The image contains a mathematical derivation with equations involving calculus and exponential functions. 1. The first line of the derivation is: \[ = -\frac{2a^2}{t} \cdot \frac{dS}{dx} \] 2. The next step simplifies to: \[ = -\frac{12a^2 \cdot \frac{dS}{dx}} \] 3. A boxed equation is shown as: \[ S = -\frac{\alpha}{2a^2} S \] 4. The final expression in this segment of the derivation is: \[ S(x) = C e^{-\frac{\alpha^2}{4a^2}} \] The equations appear to be part of a derivation involving differential equations and solving for a function \( S(x) \) in terms of an exponential function. This type of derivation is common in fields involving mathematical physics or engineering, where such functions describe certain physical phenomena.

Q: Hi, I believe the function was not entered correctly in the transcription. It should be x^2-16/x-2.…

A: Apologies for the inconvenience. First two steps were correct in the original solution. Step 3 was…

Q: What is the final answer? I tried 11e^2 - 27 it was wrong

A:

Q: differentiate ((x^2) - 1)^2

A:

Q: Which expression is equal to 2^3 ? (2^3 means 2 raised to the power of 3) Choose all that apply,…

A: which option

Q: How to solve step by step: (x^2 * y^6 / x^3 * y^2)^-2

A: For division, we subtract the exponents

Q: Find the value of the expression: x^2−(a+b)x+ab divide by x^2−(a+c)x+ac  where a = 1.8, b = 4, c =…

A: We have to find the value of the expression: x2−(a+b)x+ab divide by x2−(a+c)x+ac  where a = 1.8, b =…

Q: how do you find 87=a+b+c for x^2 and -3a-5b+2c=190 for x

A: The solution is shown in step-2

Q: At the beginning, how does x^2+y^2+z^2=64 become z^2+y^2+z^2=64

A: Solution:- Given question is x2+y2+z2=64If we put x=z then above equation becomes as- z2+y2+z2=…

Q: don't understand why it is An*r^-n + Bn*r^-n. Why is it r^-n and not r^n? Please let me know. Thank…

A:

Q: Evaluate: y=2+3x^2+4x^3 when x = 76 Give your answer to 1 decimal place

A:

Q: Use algebra to simplify the expression 1 - x^4 / x^2 - 1

A:

Q: In step 2 , how did 86=1/2 x (x-8) turn to x^2-8x-172=0? Thank you, God bless.

A:

Q: The length of a rectangle is (x^2 +7x+6)/(x+1) and the total area of the rectangle is…

A:

Q: I don't understand why it is -(r^2-3x1^2)/(r^5). Isn't it supposed to be r^3. Why is it r^2? Please…

A: Need to find  where

Q: Hi, I am confused how did you get the equation 17(1)^2-14(1)+3 in step 2 of your explanation?

A: We have to tell how to get the equation  17(1)2 - 14(1) + 3 in step 2

Q: the difference between 5^-4 and (-5)^4 ?  Find the value for each.

A:

Q: I don't understand why you started with (3)^2=2mod7. Please explain it to me. Thank you

A:

Q: Why is (-5)^2= -5 x -5 = 25 but -5^2 = -5 x 5 = -25. How does the parenthesis make a difference in…

A: Make it a thumb rule regarding this that if there is no parenthesis, then the negative part has to…

Q: don't understand how ba^2b^-1=beb^-1. Why a^2=e. I don't understand that.

A: how ba2b-1=beb-1?And a2=e?

Q: x^{2}+x+y-8=0 24x^{2}+93x+y+84=0

A: We have to solve the given equations.

Q: Simplify (7/√x) x^-1 Write your answer in the form ax^n without using radicals. You can use the…

A:

Q: What is the answer to this? 2x^2-5=3x

A:

Q: For 2x^2+5=-x what is the correct substitution for a,b,and c in general form of ax2+bx+c=0 ??

A:

Q: I thought the larger number was always A^2?

A: We need to clear doubt.