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mathematics
algebra and trigonometry graphs
Algebra And Trigonometry Graphs And Models 6th Edition Marvin Bittinger, Judith Beecher, David Ellenbogen, Judith Penna - Solutions
Simplify.sin (u - v) cos v + cos (u - v) sin v
Find an identity for cos (u + v) involving only cosines.
Solve.x - 7 = x + 3.4
Given that sin 31° = 0.5150 and cos 31° = 0.8572, find the specified function value.sec 59°
In a circus, a guy wire A is attached to the top of a 30-ft pole. Wire B is used for performers to walk up to the tight wire, 10 ft above the ground. Find the angle ϕ between the wires if they are attached to the ground 40 ft from the pole. A B 40 ft- 30 ft 10 ft ✓
An art student’s eye is at a point A, looking at a mural of height h, with the bottom of the mural y feet above the eye. The eye is x feet from the wall. Write an expression for θ in terms of x, y, and h. Then evaluate the expression when x = 20 ft, y = 7 ft, and h = 25 ft.
Given that sin 31° = 0.5150 and cos 31° = 0.8572, find the specified function value.tan 59°
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show that the equation is not an identity. Vsin²0 = sin 0
For a rope course and climbing wall, a guy wire R is attached 47 ft high on a vertical pole. Another guy wire S is attached 40 ft above the ground on the same pole. Find the angle α between the wires if they are attached to the ground 50 ft from the pole. 47 ft V 40 ft K R S 50 ft α
Solve ecos x = 1 in [0, 2π).
Given that f(x) = cos x, show that f(x + h) − f(x) h = COS X cos h h 1 ¹) sin x sin h h
Given that f(x) = sin x, show that f(x + h) = f(x) h h- h = sin x (cos / -1) + cos x (sin) h h
Why are the ranges of the inverse trigonometric functions restricted?
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show that the equation is not an identity. sin (-x) = sin x
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show that the equation is not an identity. sin 5x X = sin 5
Miles lists his answer to a problem as π/6 + kπ, for any integer k, while Jaylen lists his answer as π/6 + 2kπ and 7π/6 + 2kπ, for any integer k. Are their answers equivalent? Why or why not?
What is the difference between a trigonometric equation that is an identity and a trigonometric equation that is not an identity? Give an example of each.
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show that the equation is not an identity. cos (2a) = = 2 cos a
Derive the identity. Check using a graphing calculator. п (x - 37 2 sin x = COS X
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show that the equation is not an identity. cos 6x COS X = 6
Show that each of the following is not an identity by finding a replacement or replacements for which the sides of the equation do not name the same number. Then use a graphing calculator to show that the equation is not an identity. tan²0 + cot²0 = 1
Derive the identity. Check using a graphing calculator. sin (a +B) + sin (a - ß) = 2 sin a cos B
Find an identity for cos 2θ. 2θ = θ + θ.
Find an identity for sin 2θ. 2θ = θ + θ.
