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Jeremy
Number Theory?
Show all numbers of the form:
5·(2^n)
can be written as the sum of two squares
for all natural numbers n
2 AnswersMathematics3 years agoProve or disprove that 1 is the only integer solution?
Prove (or disprove) that 1 is the only integer solution of the form:
(x⁴ + 1) / (xy + 1)
where x and y are positive integers.
1 AnswerMathematics6 years ago
Minimize distance between two quadratics.?
Find the shortest distance between
f(x) = x² + 1
and
f(x) = √x
(approximated within 5 decimal places)
2 AnswersMathematics6 years agoElementary number theory?
Prove
(2k + 1)²
does not divide
2^(2k - 1) + k(k + 1)
for any integers k > 0.
2 AnswersMathematics6 years ago
AP Calculus Practice (without calculator)?
How would I solve this without a calculator or graphing utility?
This is taken from AP Calculus practice from college board website.
1 AnswerMathematics6 years ago
AP Calculus: Finding the slope on an interval with given data.?
Please see attached picture.
1 AnswerMathematics6 years agoVolume of a solid of revolution?
I need to find the volume of a solid of revolution in two different ways and show that they are the same:
Find the volume of the solid of revolution bounded by:
y = x^3
x = 0
x = 2
rotated about the x-axis.
1) using the disk method
2) using the cylindrical shell method
1 AnswerMathematics6 years agoProve all numbers of the form: 8n² ± 6n + 1?
Prove all numbers of the form:
8n² ± 6n + 1
is a triangular number and can be expressed as a difference of two squares in two different ways.
1 AnswerMathematics6 years agoFind the point(s) on the ellipse: x²/a² + (y - k)²/b² = 1 where the tangent lines that passes through the point: (m, n)?
NOTE:
seeking a point on the ellipse, not just the tangent line. also (m, n) is an arbitrary point NOT on the ellipse.
2 AnswersMathematics6 years ago
What is the maximum and minimum of x?
ABCD is a square. E and F can be anywhere inside the square such that
AE=EF=FC and AE is parallel to FC. What is the maximum and minimum value of the angle x?
1 AnswerMathematics7 years ago
What is the maximum and minimum value for x?
ABCD is a square. E and F can be anywhere inside the square such that
AE=EF=FC and AE is parallel to FC. What is the maximum and minimum value of x?
1 AnswerMathematics7 years agoShip A is 15 miles east of point P and moving west at 20 mph. Ship B is 60 miles south of point P and traveling north at 15 mph...?
When are the ships closest to each other?
2 AnswersMathematics7 years ago
A square with area of 4 units is partially overlapped with a circle of radius r?
A square with area of 4 units is partially overlapped with a circle of radius r. If the area of what's outside of the circle but inside the square is the same as the area of what's inside the square but outside of the circle, what is the radius of the circle?
(Area of the blue sections equal to the area of the yellow sections)
3 AnswersMathematics7 years agoIs this an identity? ∛(a + √b) - ∛(a + √b) = ∛(a - √b) - ∛(a - √b)?
Does this always hold true? These solutions arise when solving cubics by Cardano's formula, and it seems the ± sign in front of the square roots are irrelevant.
∛(a + √b) - ∛(a + √b) = ∛(a - √b) - ∛(a - √b)
2 AnswersMathematics7 years agoDoes this ALWAYS hold true?
2 AnswersMathematics7 years agoFind all the values of k such that f(x) = x^3 - 3x^2 + k has three different x-intercepts.?
Find all the values of k such that f(x) = x^3 - 3x^2 + k has three different x-intercepts.
3 AnswersMathematics7 years agoCALCULUS: Tangent on an elliptical orbit to reach a point?
You are on a spaceship that is orbiting a planet. You have ran out of fuel and the ship is therefore not navigable. However, you have an anti-gravity that acts instantaneously upon the press of a button. At which point on the elliptical orbit should you press the anti-gravity button in order to reach a nearby planet.
The elliptical orbit is:
x^2 / 4 + y^2 / 9 = 1
The nearby planet is located at the point:
(40, 3)
Questions:
1.) At which point on the elliptic orbit should you press the anti-gravity button (if you are traveling clockwise on the coordinate system)?
2.) Why is it a good idea to make the substitution of z = x/2?
(hint: quartic polynomial)
1 AnswerMathematics7 years ago
