5272道题目5525 条题源记录 · 相同内容已合并
抛物线图象与二次建模进阶
A chemist performed an experiment using a set of beakers that can each be modeled by a right circular cylinder with a height of 53 millimeters. The equation \( y=53πx^{2} \) gives the volume y, in cubic millimeters, of the right circular cylinder that models a beaker in this set, where x is the radius, in millimeters, of the base of the cylinder. Which graph best represents this equation in the xy-plane?
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抛物线图象与二次建模挑战
The graph shows the height above ground, in meters, of a ball x seconds after the ball was launched upward from a platform. Which statement is the best interpretation of the marked point (1.0, 3.9) in this context?
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抛物线图象与二次建模进阶
\( x+7=13 \)
\( y=5x^2+5 \)
At what point \( \left(x,\ y\right) \) do the graphs of the equations in the given system intersect?
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抛物线图象与二次建模挑战
An object is launched from a height of 121 feet above the ground. A quadratic function \( f \) models the height above the ground, in feet, of the object t seconds after it is launched. According to the model, 2 seconds after the object is launched, it reaches a maximum height of 185 feet above the ground. Which equation defines \( f \) ?
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抛物线图象与二次建模挑战
A chemist performed an experiment using a set of beakers that can each be modeled by a right circular cylinder with a height of 58 millimeters. The equation \( y=58πx^{2} \) gives the volume y in cubic millimeters, of the right circular cylinder that models a beaker in this set, where x is the radius, in millimeters, of the base of the cylinder. Which graph best represents this equation in the xy-plane?
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抛物线图象与二次建模挑战
An object is launched from a height of 124 feet above the ground. A quadratic function \( f \) models the height above the ground, in feet, of the object t seconds after it is launched. According to the model, 3 seconds after the object is launched, it reaches a maximum height of 268 feet above the ground. Which equation defines ?
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抛物线图象与二次建模进阶
\( h\left(t\right)=-16t^2+b \)
The function h estimates an object's height, in feet, above the ground t seconds after the object is dropped, where b is a constant. The function estimates that the object is 40.96 feet above the ground when it is dropped at \( t=0 \) . How many seconds after being dropped does the function estimate the object will hit the ground?
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抛物线图象与二次建模挑战
\( f\left(x\right)=-0.0038400x^2+15.236x-15,103 \)
The model shown gives the predicted average Arctic sea ice area \( f(x) \) , in millions of square kilometers, for September of each year x, where x represents a year and \( 1979\le x\le2012 \) . Based on the model, what is the positive difference, in millions of square kilometers, between the predicted average Arctic sea ice area for September of the year 1991 and the predicted average Arctic sea ice area for September of the year 1992? (Round your answer to the nearest thousandth.)
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抛物线图象与二次建模挑战
The graph gives the estimated revenue, in dollars, for a company when the price of the company’s product is x dollars. What does the y-value of the vertex of the graph represent in this context?
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抛物线图象与二次建模挑战
A company developed a plan to set the selling price of a product. The company determined that for a selling price of $120.00, zero products would be sold. For each $2.50 decrease in the selling price, the number of products sold would increase by one. For a revenue of exactly $1,437.50, which of the following could be the number of products sold? (revenue = price × number of products sold)
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抛物线图象与二次建模进阶
An object is launched from a height of 139 feet above the ground. A quadratic function \( f \) models the height above the ground, in feet, of the object \( t \) seconds after it is launched. According to the model, 2 seconds after the object is launched, it reaches a maximum height of 203 feet above the ground. Which equation defines \( f \)?
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抛物线图象与二次建模挑战
A company developed a plan to set the selling price of a product. The company determined that for a selling price of $90.00, zero products would be sold. For each $1.50 decrease in the selling price, the number of products sold would increase by one. For a revenue of exactly $1,336.50, which of the following could be the number of products sold?
(revenue = price × number of products sold)
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