(a) mtan refers to the slope of the tangent line. Given <em>f(x)</em> = 9 + 7<em>x</em> ², compute the difference quotient:
Then as <em>h</em> approaches 0 - bearing in mind that we're specifically considering <em>h</em> <em>near</em> 0, and not <em>h</em> = 0 - we can eliminate the factor of <em>h</em> in the numerator and denominator, so that
and so the slope of the line at <em>P</em> (0, 9), for which we take <em>x</em> = 0, is 0.
(b) The equation of the tangent line is then <em>y</em> = 9.
<u>the question is </u> Calculate the value of the copper in the coin
Step 1
Find the volume of the coin
we know that
the volume of a cylinder is equal to
where
r is the radius of the coin
h is the thickness of the coin
in this problem we have
Diameter=19 mm=1.9 cm
r=D/2------> r=1.9/2=0.95 cm
h=1.5 mm=0.15 cm
substitute the values in the formula
Step 2
<u>Find the mass of copper in the coin</u>
we know that
the density is equal to
Solve for the mass
we have
substitute in the formula
Step 3
<u>Find the cost</u>
we know that
the market price of the copper is $2.15 per pound
1 pound=453.592 grams
convert gram to pounds
3.785 gr=3.785/453.592=0.0083 pounds
0.0083*$2.15=$0.018=$0.02
therefore
<u>the answer is</u>
$0.02