Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

Solution Procedure

Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:

... C = 2√(πA)

To find ten times this circumference, we calculate:

... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm

Derivation of Formulas

The standard formulas for circumference and area are:

... C = 2πr

... A = πr²

Multiplying the area formula by π and extracting the square root yields:

... πA = (πr)²

... √(πA) = πr

Doubling this value results in the circumference formula:

... C = 2√(πA) = 2πr

Response

The first diagram displays angles 1 and 2 as vertical angles.

Clarification

In all four diagrams, the initial one illustrates the vertically opposite angles.

Angles 1 and 2 are classified as vertically opposite because they face each other.

These angles maintain equal measurement when two lines intersect, resulting in four angles where two pairs of vertically opposite angles are formed.

In contrast, all other figures depict angles 1 and 2 as adjacent angles.

When the balloon touches the ground, a(t) will equal zero.

To calculate the time it takes to reach the ground, the equation can be set up as follows:

210 - 15t = 0
Solving this yields t = 210/15, equating to 14 minutes.

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