I know how to but i don't know how to reply with a picture
Answer:β=√10 or 3.16 (rounded to 2 decimal places)
Step-by-step explanation:
To find the value of β :
- we will differentiate the y(x) equation twice to get a second order differential equation.
- We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β
y(x)=c1cosβx+c2sinβx
we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.
Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.
lastly the differential of sinx= cosx and for cosx = -sinx.
Knowing all these we can proceed to solving the problem.
y=c1cosβx+c2sinβx
y'= β×c1×-sinβx+β×c2×cosβx
y'=-c1βsinβx+c2βcosβx
y''=β×-c1β×cosβx + (β×c2β×-sinβx)
y''= -c1β²cosβx -c2β²sinβx
factorize -β²
y''= -β²(c1cosβx +c2sinβx)
y(x)=c1cosβx+c2sinβx
therefore y'' = -β²y
y''+β²y=0
now we compare this with the second order D.E provided in the question
y''+10y=0
this means that β²y=10y
β²=10
B=√10 or 3.16(2 d.p)
96
/ \
8 • 12
/ \ / \
4 • 2 • 4 • 3
/ \ / \
2 2 2 2
96 is 2•2•2•2•2•3 or 2^5•3
-7x - 2y = 19
4x + y = -12
Set y equal to each other (opposite signs are fine and you could also set x equal instead of y)
-7x - 2y = 19
8x + 2y = -76
Add equations together
x = -52
Plug x value into an equation
4(-52) + y = -12
Solve for y
-208 + y = -12
y = 196
Hope this helps! ;)
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = 
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = 
Profit on each book= $1.50
Profit = selling price - cost price
![\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}]](https://tex.z-dn.net/?f=%5CRightarrow%201.50%3D%5Cdfrac%7B330%7D%7Bx-15%7D-%5Cdfrac%7B300%7D%7Bx%7D%5C%5C%5C%5C%5CRightarrow%5C%201.50%3D%5Cdfrac%7B330%28x%29-300%28x-15%29%7D%7Bx%28x-15%29%7D%5C%5C%5C%5C%5CRightarrow%5C%201.50%3D%5Cdfrac%7B330x-300x%2B4500%7D%7Bx%5E2-15x%7D%5C%5C%5C%5C%5CRightarrow%5C%201.50%28x%5E2-15x%29%3D30x%2B4500%5C%5C%5C%5C%5CRightarrow%5C%201.50x%5E2-22.5x%3D30x%2B4500%5C%5C%5C%5C%5CRightarrow%5C%201.50x%5E2-52.5x-4500%3D0%5C%5C%5C%5C%5CRightarrow%5C%201.50x%5E2-52.5x-4500%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-25x-3000%3D0%5C%20%5C%20%5B%5Ctext%7Bdivide%20by%201.5%7D%5D)
Number of books cannot be negative.
So, there are 75 books.
Price of each book = 
So price of each book = $4.
