Explanation

Explanation

= 8/3 - 3/4

= LCM of 3 and 4 = 12

= 8/3 = 32/12, 3/4 = 9/12

= 32/12 - 9/12 = 23/12

Explanation

For the quadratic equation 3x^2 - 6x + k = 0 to have equal roots, the discriminant b^2 - 4ac must be 0.

Here, a = 3, b = -6, and c = k.

Setting the discriminant to 0 gives (-6)^2 - 4(3)(k) = 0.

Solving this, 36 - 12k = 0, which yields k = 3.

Explanation

Explanation

Given the surface area of a sphere = 81π

The formula for surface area of a sphere is:

4πr² = 81π

Divide both sides by 4π:

r² = 81/4

r² = 20.25

r = √20.25

r = 4.5 m

Explanation

Given that the two sides of the isosceles triangle are equal:

3x - 2y + 2 = x - y + 7

This simplifies to:

2x - y = 5

The sum of the two equal sides is 12 cm:

(3x - 2y + 2) + (x - y + 7) = 12

This simplifies to:

4x - 3y = 3

Solving these two equations simultaneously, we find x = 6.

Explanation

In a Passive Learning Environment, students receive information and respond to stimuli with little active engagement.

This aligns with the stimulus-response method where learning is measured by correct reactions to teacher prompts.

Explanation

Intensity of temperament describes how strongly a child experiences and expresses emotions.

It reflects the degree or strength of emotional reactions, not just their type or understanding.

Explanation

Gross motor development involves large muscle groups used in activities like running, jumping, and throwing.

It focuses on whole-body movements and coordination.

Explanation

The curriculum is the primary tool a teacher (the artist) uses to shape and guide students (the material) within the school (the studio).

It encompasses the planned content, objectives, and experiences designed to achieve educational ideals.