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mathematics
precalculus
Questions and Answers of
Precalculus
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 5, b = 3, A = 80°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 4, b = 1, C = 100°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 1, b = 3, C = 40°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 10, b = 7, c = 8
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 2, b = 3, c = 1
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 3, b = 5, B = 80°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 3, c = 1, B = 100°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 3, c = 1, C = 20°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 3, c = 1, C = 110°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” a = 2, c = 5, A = 60°
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” A = 100°, a = 5, c = 2
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” A = 10°, C = 40°, c = 2
Find the remaining angle(s) and side(s) of triangle, if it (they) exists. If no triangle exists, say “No triangle.” A = 50°, B = 30°, a = 1
Solve Triangle. 3.
Solve Triangle. 5 2.
Solve Triangle. 35 B.
Solve Triangle. 10 20° aి
Find the exact value of each expression. Do not use a calculator. tan2 40° - cos2 50°
Find the exact value of each expression. Do not use a calculator. cos240° + cos250°
Find the exact value of each expression. Do not use a calculator. tan 40°/cot 50°
Find the exact value of each expression. Do not use a calculator. sec 55°/csc 35°
Find the exact value of each expression. Do not use a calculator. tan 15° - cot 75°
Find the exact value of each expression. Do not use a calculator. cos 62° - sin 28°
Find the exact value of the six trigonometric functions of the angle in each figure. Ө V2 2.
Find the exact value of the six trigonometric functions of the angle in each figure. 2. 4,
Find the exact value of the six trigonometric functions of the angle in each figure. 3,
Find the exact value of the six trigonometric functions of the angle in each figure. 3
Use a graphing utility to graphand y = 1/x3 sin x for x > 0. That patterns do you observe? sin x - sin x, y = y =
Use a graphing utility to graph y = x sin x, y = x2 sin x, and y = x3 sin x for x > 0. What patterns do you observe?
Use a graphing utility to graph the functionBased on the graph, what do you conjecture about the value of sinx/x for x close to 0? sin x -, x > 0. f(x)
Use a graphing utility to graph the sound emitted by the * key on a Touch-Tone phone. See Problem 57.Data from problem 57On a Touch-Tone phone, each button produces a unique sound. The sound produced
On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two tones, given bywhere l and h are the low and high frequencies (cycles per second) shown in the
An oscilloscope often displays a sawtooth curve.This curve can be approximated by sinusoidal curves of varying periods and amplitudes.(a) Use a graphing utility to graph the following function, which
See the illustration. If a charged capacitor is connected to a coil by closing a switch, energy is transferred to the coil and then back to the capacitor in an oscillatory motion. The voltage V (in
The end of a tuning fork moves in simple harmonic motion described by the equation d = a sin (ωt). If a tuning fork for the note E above middle C on an even-tempered scale (E4) has a frequency of
The end of a tuning fork moves in simple harmonic motion described by the equation d = a sin (ωt). If a tuning fork for the note A above middle C on an even tempered scale (A4, the tone by which an
Added to Six Flags St. Louis in 1986, the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet
A loudspeaker diaphragm is oscillating in simple harmonic motion described by the equation d = a cos (ωt) with a frequency of 520 hertz (cycles per second) and a maximum displacement of 0.80
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and
The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume
(a) Use the Product-to-Sum Formulas to express product as a sum,(b) Use the method of adding y-coordinates to graph the function on the interval [0, 2π].g(x) = 2 sin x cos(3x)
(a) Use the Product-to-Sum Formulas to express product as a sum,(b) Use the method of adding y-coordinates to graph the function on the interval [0, 2π].H(x) = 2 sin(3x) cos(x)
(a) Use the Product-to-Sum Formulas to express product as a sum,(b) Use the method of adding y-coordinates to graph the function on the interval [0, 2π].h(x) = cos(2x) cos(x)
(a) Use the Product-to-Sum Formulas to express product as a sum,(b) Use the method of adding y-coordinates to graph the function on the interval [0, 2π].G(x) = cos(4x) cos (2x)
