Answer:
<em>good luck, i hope this helps :)</em>
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)
Helen is currently is 8 years old.
<h3>
How to solve world problem ?</h3>
Endeavor to understand the question, analyze it and interpret it into equation.
Given that Helen's age is multiples of 4. Next year it'll be a multiple of 3. Helen's older brother is now 19.
This means Helen current age is multiple of 4 and next year it will be a multiple of 3. Also, Helen's age is less than 19
The two available numbers that fit this analysis and less than 19 are 8 and 9. 8 is multiple of 4. 8 + 1 = 9 which is multiple of 3
Therefore, Helen is 8 years old now
Learn more about Arithmetic here: brainly.com/question/6561461
#SPJ1
Answer:
Step-by-step explanation:
You would never buy a 10-pack, because two 5-packs cost less.
To buy 3 bars you need a single bar and a pair of single bars for £0.82 + £0.82+ £0.41 = £2.05
To buy 30 bars you need 3 pairs of 5-bar packs = 3×£5.75 = £17.25
To buy the remaining 5 bars you need one 5-bar pack = £3
cost = £2.05 + £17.25 + £3 = £22.30
Answer:
x = 15
y = 63
Step-by-step explanation:
9x - 7 + 4x - 8 = 180
13x = 195
x = 15
9x - 7 = 2y + 2
126 = 2y
y = 63
