False

An equilateral triangle is defined by having all three sides equal in length, not just two. While it is technically a special type of isosceles triangle (which must have at least two sides equal), the defining characteristic of an equilateral triangle is that all three sides are congruent.

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First term
d/dx (3x⁴) = 4(3)x⁴¯¹
= 12x³

Second term
d/dx (5x²) = 2(5)x²¯¹
10x

Third term is a constant
Therefore, d/dx (7)=0

Final answer
12x³-10x

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DAY-5
MOST IMPORTANT FORMULAS

The image is a social media post about Euler's identity, often celebrated as one of the most beautiful equations in mathematics.
The identity connects concepts from arithmetic, geometry, algebra, and analysis.

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Good morning 🌚❤️
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DAY-6
MOST IMPORTANT FORMULAS

The image displays the limit definition of the derivative, a fundamental concept in calculus.
The formula, is used to find the instantaneous rate of change of a function f(x) at any point x. It represents the slope of the tangent line to the curve of the function at that specific point.  This specific definition, often taught as differentiation from first principles, was formalized by the French mathematician Augustin-Louis Cauchy.

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Good day everyone. I hope y'all had a good night.
We will be explaining the answers to the quiz we had yesterday.
We solve, learn and teach mathematics here. Invite your friends so that we all learn together
Thank you

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The statement is False;

if two non-vertical lines are perpendicular, the product of their slopes is -1.
Explanation

For two lines to be perpendicular, their slopes must be negative reciprocals of each other. If we denote the slope of the first line as m1 and the slope of the second line as m2,the relationship is defined by the formula:

m1 × m2 = - 1

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False

Using Cramer’s Rule and the elimination method to solve the same system of linear equations will yield the same answer, assuming the system has a unique solution. Both methods are valid mathematical techniques for finding the unique intersection point of linear equations. Both methods are designed to solve the same, unique, linear systems.

While elimination is often more computationally efficient, both methods are mathematically equivalent.
Note: Differences in answers usually only occur if there is a calculation error, such as a mistake in finding determinants in Cramer's rule or a sign error during elimination.

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True. If a quadratic equation has equal roots (i.e., its discriminant D = b²-4ac = 0), the vertex of its parabolic graph lies directly on the x-axis. This means the parabola touches or "bounces" off the x-axis at exactly one point (the root), rather than crossing it at two points.

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Let's learn for other roots as well

Distinct real roots ( D > 0): Graph crosses the x-axis at two points.

No real roots ( D < 0): Graph does not intersect the x-axis.
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True.
The minimum or maximum value of a quadratic function (a parabola) always occurs at its vertex.

If the parabola opens upward (a > 0 ), the vertex is the minimum point.

If the parabola opens downward (a < 0), the vertex is the maximum point.

The vertex acts as the turning point of the graph, and its y-coordinate represents the maximum or minimum value of the function.

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