An 8 pound box of halibut steaks is ordered costing $4.50 per pound. If each steak weighs 4 ounces, what is the cost of each ste
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(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where
then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,
(b) The velocity after 3 seconds is
(c) The particle is at rest when its velocity is zero:
(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:
In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,
By definition of absolute value, we have
In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as
and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to
Answer:
C. 17.6
General Formulas and Concepts:
<u>Math</u>
- Rounding
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u> </u>
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] tanθ = opposite over adjacent
Step-by-step explanation:
<u>Step 1: Identify Variables</u>
Angle θ = 40°
Opposite Leg = <em>x</em>
Adjacent Leg = 21
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [tangent]:
- [Multiplication Property of Equality] Isolate <em>x</em>:
- Rewrite:
- Evaluate:
- Round: