Quadratic equation + right triangle - practice problems - page 4 of 6
Number of problems found: 110
- Right triangle from axes
A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Prove
Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0 - Ellipse
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the ellipse's center. - Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
- Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r - Thunderstorm
The height of the pole before the storm is 10 m. After a storm, when they check it, they see that the ground from the pole blows part of the column. The distance from the pole is 3 meters. At how high was the pole broken? (In fact, the pole created a rect - ABCDA'B'C'D 6261
The ABCDA'B'C'D 'prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC 'is 11.4 cm long. Calculate the surface area and volume of the prism. - Diamond diagonals
Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square and the side length is 13 cm.
- A bridge
The bridge over the river has the shape of an arc. The bridge is 10 feet above the water at the center of the river. At 27 feet from the river's edge, the bridge is 9 feet above the water. How wide is the river? - Bamboo
At a certain height, the wind broke the bamboo high 32 feet, so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Right-angled triangle
Determine the area of a right triangle whose side lengths form successive members of an arithmetic progression, and the radius of the circle described by the triangle is 5 cm. - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
- Diameter 5668
The span of the arc is 247 cm, and the height of the arc is 21.5 cm. What is the diameter of the circle? - Perpendicular 5516
In a right triangle, one perpendicular is 1 m shorter than the hypotenuse. The other perpendicular is 2 m shorter than the hypotenuse. Find the lengths of all sides of the triangle. - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Right angled triangle 2
LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n - Diagonal 20
The rectangular town plaza's diagonal pathway is 20 m longer than the width. Suppose the pathway is 20 m shorter than twice the width. How long should the pathway be?
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