Mathematics
If a + b = 5 and ab = 6, Find: (a³ + b³)² - 9a²b²(a + b)²
Given that W : X = 5 : 6, X : Y = 3 : 7, and Y : Z = 8 : 9, find the compound ratio W : X : Y : Z.
What is the value of √(6+√(6+√(6+...)))?
A vendor purchases seven shirts at the marked price of six shirts. If he sells each shirt after giving a 4% discount on its marked price, what is his profit percentage?
Pipe A is capable of filling a tank in 16 minutes while Pipe B can fill the same tank in 24 minutes. Both pipes are opened together, but after 4 minutes, the rate of Pipe A doubles and the rate of Pipe B becomes half of its original. How many more mi...
Simplify: √(12 + 6√3)
A sum of 10000 is lent out in two parts, one at 7% simple interest and the other at 12% simple interest. If the annual interest is 900, the sum lent at 12% is:
900 is lent at a certain rate of simple interest. After 9 months, another 600 is lent at a rate that is 1.5 times the original rate. If the total simple interest after 1 year is 72, find the original rate.
A flagpole has a shadow measuring 10 metres. Given that the height of the flagpole is 10√3 metres, What is the angle at which the sun is elevated?
A hollow metallic sphere has outer radius 10 cm and is melted to make 50 smaller solid spheres of radius 2 cm. What is the inner radius of the original sphere?
The volume of a hemisphere is numerically equal to four times its curved surface area. Find its radius.
What is the minimum number of cuts required to divide a cuboid into 8 equal cuboids?
If the height of a cone is tripled and the radius is halved, how does the volume change?
If sin θ = 12/13, and θ ∈ (0, π/2), then what is the value of tan θ?
What is the value of tan A + cot A if tan A = 2?
What is the slope of the line 2x + 3y = 6?
A sector of a circle has a central angle of 60° and a radius of 8 cm. Another sector of the same circle has a central angle of π/3 radians. What is the ratio of the area of the first sector to the area of the second sector?
A triangle can have:
A line L is the perpendicular bisector of the line segment connecting points A (2, 5) and B (8, 1). What is the y-intercept of line L?
The area of a triangle ABC is 16 cm². If a similar triangle DEF has sides that are twice the length of ΔABC's sides, what is the area of ΔDEF?
44³ + 35³ - 53³ + 159 is equal to
If sin A + cos A = 5/4, find sin 2A.
From an outside point P, two tangents, PA and PB, are drawn to a circle. Given that the length of PA is 12 cm, what is the length of PB?
A circle is inscribed within a right triangle. Considering that the lengths of the two legs measure 6 cm and 8 cm, what is the radius of the inscribed circle?
If a = 0.02, b = 0.03, c = -0.05, and a + b + c = 0 find (a³ + b³ + c³) ÷ (3abc)