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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
Find the exact value of sin π/6.
For the following exercises, find the exact value of each expression.tan π/4
For the following exercises, find the exact value of each trigonometric function.sin π/2
For the following exercises, find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.cos B = 4/5, a = 10
For the following exercises, find the angle between 0 and 2π in radians that is coterminal with the given angle.14π/5
For the following exercises, draw an angle in standard position with the given measure.−150°
For the following exercises, draw an angle in standard position with the given measure.135°
A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?
For the following exercises, find the exact value of each expression.cot π/6
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by t lies.sin(t) < 0 and cos(t) > 0
For the following exercises, use cofunctions of complementary angles.tan (π/4) = cot(_____)
For the following exercises, find the angle between 0 and 2π in radians that is coterminal with the given angle.−20π/11
For the following exercises, draw an angle in standard position with the given measure.−80°
Draw the angle −π/6 in standard position on the Cartesian plane.
For the following exercises, find the exact value of each expression.csc π/6
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by t lies.sin(t) > 0 and cos(t) < 0
For the following exercises, find the angle between 0° and 360° that is coterminal with the given angle.−80°
For the following exercises, use cofunctions of complementary angles.csc(21°) = sec(_____°)
For the following exercises, draw an angle in standard position with the given measure.300°
For the following exercises, find the exact value of each expression.sec π/6
Draw the angle 315° in standard position on the Cartesian plane.
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by t lies.sin(t) > 0 and cos(t) > 0
For the following exercises, use cofunctions of complementary angles.cos (π/3) = sin(______)
For the following exercises, find the angle between 0° and 360° that is coterminal with the given angle.420°
For the following exercises, draw an angle in standard position with the given measure.30°
Find the angle between 0 and 2π in radians that is coterminal with −4π/7 .
For the following exercises, find the exact value of each expression.tan π/6
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by t lies.sin(t) < 0 and cos(t) < 0
For the following exercises, use cofunctions of complementary angles.cos(34°) = sin(_____°)
For the following exercises, convert the angle measures to radians.Find the area of the sector of a circle with diameter 32 feet and an angle of 3π/5 radians.
Explain the differences between linear speed and angular speed when describing motion along a circular path.
Find the angle between 0° and 360° that is coterminal with 375°.
Tangent and cotangent have a period of π. What does this tell us about the output of these functions?
Explain how the sine of an angle in the second quadrant differs from the sine of its reference angle in the unit circle.
Explain the cofunction identity.
For the following exercises, convert the angle measures to radians.Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85°.
How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.
What is the relationship between the two acute angles in a right triangle?
Find the area of the sector with radius of 8 feet and an angle of 5π/4 radians.
Describe the secant function.
Explain how the cosine of an angle in the second quadrant differs from the cosine of its reference angle in the unit circle.
For the following exercises, convert the angle measures to radians.180°
State what a positive or negative angle signifies, and explain how to draw each.
Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of 30°.
The tangent of an angle compares which sides of the right triangle?
For any angle in quadrant II, if you knew the sine of the angle, how could you determine the cosine of the angle?
When a right triangle with a hypotenuse of 1 is placed in the unit circle, which sides of the triangle correspond to the x- and y-coordinates?
Discuss the difference between a coterminal angle and a reference angle.
For the following exercises, convert the angle measures to radians.−210°
Explain why there are an infinite number of angles that are coterminal to a certain angle.
What would you estimate the cosine of π degrees to be? Explain your reasoning.
For the following exercises, convert the angle measures to degrees.−5π/3
Draw an angle in standard position. Label the vertex, initial side, and terminal side.
Convert 5π/6 radians to degrees.
On an interval of [0,2π), can the sine and cosine values of a radian measure ever be equal? If so, where?
For the following exercises, convert the angle measures to degrees. π/4
For the given right triangle, label the adjacent side, opposite side, and hypotenuse for the indicated angle.
For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.
For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. y= 2.25(e)-2
For the following exercises, evaluate the common logarithmic expression without using a calculator.log(0.001)
For the following exercises, refer to Table 10.Use the LOGarithm option of the REGression feature to find a logarithmic function of the form y = a + bln(x) that best fits the data in the table. X f(x) 1 7.5 2 16 3 4 5.2 4.3 Table 10 5 3.9 10 6 3.4 7 3.1 8 2.9
For the following exercises, use the definition of common and natural logarithms to simplify.eln(10.125) + 4
Find the exact solution for 5e3x − 4 = 6 . If there is no solution, write no solution.
