Functions + analytic geometry - practice problems
Number of problems found: 55
- Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - Line equation:
Line equation: y-3=8/9(x-5) Solve for slope - Y-intercept 2
What is the y-intercept of 4x + 8y =16? Write coordinates of x0, y0 of that y-intercept. - Slope of the line
What is the slope of the line passing through two points (-3,5) and (2, -1) - A function
A function follows the rule "y is 3 less than half of x". Express y as a function of x in the form of an equation. - Line slope
What is the slope of the line with points (-1,-3) and (-5, 2)? - Temperature - linear function
In the morning, at 08:00 hours, the temperature was -8°C, and in the afternoon, at 16:00 hours, the temperature was 24°C. Assuming that the temperature changes steadily, what was the temperature at 1300 hours, and what was the time when the temperature wa - The linear
The linear equation 5y-3x-4=0 Can be written in the form y=mx+c. Find the values of m and c. - Slope of line
What is the slope of the line that passes through the points: (-2, 4) and (-3, 1)? - Coordinates 83025
Given are points A [1;a2;a3], B [3;-4;-1], C [-3;-1;8]. Points A, B, and C lie in a straight line. Calculate the coordinates a2, a3 - Determine 83003
Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common. - Coordinate 82855
What is the ratio of the distance of the nearest and farthest point of the circle described by the equation x2+y2-16x-12y+75=0 from the origin of the coordinate system? - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4]. - Coordinate 82580
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Closest 82051
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Intersections 80587
Draw the graph of the function y = -2x + 3. Calculate the coordinates of the intersections of the function's graph with the x and y axes. - Parabolic 79764
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court?
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