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:
x = 71/8
Step-by-step explanation:
Solve for x:
5 X (8 x - 71) = 0
Divide both sides by 5 X:
8 x - 71 = 0
Add 71 to both sides:
8 x = 71
Divide both sides by 8:
Answer: x = 71/8
Answer:
Tony can buy three games with his savings over two months and Alice can buy six concert tickets.
Step-by-step explanation:
Over two months, Tony has watched a total of 53.6 hours of television (35.4 + 18.2). If he save $2.50 for each hour, we can multiply his total hours by the amount per hour, or 53.6 x 2.50 = $134.00. Since each game that Tony wants to buy costs $35.75, we need to divide his total savings by the cost of each game, or 134/35.75 = 3.75. Since Tony can't buy a portion of the game, the most amount of games he can buy is 3. Alice watched a total of 48.4 hours of television (21.8 + 26.6). If she also saves $2.50 per hour, then her total savings is 2.50 x 48.4 = $121.00. Since her concert tickets are $17.50 a piece, we divide her total savings: 121/17.50 = 6.9. Alice can also not buy a partial ticket, so the total amount she can buy is 6.
I think it’s 4 if the lines are going up by 2
