4 + 3
= 16 - 4 + 3
= 12 + 3
= 15
hopefully this helped you :)
(3x + 5)° + (10x - 7)° = 180°
13x + (-2) = 180
13x = 180 + 2
13x = 182
x = 14
∠QRT = 3 * 14 + 5 = 42 + 5 = 47°
∠TRS = 10 * 14 - 7 = 140 - 7 = 133°
