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)
Answer:
Step-by-step explanation:
value of 4, and you want to square it or exponent 2
so 4^2 = 4x4
=16
What is ^-2
It does the same operation however because to is negative it really means putting 4 in the denominator so 2 becomes positive. Inverse of the exponent 2
1/4^2 is the same as 4^-2
which will both give 1/16
Answer:
x = 6.3375
Step-by-step explanation:
sin53 = 4/5 (roughly) = 5.07/x
=> 4x = 25.35
=> x = 6.3375
2/3 would be the answer hope this helps.
Answer:
The equations that represent the reflected function are
Step-by-step explanation:
The correct question in the attached figure
we have the function
we know that
A reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and −x.
therefore
The reflection of the given function across the y-axis will be equal to
(Remember interchanges positive x-values with negative x-values)
An equivalent form will be
![f(x)=5(\frac{1}{5})^{(-1)(x)}=5[(\frac{1}{5})^{-1})]^{x}=5(5)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B%28-1%29%28x%29%7D%3D5%5B%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-1%7D%29%5D%5E%7Bx%7D%3D5%285%29%5E%7Bx%7D)
therefore
The equations that represent the reflected function are
