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
A 3 digit number is such that its tens digit is equal to the product of the other two digits which are prime. Also, the difference between its reverse and itself is 99. What is the sum of the three digits?
11
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)