A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base

We need to specify the interval for numbers ranging from -5 to 4.

Moreover, we must exclude the values -1 and 4 from this range.

First, let’s note some crucial guidelines regarding interval notation.

It’s essential to identify which values are included and which ones are not in the specified range.

An open interval (or) indicates excluded numbers, while a closed interval [or] shows included numbers.

In this scenario, we notice three key numbers: -5, -1, and 4.

It is explicit that -1 and 4 are excluded, though -5 is not indicated as excluded, hence it remains included.

-1 lies between -5 and 4 on the number line.

Consequently, we can represent the interval notation from -5 to -1. (Note: -5 is included and -1 is not).

Thus, we write a closed interval " [ " on the left side of -5 and an open interval " ( " on the right side of -1. This gives us,

[-5, -1 ).

Next, we represent the interval from -1 to 4.

Since both endpoints are excluded, we will use open intervals ( ) on both sides of -1 and 4.

This results in the interval being

(-1,4).

We combine the two interval notations using the union symbol. So, the final interval representation is

[-5, -1 ) ∪ (-1,4).

we understand that

A fast method for estimating the total of two numbers involves rounding each number and adding the rounded results.

case a) We round to the nearest hundred

so

Round up equals

Round up equals

Calculate the estimated sum

case b) We round to the nearest ten

so

Round up equals

Round down equals

Calculate the estimated sum

Let's sketch the triangle.

The sides are a= 37.674 miles

b= 11.164 miles

c= 36.318 miles

We'll apply the cosine rule for angle calculations

(since the sine law cannot be employed without knowing any angle measurements).

The cosine law is given by

Substituting the values results in

C = 74.48°

We can find angle A using the sine law

A=

A = 87.38°

The third angle B can be determined by calculating 180° minus the sum of angles A and C

B = 180 - 161.86

B = 18.14°

Thus, we have calculated all three angles (as shown in the attached figure).

Answer:

Step-by-step explanation:

We start with the information provided

To carry this out, we simply plug the values of P, r, and t into the formula.

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Convert the percentage to decimal form

Convert it to cents.

-- Approximated