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:
The largest number of pyramids she can make from 20 bars of chocolate is:
Step-by-step explanation:
Firstly, you must find the volume of the 20 bars of chocolate, remember that each bar contains 6 cubic inches of chocolate (6 in^3), so:
- Volume of the bars = 6 in^3 * 20
- <u>Volume of the bars = 120 in^3</u>
Now, you must find the volume of each pyramid, using the next formula:
- Volume of a pyramid = 1/3 B * h
Where:
<em>B = area of the square base.</em>
<em>h = height of the pyramid.</em>
How these values are given in the problem, we only replace the values in the formula:
- Area of a pyramid = 1/3 (1 in^2) * 2 in
- <u>Area of a pyramid = 2/3 in^3</u>
Finally, we divide the volume of the bars in the volume of each pyramid:
- Total number of pyramids = 120 in^3 / 2/3 in^3
- <u>Total number of pyramids = 180</u>
Answer: -2
Step-by-step explanation:
So basically I located the y-intercept first. Where is that? At the point (0,-2). Now from there, I found the nearest point on an intersecting grid line, in this case it would be (-1,0). So from the y-intercept, I looked at how many spaces I would have to move to get to (-1,0). You would have to go up 2 spaces and to the left 1 space. This is also written as 2/-1. Simplify this and you get -2! Hope this helped!
$42.50 divided by 4 is 10.625
Than rounding that up to the nearest hundreds which is the number 2, the total is $10.63.
Answer:
The correct quotient is 3.
I think Derek has mistaken to divide 
by 
.
Step-by-step explanation:
We have to check the quotient of 
.
Part A:
Now, .
= 
So, the correct quotient is 3.
Part B:
Derek says that the quotient is 
.
So, I think Derek has mistaken to divide by . (Answer)
