Tutor profile: Marisa V.
Find an equation of the curve which results by translating the graph of y=x^2 5 units to the right and 3 units down.
First we will replace x by x-5 since we need to translate our curve 5 units to the right. Then we will replace y by y+3 since we need to shift our equation 3 unites down. This gives the equation y+3=(x-5)^2 or, written another way as, y=(x-5)^2-3.
Find f (3) and f ‘ (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.
To solve the problem we need to realize that the tangent line and the function intersect at the point where x = 3. So f (3) was the same as the point on the line where x = 3. Therefore, f (3) = 5(3) + 2 = 17. Then you have to realize that the derivative is the slope of the tangent line and we know the tangent line’s equation and we can read the slope. So f ‘ (3) = 5
5(z + 1) = 3(z + 2) + 11 Solve for Z.
In this problem we will need to use distribution, addition, division, and subtraction. Step 1: distribute 5z + 5 = 3z + 6 + 11 Step 2: combine like terms 5z + 5 = 3z + 17 Step 3: subtract to get all of the z's to one side 2z = 12 Step 4: divide each side by 2 to get the z variable by itself z = 6
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