Derive the identity. Check using a graphing calculator. sin (a + B) cos (a - B) tan a + tan B 1 + tan a tan B
Determine the horizontal asymptote of the graph of the function. f(x) = x5 x³ + x X
Solve.2x3 + x2 < 10 + 11x
Solve.x3 + 5x2 - 25x ≤ 125
Simplify. i11
Simplify.i7
Simplify. i35
Simplify.i24
Simplify. i64
Simplify.i42
Simplify.( -i)71
Simplify. (5i)4
Simplify.(2i)5
Solve.2x2 > 5x + 3
Solve.x2 + x - 2 > 0
Solve.x2 - x - 6 > 0
Solve.x2 - x - 5 ≥ x - 2
Solve.x2 > 25
Graph the piecewise function. g(x) -x+ 3, for x = -2, 4, 2x 3 for 2 < x < 1, for x ≥ 1
Graph the piecewise function. -x², h(x)=x+1, for x < -2, for-2 ≤ x < 0, x³ - 1, for x ≥ 0
Solve.x2 + 4x + 7 ≥ 5x + 9
Solve.x2 ≤ 1
Solve.4 - x2 ≤ 0
Solve.11 - x2 ≥ 0
Solve.6x - 9 - x2 < 0
Solve.x2 + 2x + 1 ≤ 0
Solve.x2 + 12 > 4x
Solve.x2 - 8 > 6x
Solve.4x3 - 7x2 ≤ 15x
Solve.2x3 - x2 < 5x
Solve.x3 + 3x2 - x - 3 ≥ 0
Solve.x3 + x2 - 4x - 4 ≥ 0
Solve.x3 - 2x2 < 5x - 6
Solve.x3 + x ≤ 6 - 4x2
Solve.x5 + x2 ≤ 2x3 + 2
Solve.x5 + 24 > 3x3 + 8x2
Solve.2x3 + 6 ≤ 5x2 + x
Solve.x3 - 9x + 27 ≤ 3x2
Solve.0.1x3 - 0.6x2 - 0.1x + 2 < 0
Solve.19.2x3 + 12.8x2 + 144 ≥ 172.8x + 3.2x4
Solve. Find exact solutions.2x2 + 12 = 5x
Solve. Find exact solutions.7x2 + 4x = 3
The following table lists the newspaper revenue, in billions of dollars, from classified ads for selected years from 1975 to 2013.a) Use a graphing calculator to fit cubic and quartic functions to the data. Let x represent the number of years after 1975. Using R2-values, determine which function is
For what values of k will the remainder be the same when x2 + kx + 4 is divided by x - 1 and by x + 1?
Find a 15th-degree polynomial for which x - 1 is a factor.
A dog’s life span is typically much shorter than that of a human. Age equivalents for dogs and humans are listed in the following table.a) Use a graphing calculator to fit linear and cubic functions to the data. Which function has the better fit?b) Using the function from part (a), estimate the
Find the nonlinear asymptote of the function. f(x) x² + 3x² 4 x² + 1 2
Graph the function. f(x) = = 2x³ + x² x³ 3 8x - 4 + x² - 9x - 9
Graph the function. f(x) = x³ + 4x² + x - 6 x²-x-2
Solve.2y - 3 ≥ 1 - y + 5
Solve.(x - 2)(x + 5) > x(x - 3)
Raleigh, North Carolina, is one of the fastest growing cities in the United States. In 2014, the population was approximately 438,000, and the growth rate was about 3.4% per year.a) Find the exponential growth function.b) Estimate the population of Raleigh in 2017.c) When will the population of
Solve.| x + 6| ≥ 7
Find each of the following, to four decimal places, using a calculator.e4
Find each of the following, to four decimal places, using a calculator.e10
Find each of the following, to four decimal places, using a calculator. e 2
Find each of the following, to four decimal places, using a calculator.e-2.458
On November 20, 2014, Georgia O’Keeffe’s painting, “Jimson Weed/White Flower No. 1,” sold at Sotheby’s auction in New York City for $44.4 million, a record price for any female artist’s work that was sold at auction. The painting had previously sold for $1 million in 1994. Assuming that
Express as a product.logb t3
Find each of the following. Do not use a calculator.log2 16
Express as a product.loga x4
Find each of the following. Do not use a calculator.log3 9
Graph the function.f(x) = 4-x
Express as a product.log y8
Find each of the following. Do not use a calculator.log5 125
Graph the function.f(x) = log x
Express as a product.ln y5
Find each of the following. Do not use a calculator.log2 64
Graph the function.f(x) = ex - 3
Graph the function.f(x) = ln (x + 2)
Express as a product.logc K-6
Find each of the following. Do not use a calculator.log 0.001
Find each of the following. Do not use a calculator.log 0.00001
Express as a product.logb Q-8
Find each of the following. Do not use a calculator.log 100
Find each of the following. Do not use a calculator.ln e
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