Trigonometry and Geometry Problems

<p>-1, 15 (C)</p> Signup and view all the answers

<p>rac{5 ext{sqrt{2}}}{2} (D)</p> Signup and view all the answers

<p>rac{p imes 2 ext{π} R}{180} (A)</p> Signup and view all the answers

<p>rac{2}{3} (D)</p> Signup and view all the answers

<p>5 ext{sqrt{3}} (C)</p> Signup and view all the answers

A number ending with zero is divisible by 10. A number is divisible by 10 if it is divisible by both 2 and 5. For a product to end in zero, one of the factors must be divisible by 5. Therefore, the value of 'a' must be divisible by 5.

The pair of equations have no solution if the lines are parallel (same slope, different y-intercepts). The slope of the first equation is -2/3. The slope of the second equation is -2k/9. For the lines to be parallel, the slopes must be equal.

If the zeroes of a quadratic are reciprocals, then the product of the zeroes is 1. The product of the zeroes of the quadratic ax^2 + bx + c = 0 is equal to c/a.

The discriminant of a quadratic equation is the value under the radical in the quadratic formula. It tells us about the nature of the roots. The discriminant of the equation bx^2 + ax + c = 0, b≠ 0 is a^2 - 4bc.

An arithmetic progression (AP) is a sequence where each term is equal to the previous term plus a constant difference (common difference). To be in AP, the difference between consecutive terms must be constant. The common difference between the first and second term equals the common difference between the third and fourth term. The common difference between the second and third term equals the common difference between the fourth and fifth term.

The diameter of a circle is the line segment that passes through the center and connects two points on the circle. The radius of a circle is half the length of its diameter. The distance formula is used to calculate the distance between two points.

A triangle with one right angle is called a right triangle. A triangle with two sides of equal length is called an isosceles triangle. A triangle with all sides of equal length is called an equilateral triangle. A triangle with all sides of different lengths is called a scalene triangle.

The area of a sector of a circle is a portion of the circle's area. The area of a sector is proportional to the central angle of the sector. The area of the whole circle is πR^2. The area of a sector with central angle 'p' is (p/360) times the area of the whole circle.