Find the derivative of x^3-x^2+x-1
The general formula to find the derivative of an equation x^n is n(x)^(n-1). Apply this formula to each term of the equation. 3x^2-2x^1+1x^0+0 3x^2-2x+1
Combine like terms 2x^2+(x-3x)+(5-1) Simplify. 2x^2-2x+4
A student is at the store buying school supplies. She buys x notebooks and y pencils. Each notebook costs $0.50, and each pencil costs $0.25. In all she buys 12 items and spends $4.00. How many of each item does she buy?
x=number of notebooks y=number of pencils For this problem you will need a system of equations: x+y=12 to show that the total number of items adds up to 12. .50x+.25y=4 to show that the total cost of notebooks and pencils adds up to $4.00. In the first equation solve for y. y=12-x Now substitute y=12-x into the second equation. .50x+.25(12-x)=4 Distribute. .50x+3-.25x=4 Combine like terms. .25x=1 Solve for x. x=4 Substitue 4 for x into the first equation. 4+y=12 Solve for y. y=8 The student bought 4 notebooks and 8 pencils. Check your work by substituting your answer into both equations. 4+8=12 .50(4)+.25(8)=4