For the following exercises, find an exponential equation for the graph. y -5-4-3-2-0 1 2 3 4 5 TIT x
Does log81(2401) = log3 (7)? Verify the claim algebraically.
For the following exercises, use the one-to-one property of logarithms to solve.log9 (2n2 − 14n)= log9 (−45 + n2)
For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.f(x) = 1.2e2x − 0.3, for f(3)
For the following exercises, evaluate the natural logarithmic expression without using a calculator. 25ln(e)
For the following exercises, solve the equation for x, if there is a solution. Then graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution.log(4) + log(−5x) = 2
Use logarithms to find the exact solution for −9e10a − 8 −5 = −41. If there is no solution, write no solution.
For the following exercises, refer to Table 8.Use the regression feature to find an exponential function that best fits the data in the table. X f(x) 1 2 383 555 3 307 Table 8 4 210 5 158 6 122
Rewrite log8 (x)+log8 (5)+log8 (y)+log8 (13) in compact form.
Rewrite ln (1/x5) as a product.
For the following exercises, use the compound interest formula, How much more would the account in Exercises #31 and #34 be worth if it were earning interest for 5 more years? A(t) = P(1 + 7)". r nt
Rewrite log3 (12.75) to base e.
For the following exercises, use the definition of common and natural logarithms to simplify.log(1008)
For the following exercises, use the compound interest formula, Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $9,000 and was worth $13,373.53 after 10 years. A(t) = P(1 + 7)". r nt
For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.log1/2 (4.7)
For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. y = 3742(e)0.75t
For the following exercises, use the one-to-one property of logarithms to solve.log(x + 3) − log(x) = log(74)
For the following exercises, evaluate the base b logarithmic expression without using a calculator. log, (27)
For the following exercises, evaluate the exponential functions for the indicated value of x. g(x) = (7)x-² for g(6). 1/3
For the following exercises, sketch the graph of the indicated function.f(x) = 2log(x)
For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F.To the nearest degree, what will the temperature be after 2
For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth. log (x) H + + + -5 -4 -3 -2 -1 0 1 2 3 4 5 +++ H
For the following exercises, refer to Table 11.Use the LOGISTIC regression option to find a logistic growth model of the form y = c/1 + ae−bx that best fits the data in the table. 1 f(x) 8.7 8 2 3 12.3 15.4 4 5 18.5 20.7 Table 11 16 22.5 7 23.3 8 9 10 24 24.6 24.8
For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain.How much less would the account from Exercise 42 be worth after 30 years if it were compounded monthly instead?
For the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth. f(x) = abx + d. -50= (1) * 2
For the following exercises, sketch the graph of the indicated function.g(x) = log(4x + 16) + 4
For the following exercises, sketch the graph of the indicated function.g(x) = log(6 − 3x) + 1
For the following exercises, sketch the graph of the indicated function.h(x) = −1/2 ln(x + 1) − 3
For the following exercises, evaluate the common logarithmic expression without using a calculator.log(10, 000)
For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.f (x) = ex, for f (3)
For the following exercises, write a logarithmic equation corresponding to the graph shown.Use y = log2 (x) as the parent function. IIII IIII 5- 4 3- -5-4-3 2 3 4 -2-
For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth. -5 -4 -3 -2 -1 0 1 2 log (x) + + 3 4 5
For the following exercises, refer to Table 11.Graph the logistic equation on the scatter diagram. x 1 f(x) 8.7 2 12.3 3 4 5 15.4 18.5 20.7 Table 11 6 22.5 7 23.3 8 9 10 24 24.6 24.8
For the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth. f(x) = abx + d. 116 = 1 4 1 8 x
Use the definition of a logarithm to find the exact solution for 9 + 6ln(a + 3) = 33.
For the following exercises, solve each equation for x.ln(7) + ln(2 − 4x2) = ln(14)
For the following exercises, write a logarithmic equation corresponding to the graph shown.Use f(x) = log3 (x) as the parent function. y 5+ 4 ·3- 2- III 2 3 4 5 X
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