We can expand

Then using the product and chain rules,



Ok, here we go. Pay attention. The formula for the arc length is

. That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is

(that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of

. Integrating that we have

from -1 to 2.

gives us

. Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly:

which simplifies to

. The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with

. And there you go!
Hello there! The answer to your question is a = 4.
To solve for a in the equation -4 + 4a = 12 you want to isolate, or separate, a from all of the equation's other values.
Our first step is to add 4 to both sides so the 4 cancels out on the left side.
-4+4 + 4a = 12+4
4a = 16
Next, we divide both sides by 4 to finish isolating a.
4/4a = 16/4
a = 4
Want to verify that this is correct? Place the value we found for a (4) into the equation in place of a and if it comes out as a true statement, the answer is correct.
-4 + 4(4) = 12
-4 + 16 = 12
12 = 12
Since 12 is in fact equal to 12, i can guarantee you that i have provided you with the correct answer. I hope this helps & have a great rest of your day! :)
Answer:
a>−6
Step-by-step explanation:
−4(1−5a)>−124
Step 1: Simplify both sides of the inequality.
20a−4>−124
Step 2: Add 4 to both sides.
20a−4+4>−124+4
20a>−120
Step 3: Divide both sides by 20.
20a/20> −120/20
a>−6