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How do you do 34 and 35?

How do you do 34 and 35?-example-1
User Ron Srebro
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#34

f(x)=x^2+4x+4=(x+2)^2

f(x-h)=x^2 => f(x)=(x+h)^2

=> (x+2)^2=(x+h)^2 => h=2


#35

Volume of a right circular cylinder

= π r^2h

=> volume proportional to height h.

Given

32 π = π r^2 (4"/2)

Solve for r

r=sqrt(32*2/4)=4 inches

=> Diameter of can is 2*4=8 inches.


User Frodik
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5 votes

34. As with many problems, substitute the given information into the given formula and solve for the variable of interest. Here, it can be helpful to rewrite f(x) as a square.

... f(x) = x² +4x +4 = (x +2)²

Substituting in accordance with the problem statement, you have

... f(x-h) = x² = (x -h +2)²

In order to make the term on the right match the term in the middle, we must choose h=2. This gives

... f(x -2) = x² = (x -2 +2)²

_____

You can also work it out the long way.

... f(x -h) = (x -h)² +4(x -h) +4 = x²

... x² -2hx +h² +4x -4h +4 = x² . . eliminate parentheses

... x(4 -2h) +(4 -4h +h²) = 0 . . . . . subtract x² and collect terms

We know both the coefficient of x and the constant must be zero, so we have two equations:

... 4 -2h = 0 ⇒ h = 2

... h² -4h +4 = 0 = (h -2)² ⇒ h = 2

35. Use the formula for the volume of a cylinder, fill in the given information, and solve for the unknown value. If you use a formula that involves radius, you must then convert that to diameter. (Diameter is twice the radius.)

The volume is given by

... V = π·r²·h

Since the can is half full, h = (1/2)·(4 in) = 2 in. Substituting the given values, we have

... 32π in³ = π·(2 in)·r²

... 16 in² = r² . . . . . divide by 2π in

... √(16 in²) = r = 4 in . . . . take the square root. This gives the radius.

The diameter of the can is 8 inches,

User Telson Alva
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