(b) if the length, width, and height are increasing at a rate of 0.1 ft/sec, 0.2 ft/sec, and 0.5 ft/sec respectively, find the r

Answer and image included:

Answer:

On a coordinate grid, a triangle is defined by the points R' (1, 2), S' (3, -1), T' (7, 1)

Step-by-step explanation:

We can interpret the coordinates of the triangle's vertices as...

R(-2, 1), S(1, 3), T(-1, 7)

Applying the transformation (x, y) ⇒ (y, -x), these coordinates change to...

R'(1, 2), S'(3, -1), T'(7, 1) . . . . . (this corresponds to the first option)

To find the answer, subtract the total percentage of 24.65% and $48 from 1986, resulting in the final value.

The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.

In this scenario, the first step is to assign variables.

We define:

x: time measured in minutes

y: distance covered.

The equations formulated are as follows:

For Kathleen:

For Arnob:

At the moment Arnob meets Kathleen, we have:

Next, we isolate x.

We now have:

Answer:

Arnob takes a total of 75 minutes to catch up to Kathleen:

d. 75