A castle entrance has walls that can be modeled by the equation the fraction with numerator x squared and denominator 10 squared minus the fraction with numerator y squared and denominator 30 squared is equal to 1 with units in feet. How wide is the entrance where the walls are closest together?
An architect designed a lobby wall to have an embedded circular clock. The equation open paren x minus 4 close paren squared plus open paren y minus 7 close paren squared is equal to 1 , with units in meters, represents the location of the clock relative to the bottom left corner of the wall. How high above the ground is the center of the clock?
Lori tosses a ball into the air. The equation y is equal to negative 16 times open paren x minus 1 close paren squared plus 25 models the height, y , in feet, of the ball after x seconds. What is the maximum height the ball reaches?
Ailani draws a map of her local town. She places the town hall at the origin of a coordinate plane and represents a lake with a circle drawn on the map. The center of the lake is 19 miles east and 3 miles south of the town hall, and the radius of the lake is 0 point 5 miles. If the positive x -axis represents east and the positive y -axis represents north, which equation represents the lake?
A mirror is the shape of an ellipse defined by the fraction with numerator y squared and denominator 7 point 2 9 plus the fraction with numerator x squared and denominator 6 point 2 5 is equal to 1 with units in feet. Which statement identifies the orientation of the mirror and its greatest dimension?
A pair of radar stations monitors the path of a helicopter. Station A is located at the origin of a coordinate plane. Station B is located 100 miles east of station A. The difference in the distances from the helicopter to each station is 60 miles. Which equation represents the possible locations of the helicopter?
A serving dish has a parabolic surface with the vertex open paren 0 comma 0 close paren at the center of the dish. When the width of the dish is 6 inches, the depth of the dish is 3 inches. The equation that models the shape of the serving dish is y is equal to A x squared What is the value of A ?
A carpenter designs a tabletop in the shape of an ellipse 7 feet long and 4 feet wide. The carpenter sketches a drawing of the tabletop on a coordinate plane. The center of the tabletop is at the origin, the length falls along the x -axis, and the width falls along the y -axis. Which equation represents the tabletop?
A drone has an effective range represented by a circle on a coordinate plane. The points open paren negative 12 comma 3 close paren and open paren negative 6 comma negative 5 close paren are endpoints of a diameter of this boundary. Which equation represents the effective range boundary for the drone?
A company is introducing a new product. The equation y is equal to negative 0 point 0 0 1 times open paren x minus 600 close paren squared plus 90 predicts the expected profit, in thousands of dollars, where x represents the number of thousands of units of the product sold by the company. How many units must be sold to yield a maximum profit?
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