For Exercises 86-88, a. Shade the area bounded by the given inequalities on a coordinate grid showing − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . Find the probability that a dart thrown at the target will land in the shaded region. y ≥ x and y ≤ 4
For Exercises 86-88, a. Shade the area bounded by the given inequalities on a coordinate grid showing − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . Find the probability that a dart thrown at the target will land in the shaded region. y ≥ x and y ≤ 4
Solution Summary: The author illustrates how to graph a coordinate grid with yge left|xright|, and the coordinates of the modulus graph.
a. Shade the area bounded by the given inequalities on a coordinate grid showing
−
5
≤
x
≤
5
and
−
5
≤
y
≤
5
.
b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by
−
5
≤
x
≤
5
and
−
5
≤
y
≤
5
. Find the probability that a dart thrown at the target will land in the shaded region.
y
≥
x
and
y
≤
4
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?
Consider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.
College Algebra with Modeling & Visualization (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.