A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake

B. The correct ratio is sen α = BC/b. Step-by-step explanation: Trigonometric identities are utilized for resolving problems involving right angles. In any right-angled triangle, the side opposite to the angle is known as the opposite side, while the adjacent side runs parallel to the angle, ultimately leading to the longest side, called the hypotenuse.

The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here,  and are proportional with a constant of proportionality of 14.

Answer:

The highest achievable volume for the box is 2000000 cubic meters.

Step-by-step explanation:

Below is an outline of the volume (), measured in cubic centimeters, and surface area (), measured in square centimeters, for a box featuring a square base:

(1)

(2)

Where:

- The length of the base's side, in centimeters.

- The height of the box, in centimeters.

Using (2), we isolate in the formula:

Then, we substitute into (1) and simplify the outcome:

(3)

Next, we calculate the first and second derivatives of this expression:

(4)

(5)

If and , then we find that the critical value for the base's side length is:

Subsequently, we assess this outcome using the second derivative's expression:

According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:

The highest achievable volume for the box is 2000000 cubic meters.

In each instance, when it sheds a shell, its size increases by a factor of 1 1/3. To determine the growth after the first molt, multiply 1 cm by 1 1/3 to get 1 1/3 cm. To find the next size, repeat the multiplication: 1 1/3 cm times 1 1/3 cm equals 16/9. This process will continue by multiplying by 1 1/3. We can express it mathematically as (initial size) * 1 1/3 *(number of shells) equals length or 1 cm * 1 1/3 * n equals L. Given that the final length is 10 cm, accordingly, 1 1/3 * n equals 10 cm, leading to n being 7.5 shells, which translates to either about 7 or 8 shells.

Answers:

C - The value of w cannot be negative.

D - The variable l is substituted with the value 20.

E - To isolate the variable w, the subtraction property of equality is applied.

~ .