Volume of a Box. A rectangular box with a volume of 2√2 ft to the power of 3 has a square base as shown below. The diagonal of the box (between a pair of opposite corners) is 1 feet longer than each side of the base. a)If the base has sides of the length x feet, show that x^6-2x^5-x^4+8=0 b) Show that two different boxes satisfy the given conditions. Find the dimensions in each case, rounded to the nearest hundredth of a foot.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
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Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Volume of a Box. A rectangular box with a volume of 2√2 ft to the power of 3 has a square base as shown below. The diagonal of the box (between a pair of opposite corners) is 1 feet longer than each side of the base.
a)If the base has sides of the length x feet, show that
x^6-2x^5-x^4+8=0
- b) Show that two different boxes satisfy the given conditions. Find the dimensions in each case, rounded to the nearest hundredth of a foot.
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