A pendulum is 0.470m long, and the bob has a mass of 1.00kg . At the bottom of its swing, the bob's speed is 1.60m/s .

What is the tension in the string at the bottom of the swing?

\(\square \)N

The base of a rectangular box is three times as long as it is wide.

The volume of the box is 756 cubic inches. The material for the top cost $0.08 per square inch, for the bottom it cost $0.04 per square inch, and for the sides cost $0.04 per square inch. Find the width, length, and height of the box to minimize the cost. Round answers to 2 decimal places. V=LWH

The width is

The length is

The height is

Hint: find C(w)

Required information A 443-kg pile driver is raised 12.3m above ground.

How much work must be done to raise the pile driver?

\(\square \)kJ

You shoot a 53.8-g pebble straight up with a catapult whose spring constant is 320.0 N/m. The catapult is initially stretched by 0.190 How high above the starting point does the pebble fly? Ignore air resistance.

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Write a function\( g \)whose graph represents the indicated transformations of the graph of\( f \).

14. Let\( g \)be a translation 2 units down and a horizontal shrink by a factor of\( \frac { 2 } { 3 } \)of the graph of\( f ( x ) = x \).