Which of the following scenarios best describes division of a polynomial using synthetic division? Select all that apply. The di

Answer:

The tangent plane equation for the hyperboloid

.

Step-by-step explanation:

We have

The ellipsoid's equation is

The equation for the tangent plane at the point

 (Given)

The hyperboloid's equation is

F(x,y,z)=

The tangent plane equation at point

The tangent plane equation for the hyperboloid is

The tangent plane equation

Hence, the required tangent plane equation for the hyperboloid is

Response:

354

Detailed explanation:

Answer:

Refer to the explanation below.

Step-by-step explanation:

We start with a small aircraft that flies 760,320 yards within a duration of 2 hours.

A)

The formula for distance is:

To isolate the rate r, we divide both sides by time:

B)

To calculate the rate in yards per hour, divide the total yards by the hours taken. Therefore:

Perform division:

Thus, the aircraft speeds at 380,160 yards every hour.

C)

There are 1,760 yards in a mile.

To compute the speed in miles per hour, we apply dimensional analysis.

We recognize the rate is 380,160 yards per hour:

To cancel "yards" from the numerator, we multiply by 1 mi/1,760 yards. Therefore:

This eliminates yards:

Now, multiply the values across:

Then divide:

The final rate for the plane is 216 miles per hour.

D)

Miles are a more appropriate measurement in this context because the distance is substantial, making it impractical to express using yards. A rate of 380,160 yards per hour is excessive, whereas 216 miles per hour provides a clearer understanding.

Response:

Detailed breakdown:

Area of shaded region = 12 - 3.142