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For each of the items below complete the sentence with quantitative words. Use words such as “not change”, “double”, “triple”, “halve”, etc. If you prefer, you may write, =, X2, X4, ÷2, ÷3, to mean equal, doubled, quadruples, halved, divided by three, etc. (Note that “increases” or “decreases” is NOT sufficient.)

(a) The interior of a water pipe bringing water into your hot water heater has narrowed as a result of the buildup of scale from the fact that your water is very hard (contains dissolved chemicals). The radius of the open area inside the pipe has decreased by a factor of two. If the pressure differential remains the same, the flow into the heater will _______.

(b) You have a single window in the wall of your kitchen and you are contemplating putting a second identical window into that wall. In the winter, for a given inside-outside temperature difference, that change will ________ the flow of heat out of your house through the windows in that wall.

(c) Blood is flowing through an artery that has a partial blockage in a part of the artery so that half its cross sectional area is blocked. In the part with the blockage, the velocity of the blood is ________ the velocity of the blood in the unblocked part of the artery.

(d) I blow as hard as I can through a single straw. If instead, I blow as hard as I can through two straws (of the same length as the single straw) placed side by side, the rate of flow will ________.

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