The number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater

Detailed derivation:

dA/dt = 6 - 0.02A

dA/dt = -0.02 (A - 300)

Rearranging terms.

dA / (A - 300) = -0.02 dt

Integrate both sides.

ln(A - 300) = -0.02t + C

Isolate A.

A - 300 = Ce^(-0.02t)

A = 300 + Ce^(-0.02t)

Apply initial condition to determine C.

50 = 300 + Ce^(-0.02 × 10)

50 = 300 + Ce^(-0.2)

-250 = Ce^(-0.2)

C = -250e^(0.2)

A = 300 - 250e^(0.2)e^(-0.02t)

A = 300 - 250e^(0.2 - 0.02t)

Answer:

(A)(12, 9)

Step-by-step explanation:

Provided:

The starting point of the stencil's left edge is at (2, -1).

A designated point, referred to as Q on the stencil, is located at (4, 1).

Point Q divides the stencil in a 1:4 ratio.

We are tasked with determining the endpoint of the stencil.

Mathematically, Point Q segments the stencil internally in a 1:4 ratio.

For calculating the internal division of a line segment with initial point and end point in the ratio m:n, we apply the formula

, , Q(x,y)=(4,1), m:n=1:4

Consequently:

The selected choice is A.

A line and a point.

Additional explanation

A ray consists of a segment of a line emerging from one endpoint. It represents an infinite straight path extending in one direction from a starting point, exemplified by .

The arrow indicates the direction along which the ray extends. The ray's length isn't quantifiable.

In geometry, undefined terms refer to fundamental figures that are not defined by other figures. The primary undefined terms in geometry include a point, line, and plane.

These crucial concepts cannot be precisely defined in mathematical terms using other established words.

• A point indicates a specific location without any size; it is marked with a capital letter and a dot.
• A line comprises an infinite collection of points stretching in both directions with just one dimension; it is a straight path without thickness.
• A plane represents a flat surface encompassing numerous points and lines, extending infinitely in all directions. It is two-dimensional, and any three points that are not collinear define a unique plane.

Explore more

1. Which points are both coplanar and noncollinear?
2. Definition of line segments
3. What are three collinear points on a line?

Keywords: which undefined terms define a ray, point, line, plane, endpoint, one direction, the ray's arrow