Triangles A B C and T P Q are shown. Sides A C and T Q are congruent. Angles B C A and P Q T are congruent. Which statements are

If a component must measure 5.72 inches with a tolerance of 0.02 inches (assuming the symbol before 0.02 indicates a +/-), its length must fall between 5.70 and 5.74 inches. Given that the current length is 5.85 inches, the maximum reduction possible is 0.15 inches.

Answer:

A tangent touches the curve at a single point, while a chord meets the curve at multiple points.

Step-by-step explanation:

A tangent line makes contact with the curve while a chord intersects it.

Only the tangent intersects the curve at a solitary point, unlike the chord, which contacts the curve at several points.

In the diagram provided, line BD acts as a tangent, whereas line BC serves as a chord.

Answer:

To identify the critical point, we set the derivative equal to zero, resulting in:

Calculating the second derivative yields:

This indicates that t = 3.4375 marks the minimum value for the function. Substituting this back into the original function gives us:

Thus, the minimum annual income is found at t = 3.43 (between the years 2008 and 2009), with a value of 25.094

Step-by-step explanation:

In this scenario, we have the function:

Where P represents the annual net income from 2007-2011, and

t is the number of years since early 2005

To discover the lowest income, we utilize the derivative given by:

Setting this derivative to zero allows us to find the critical point, leading to:

Calculating the second derivative reveals:

Therefore, we conclude that t = 3.4375 is the minimum value, substituting into the original function results in:

Thus, the minimum annual income occurs at t = 3.43 (between 2008 and 2009) with the value being 25.094

Response:

a)

b) 0.044

Step-by-step breakdown:

Part a)

A Sonet consists of 14 lines. Raymond Queneau published a collection of 10 sonnets, each placed on separate pages. This implies that every page contains a 14-line poem. We are to determine how many unique sonnets can be created from the 10 published sonnets.

As the first line of a new sonnet can be chosen from any of the 10 published sonnets, it offers 10 options for the selection of the first line. Likewise, the second line of the new sonnet can also be from any of the 10 sonnets, leading to another 10 choices for the second line, and this applies identically for all 14 lines, resulting in 10 options for each line.

According to the fundamental principle of counting, the total number of possible sonnets would equal the product of the options available for all 14 lines.

Thus,

the number of sonnets created from those in the book = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =

sonnets

Therefore,

can be formed from the 10 in the book.

Part b)

Next, we will ascertain how many sonnets can be generated that utilize none of the lines from the first and last page. Given that there are 10 pages total, the exclusion of the 1st and last leaves us with 8 pages (8 sonnets).

Consequently, the number of options for each line of such a sonnet will be restricted to 8 choices. Applying the fundamental principle of counting, the total sonnets with no lines from either the first or last sonnet is calculated as

This shows the number of favorable outcomes that ensure the selection of a sonnet does not result in lines from the first or last sonnet in the collection.

Thus,

The probability that no lines are selected from either the first or the last sonnet =

Response:

4.3

Detailed explanation:

4.3