Mark spends a total of $68.82 for 2 pairs of sneakers with the same cost. The sales tax is $5.32. Mark also uses a coupon for $3
1 answer:
Each pair of sneakers cost $33.25
Step-by-step explanation:
Given,
Total spent by Mark = $68.82
Sales tax = $5.32
Coupon used = $3.00
Price without sales tax = Total spent - sales tax
Price without sales tax = 68.82 - 5.32 = $63.50
As Mark used coupon, we will add this amount.
Amount of sneakers = Price without sales tax + Coupon used
Amount of sneakers = 63.50+3.00 = $66.50
As this is price of two sneakers, we will divide it by 2;
Cost of one sneaker =
Each pair of sneakers cost $33.25
Keywords: subtraction, addition
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f(x) = x(x^2 + 6x + 9)(1 - x)/3
f(x) = x(x^2 + 6x + 9 - x^3 - 6x^2 - 9x)/3
f(x) = x(- x^3 - 5x^2 -3x +9)/3
f(x) = (-x^4 - 5x^3 -3x^2 +9x)/3
f'(x) = (-4x^3 - 15x^2 -6x + 9)/3
We know there's f'(-3)=0 so x+3 must be a factor here,
f'(x) = (x + 3) (-4x^2 - 3x + 3)
We get stationary points when x = -3 or
x = (-1/8)( 3 ± √(9 - 4(-4)(3))) = (-3 ± √57)/8 about -1.3 and 0.6 which are a local minimum and maximum respectively.
f''(x) = (-12x^2 - 30x -6)/3 = -4x^2 - 10x - 2
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Concave Down, Negative. (-3,0) is a local maximum.
f''((-3 - √57)/8) = -4(-1.3)^2 - 10(-1.3) - 2 = 4.24
Concave up, positive, a CUP
(-3 - √57)/8, f((-3 - √57)/8) ) is a minimum.
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CDN, ( ((-3 + √57)/8), f((-3 + √57)/8) ) is a maximum.
I didn't evaluate f((-3 ±√57)/8) which are around -3 and 1 but I leave that calculation to you.
