I don’t think it is a function because you can’t have two 0’s on the Y axis it doesn’t work
Answer: x = 2.65, y = 3.81
Step-by-step explanation:
ABC similar to PQR
1) Find the ratio of corresponding sides
2) Use that ratio to find values for x & y
1) Side AB = 2.76cm & Side PR = <em>y</em><em> </em>cm
Side BC = <em>x</em> cm & Side RQ = 3.66 cm
Side CA = 3 cm & Side QP = 4.14 cm (both lengths given)
Can match 3 to 4.14 & ratio of sides in ABC to PQR= 3 /4.14
Length of sides ABC = 3/4.14 times the length of sides PQR
2) x = (3 / 4.14) * 3.66 = 2.65
Now solve for y, ABC to PQR: 2.76 = (3 / 4.14) (<em>y </em>)
<em>equality property</em> (both sides) & inverse operation to isolate <em>y : </em> . 2.76 ÷ (3 / 4.14) = (3 / 4.14 ) ÷ (3 / 4.14) (<em>y</em><em>)</em>
2.76 * (4.14 / 3) = 3 / 4.14 * (4.14 / 3) (<em>y</em><em>)</em>
(2.76 * 1.38 ) = 3.81 = <em>y</em>
<em></em>
<em>Scale Factor Method: Determine the Multiplier</em>
Small to Big or Big to Small ➜ Be sure not to switch
Answer: The required derivative is 
Step-by-step explanation:
Since we have given that
![y=\ln[x(2x+3)^2]](https://tex.z-dn.net/?f=y%3D%5Cln%5Bx%282x%2B3%29%5E2%5D)
Differentiating log function w.r.t. x, we get that
![\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5Bx%27%282x%2B3%29%5E2%2B%282x%2B3%29%5E2%27x%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5B%282x%2B3%29%5E2%2B2x%282x%2B3%29%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B4x%5E2%2B9%2B12x%2B4x%5E2%2B6x%7D%7Bx%282x%2B3%29%5E2%7D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B8x%5E2%2B18x%2B9%7D%7Bx%282x%2B3%29%5E2%7D)
Hence, the required derivative is 
Keep the denominators the same and subtract the numerators. So for example in your example:
7/8 - 3/8
Leave the 8 alone. Subtract 3 from 7.
7 - 3 = 4
So answer is:
4/8
Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2
Hello from MrBillDoesMath!
Answer:
225
Discussion:
Sum ( 2n - 1) from n = 1 to 15
= Sum(2n) - Sum(1) from n = 1 to 15
= 2 Sum(n) - Sum(1) from n = 1 to 15
= 2* 15(15+1)/2 - (1 + 1 + .. + 1)
The first value comes from the fact that the sum of the first n integers is n(n+1)/2. The latter value sums 15 1's.
= 2 * 15 * 16/2 - 15 => 2/2 = 1
= 15*16 - 15 => 15*16 = 240
= 240 - 15
= 225
Thank you,
MrB