Algebra
Solve for x:
log3(x)=2
x = 9
A curve has the equation y=x^2. If the curve is translated by 2 units to the right, what is the new equation?
y=(x−2)2
Find the derivative of f(x) = 5x^3 + 2x
15x^2 + 2
Who introduced the concept of a function in mathematics?
Leonhard Euler
Find the area of a sector of a circle with radius 6 cm and angle 60∘
6pi square cm
Solve for x and y:
3x+4y=12 and x−2y=1
x = 4, y = 0
Find two consecutive integers such that the sum of their cubes is 189.
4 and 5
Integrate ∫4x^3 dx
x^4 + C
In what century did Isaac Newton and Gottfried Wilhelm Leibniz develop calculus?
17th Century
Find the angle between two lines with slopes m1=2 and m2=−1/2
90∘
Find the roots of the quadratic equation:
3x2−2x−1=0
x = 1, x = -1/3
Soduko:
|_|_|_|4|
|_|_|_|_|
|2|_|_|3|
|4|_|1|2|
|1|2|3|4|
|3|4|2|1|
|2|1|4|3|
|4|3|1|2|
Find the turning points of f(x)=x^3−3x^2+2
Turning points at x=0 and x=2
Who introduced the polar coordinate system?
Isaac Newton
What is the volume of a cone with radius 3 cm and height 4 cm?
(1/3)(pi)(r2)(h)=12pi cubic cm
Simplify (x3+2x2−x−2x+2)/(x+2)
x2−1
Countdown:
Result to be obtained --> 253
Given Numbers --> 75, 7, 2, 5, 4, 6
75*4 - 6*2 - 5*7 (Possible Answer)
Evaluate ∫20 (3x^2−2x) dx
4
Who was the first woman to receive a PhD in mathematics?
Sofia Kovalevskaya
Find the equation of the circle with center (1,2) and radius 5
(x−1)2 + (y−2)2 = 25
Solve for x in the equation:
2x3−5x2−8x+12=0
x=2, x=3, x=−3/2
Solve the differential equation dy/dx=2x with y(1)=3
y = x^2 + 2
Which mathematical conjecture, proposed in the 1950s, established a deep connection between elliptic curves and modular forms, and played a crucial role in Andrew Wiles' proof of Fermat’s Last Theorem?
The "Taniyama-Shimura" conjecture (also known as the Modularity Theorem)
Given a triangle with vertices A(1,2), B(4,6), C(6,1), find the equation of the perpendicular bisector of side AB
y−4=(−3/2)(x−2.5)