Hello :
the tangent has same slope of the line 16x -y +5 = 0 because parallel.
y = 16x + 5
the slope is : 16
but : f'(x) = 16
f'(x) = 16x^3 - 16x +16
solve : 16x^3 - 16x +16 = 16
x^3 - x +1 =1
x^3 - x = 0
x(x² - 1 ) =0
x(x -1 )(x +1) =0
x=0 or x-1 =0 or x +1= 0
x=0 or x = 1 or x = -1
if : x = 0 : y = 4(0)^4 -8(0)^2+16(0) +7 =7
if : x =1 : y = 4(1)^4 -8(1)^2+16(1) +7 = 19
if : x = -1 : y = 4(-1)^4 -8(-1)^2+16(-1) +7 = -13
<span>the points : A(0,7) , B(1 , 19) , c ( -1 , -13)</span>
Okay, so if your rectangle is 16 by 8, that means that the circle diameter of 8 because that would be outside of the card's width,
the area of the rectangle is 16 x 8 or 128
the radius of the circle would be 4 (because 1/2 of the diameter is radius)
we know that the equation of the circle PIr^2, so the area of the circle is 16PI
then, the remaining area would be calculated by 128-16PI
This comes out to be approximately 77.73
114.50 if you add everything together and then subtract 67.50 you’ll get your answer
<em>Hi there!</em>
<em>~</em>
<em>If my logic doesn't fail me here, we have a total of 290 + 145 + 4 = 439 total 6s.</em>
<em>Hope this helped you!</em>
