The formula for the perpendicular distance of a point (x1, y1) from a line Ax + By + C = 0 is: Distance = |Ax1 + By1 + C| / √(A² + B²). For the line 2x - 3y = 12, rewrite it as 2x - 3y - 12 = 0. Substitute x1 = 4 and y1 = 5: Distance = |2(4) - 3(5) - 12| / √(2² + (-3)²) = |8 - 15 - 12| / √(4 + 9) = |-19| / √13 = 19 / √13 ≈ 5.27 units. Answer: d
What is the average production of Bananas and Grapes together for the entire period from 2018 to 2022?
If sinθ + cosθ = 2a and tanθ + cotθ = b, then find a in terms of b.
A circle has a radius of 21 cm, and a sector makes an angle of 60° at the center. Find the area of the sector and the length of the arc (use π = 22/7...
The angle of elevation of the top of a building from a point on the ground is 60°. After walking 20 meters towards the building, the angle of elevation...
A retailer offers a discount of 20% on a product. If the product’s marked price is ₹500 and the retailer still makes a profit of 12%, find the cost ...
A solution contains vinegar and water in equal proportions. If this solution is mixed with another solution of water in the ratio 1:4, what is the resul...
If the ratio of the ages of A, B, and C is 2:3:5 and the sum of their ages is 50 years, what is the age of the youngest person?
A company produces two types of gadgets, Type X and Type Y. How many total gadgets does the company produce in a month?
Statements:
I: ...
Simran goes to a grocery store with some money. She can buy 80 packets of rice or 40 packets of flour with the money with her. However, instead of spend...
Which of the following scheduling algorithms is designed to reduce the turnaround time and waiting time in a multitasking environment?