(a) Use the Product-to-Sum Formulas to express product as a sum,(b) Use the method of adding y-coordinates to graph the function on the interval [0, 2π].F(x) = sin(3x) sinx
(a) Use the Product-to-Sum Formulas to express product as a sum,(b) Use the method of adding y-coordinates to graph the function on the interval [0, 2π].f(x) = sin(2x) sinx
Use the method of adding y-coordinates to graph the function.g(x) = cos(2x) + cos x
Use the method of adding y-coordinates to graph the function.g(x) = sin x + sin(2x)
Use the method of adding y-coordinates to graph the function.f(x) = sin(2x) + cos x
Use the method of adding y-coordinates to graph the function.f(x) = sin x + cos x
Use the method of adding y-coordinates to graph the function.f(x) = x - cos x
Use the method of adding y-coordinates to graph the function.f(x) = x - sin x
Use the method of adding y-coordinates to graph the function.f(x) = x + cos(2x)
Use the method of adding y-coordinates to graph the function.f(x) = x + cos x
Graph damped vibration curve for 0 ≤ t ≤ 2π.d(t) = e-t/4π cos t
Graph damped vibration curve for 0 ≤ t ≤ 2π.d(t) = e-t/2π cos t
Graph damped vibration curve for 0 ≤ t ≤ 2π.d(t) = e-t/2π cos(2t)
Graph damped vibration curve for 0 ≤ t ≤ 2π.d(t) = e-t/π cos(2t)
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
The displacement d (in meters) of an object at time t (in seconds) is given.(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time
Rework Problem 8 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.Data from problem 8a = 4; T = π/2 seconds
Rework Problem 7 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.Data from problem 7a = 6; T = π seconds
Rework Problem 6 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.Data from problem 6a = 10; T = 3 seconds
Rework Problem 5 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.Data from problem 5a = 5; T = 2 seconds
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates
True or FalseIf the distance d of an object from its rest position at time t is given by a sinusoidal graph, the motion of the object is simple harmonic motion.
When a mass hanging from a spring is pulled down and then released, the motion is called _____ ________ if there is no frictional force to retard the motion, and the motion is called _____if there is
The motion of an object obeys the equation d = 4 cos(6t). Such motion is described as _____ _______. The number 4 is called the _______.
The amplitude A and period T of f(x) = 5 sin(4x) are ______ and ______.
Show that the area K of triangle PQR is K = rs, where s = ½(a + b + c). Then show thatThe lines that bisect each angle of a triangle meet in a single point O, and the perpendicular distance r from O
Show thatThe lines that bisect each angle of a triangle meet in a single point O, and the perpendicular distance r from O to each side of the triangle is the same. The circle with center at O and
Use the result of Problem 50 and the results of Problems 56 and 57 in Section 8.3 to show thatwhereThe lines that bisect each angle of a triangle meet in a single point O, and the perpendicular
Apply the formula from Problem 49 to triangle OPQ to show thatThe lines that bisect each angle of a triangle meet in a single point O, and the perpendicular distance r from O to each side of the
Show that a formula for the altitude h from a vertex to the opposite side a of a triangle is a sin B sin C sin A
If h1, h2, and h3 are the altitudes dropped from P, Q, and R, respectively, in a triangle (see the figure), show thatwhere K is the area of the triangle and s = ½ (a + b + c). h3 h2 K hị 이K ||
A perfect triangle is one having natural number sides for which the area is numerically equal to the perimeter. Show that the triangles with the given side lengths are perfect.(a) 9, 10, 17(b) 6, 25,
If the barn in Problem 45 is rectangular, 10 feet by 20 feet, what is the maximum grazing area for the cow?Data from problem 45 10 Ag U 10 A2 A1 Barn Rope
A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rope 100 feet long. What is the maximum grazing area for the cow? 10 Аз 10 A2 A1 Barn Rope
Refer to the figure, in which a unit circle is drawn. The line segment DR is tangent to the circle and 0 is acute (a) Express the area of ΔOBC in terms of sin θ and cos θ. (b) Express
Geometry Refer to the figure. If |OA| = 1, show that: (a) Area ΔOAC = 1/2 sin α cos α(b) Area ΔOCB = 1/2 |OB|2 sin β cos β (c) Area ΔOAB = 1/2 |OB| sin(α + β)(d) |OB| = cos
The Bermuda Triangle is roughly defined by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida. The distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San
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