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question:Which sensory receptor allows us to perceive vibrations?
answer:The Pacinian corpuscles are the sensory receptors that allow us to perceive vibrations. They are located in the skin and are responsible for detecting pressure and vibration. The Pacinian corpuscles are part of the somatosensory system, which is responsible for our sense of touch.
question:An acute angle of a right triangle increases at a constant rate of 3 radians per minute. If the hypotenuse is 5 cm, at what rate is the side opposite the acute angle increasing in centimeters per minute when the opposite side equals 3 cm?
answer:Given data: Rate of change of acute angle: {eq}dfrac{{dtheta }}{{dt}} = 3;{{{rm{rad}}} {left/ {vphantom {{{rm{rad}}} {{rm{min}}}}} right. } {{rm{min}}}} {/eq} Length of hypotenuse: {eq}h = 5,{rm{cm}} {/eq} Length of opposite side: {eq}x = 3,{rm{cm}} {/eq} Using the trigonometric ratio, we have: {eq}sin theta = dfrac{x}{h} {/eq} Differentiating both sides with respect to time, we get: {eq}cos theta dfrac{{dtheta }}{{dt}} = dfrac{1}{h}dfrac{{dx}}{{dt}} {/eq} Substituting the given values, we have: {eq}cos theta left( 3 right) = dfrac{1}{5}dfrac{{dx}}{{dt}} {/eq} To find {eq}cos theta {/eq}, we use the Pythagorean theorem: {eq}{h^2} = {x^2} + {y^2} {/eq} {eq}y = sqrt {{h^2} - {x^2}} {/eq} {eq}cos theta = dfrac{y}{h} = dfrac{{sqrt {{h^2} - {x^2}} }}{h} {/eq} Substituting this expression for {eq}cos theta {/eq}, we get: {eq}dfrac{{sqrt {{h^2} - {x^2}} }}{h} left( 3 right) = dfrac{1}{5}dfrac{{dx}}{{dt}} {/eq} Simplifying, we have: {eq}dfrac{{dx}}{{dt}} = dfrac{3}{5}sqrt {{h^2} - {x^2}} {/eq} Substituting the given values, we get: {eq}dfrac{{dx}}{{dt}} = dfrac{3}{5}sqrt {{5^2} - {3^2}} = dfrac{3}{5}sqrt {16} = dfrac{3}{5} cdot 4 = dfrac{12}{5} {/eq} Therefore, the rate at which the side opposite the acute angle is increasing is {eq}dfrac{12}{5} {/eq} centimeters per minute.
question:Why did Texas colonists object to the merger of Texas and Coahuila as a single state in Mexico?
answer:The Texas colonists opposed the merger with Coahuila primarily because they [D] aspired to maintain their autonomy and eventually seek independence from Mexico. They believed that the combination would increase Mexican control over their region and hinder their desires for self-governance and closer ties with the United States. The desire for independence was a key factor in the Texas Revolution that followed, ultimately leading to Texas becoming a state in the United States.
question:Which of the following best describes an oligopoly market structure? A. A market with a single firm having complete control over prices and production. B. A market with multiple firms, where entry and exit are unrestricted, and each firm has limited market power. C. A market with a few large firms that possess market power and face significant barriers to new entry. D. A market with many firms, where each has no control over prices and can enter or exit the market freely.
answer:The correct description of an oligopoly is (C). In an oligopoly, the market is dominated by a small number of firms that have substantial market power, and there are significant barriers to entry for new firms. These barriers can include high capital requirements, legal restrictions, or economies of scale that make it difficult for smaller firms to compete effectively.