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ololo11 [35]
3 years ago
8

The US Postal rates for a first class letter are $0.46 for up to and including 1 ounce $0.66 for 1 to 2 including 2 ounces $0.86

for 2 to 3 including 3 ounces $1.06 for 3 to 3.5 including 3.5 ounces What is the cost for a letter weighing 1.03 ounces?
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0
1.03 oz is in the range 1–2 oz, so will cost $0.66.
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Given the position of the particle, what the position(s) of the particle when it’s at rest
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The velocity function is the derivative of the position:

\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}

The particle will be at rest when the velocity is 0, thus we solve the equation:

2t^2-9t-18=0

The coefficients of this equation are: a = 2, b = -9, c = -18

Solve by using the formula:

t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

Substituting:

\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}

We have two possible answers:

\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}

We only accept the positive answer because the time cannot be negative.

Now calculate the position for t = 6:

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