Explanation

- f tan xdx = ln[cos x] + C.

This is a standard result from integral calculus involving trigonometric functions.

Explanation

A function is concave down on an interval if its second derivative is negative over that interval.

Graphically, this means the curve bends downward like an upside-down bowl.

Explanation

The X-axis and Y-axis intersect at the point (0, 0), known as the origin.

It is the central reference point in the coordinate plane.

Explanation

In ax² + bx + c = 0, if > 0, b > 0, and c > 0, the parabola opens upward and lies entirely above the x-axis unless discriminant D = b² - 4ac ≥ 0.

If real roots exist, they are negative because both b and c are positive.

Explanation

Step 1: Add the two equations to eliminate y

(x + y) + (x - y) = 10 + 10

2x = 202x = 10

Step 2: Solve for x

x = 20/2x = 10

Explanation

Using the identify 2 sin A cos A = sin 2A, so 2 sin 45° cos 45° = sin 90°.

Since sin 90° = 1, the expression equals 1.

Explanation

Degree of a term = sum of the powers of variables in that term.

Highest degree term is 8x²y³ with degree 2 + 3 = 5.

Explanation

a^2 (-2b)^2 = a^2 × 4b^2 = 4a^2b^2

Explanation

This is an example of the associative property of multiplication:

  a × (b × c) = (a × b) × c

So, 8 × (6 × 7) = (8 × 6) × 7

Explanation

The associative property w.r.t addition states that the order in which we add numbers does not change the result.

The correct equation is:

1 + (4 + 3) = (1 + 4) + 3

This equation represents the associative property of addition.