# TayB

Popular questions and responses by TayB
1. ## Math

Express the function in the form f o g. (Use non-identity functions for f and g.) G(x)= cube root of (x/(9+x)) {f(x),g(x)}=?

2. ## Calculus 1

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = sqrt(x), [0,16]

3. ## Calculus 1

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh 9 (b) cosh(ln 9)

4. ## Calc 1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = 6 sin x, 0 ≤ x ≤ π

5. ## Calculus 1

The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2, 2)

6. ## Calculus 1

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 5. (Round your answers to two decimal places.) f(t) = t^−1 − t *We havent learned derivative

7. ## Math

Express the function in the form f compose g. (Use non-identity functions for f and g.) u(t) = cot t/(9+cot t) {f(t), g(t)}=?

8. ## Calculus 1

Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

9. ## Calculus 1

If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1/R= 1/R1+ 1/R2. If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how

10. ## Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^(5)e^(-6x)

11. ## Calculus 1

The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a/(1 + be^−0.5t) where t is measured in hours. At time t = 0 the population is 10 cells and is

12. ## Calculus 1 optimization

A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the

13. ## Calculus 1

A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for

14. ## Calculus 1

Find the linear approximation of the function g(x)=cube root(1+x) at a=0.

15. ## Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(t) = t^(3/4) − 3t^(1/4)

16. ## math

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→∞ (sqrt(49x^2+x)−7x)

17. ## Calculus 1

Consider the following. B(x) = 3x^(2/3) − x (a) Find the interval of increase.(Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local maximum value(s).(Enter your answers

18. ## Calc 1

Consider the position function s(t)=sin((pi)(t)) representing the position of an object moving along a line on the end of a spring. Sketch a graph of s with the secant line passing through (0,s(0)) and (0.5,s(0.5)). Determine the slope of the secant line

19. ## math just for fun

A long year-end status report for work is 111 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for \$3.88 each. Give your answer to the nearest cent,

20. ## Calculus 1

Find the equation of the tangent line to the curve y = (9 ln x)/x at the points (1, 0) and (e, 9/e).

21. ## Math

lim x→−12 sqrt(x^2 +25 −13)/x+12

22. ## Calculus 1

Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.) (d) y= -2f(x) shift 2 units upward shift 2 units downward shift 2 units to the right shift 2 units to the left stretch the graph vertically by a factor of 2

23. ## Calculus 1

Find the derivative of the function. F(t) = e^(4t sin 2t)

24. ## Calculus 1

Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x

25. ## Calculus 1

If f(x)=3 sin x+ln(5x), find f '(x).

26. ## calculus 2

Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.

27. ## Calc 1

Evaluate the limit. lim x → 1 ln x/sin 5πx

28. ## Calc 2

A hemispherical plate with diameter 10 ft is submerged vertically 2 ft below the surface of the water. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Recall that

29. ## Calculus 1

A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 4.7 days, the average brightness (or magnitude) of the star is 5.3, and its brightness varies by ±0.35

30. ## Calculus 1

Related Rates: The minute hand on a watch is 9 mm long and the hour hand is 6 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

31. ## Calculus 1

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) = 6 cos t, −3π/2 ≤ t ≤ 3π/2

32. ## Calc 1

Consider the following function. f(x) = x^6 ln x (a) Use l'Hospital's Rule to determine the limit as x → 0+. (b) Use calculus to find the minimum value. Find the interval where the function is concave up. (Enter your answer in interval notation.) Find

33. ## Calculus 1

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one

34. ## philosophy

Libertarianism believes that causal determinism is true. Select one: True False I think true Whether or not we have free will seems to have implications for which of the following? Select one: a. Our idea of God b. Our idea of the physical laws of the

35. ## Calculus 1

Use Newton's method with initial approximation x1 = −2 to find x2, the second approximation to the root of the equation x^3 + x + 1 = 0. *I got -1.307692 for my answer but it said that was wrong, so then I tried rounding it to two decimal places and got

36. ## Calculus 1

Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.) (a) y=7f(x) shifts 7 units upward shifts 7 units downward shifts 7 units to the right shifts 7 units to the left stretch the graph vertically by a factor of 7

37. ## Calc 1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = 5th root(x), 0 ≤ x ≤ 32

38. ## Calc 1

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin.

39. ## Calc 1

Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=? y=? (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is

40. ## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (sin^−1 x)/7x Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim

41. ## calculus

Find the area of the region that lies inside the first curve and outside the second curve. r = 1 + cos(θ), r = 2 − cos(θ)

42. ## Calculus 1

If tanh x=4/5, find the values of the other hyperbolic functions at x. sinh x= cosh x= coth x= sech x= csch x=

43. ## Calculus 1

Related Rates Problem: Two cars start moving from the same point. One travels south at 40 mi/h and the other travels west at 30 mi/h. At what rate is the distance between the cars increasing three hours later?

44. ## Calc 1

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 4 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval.

45. ## Calc 1

Find f. f ''(x) = 6 + cos x, f(0) = −1, f(7π/2) = 0

46. ## History

William McKinley justified annexation of the Philippines because, according to McKinley, the United States: Select one: a. Needed to bring civilization to the Filipinos. b. Needed the islands for business and trade. c. Felt the Filipinos were not ready for

47. ## calc 2

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem y' = y − 3x, y(4) = 0.

48. ## Calculus 1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = x^−3, 2 ≤ x ≤ 5

49. ## Calculus 1

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin.

50. ## Calculus 1

simplify the expression. cos(2 tan^-1 x)

51. ## Calculus 1

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a

52. ## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→∞ x^7e^−x^6 Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim

53. ## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (7x−sin 7x)/(7x−tan 7x)

54. ## Calculus 1

Use logarithmic differentiation to find the derivative of the following equation. y = (2x+1)^5(x^4−3)^6

55. ## Calculus

Differentiate the function. g(u) = sqrt(2)u+sqrt(7u) g'(u)=?

56. ## Math

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 26 ft, express the area A of the window as a function of the width x of the window.

57. ## calculus 2

Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

58. ## calculus 2

Sketch the region enclosed by the given curves. Find its area. y=7cos pi x, y=12x^2-3

59. ## calculus 2

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, y = x^3−8x+ 2

60. ## Calculus 1

Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ) = 4 cos θ + 2 sin^2 θ

61. ## Calculus 1

Find y' if y=ln(9x^2+7y^2).

62. ## Calc 1

True or False. Explain. The graph of any function can have at most two horizontal asymptotes.

63. ## Calc 1

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin.

64. ## Calc 1

A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for

65. ## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0+ (sinx ln2x)

66. ## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→3 (x^2+3x−18)/(x−3)

67. ## Calculus 1

Water is leaking out of an inverted conical tank at a rate of 12,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of

68. ## Calculus 1

Use logarithmic differentiation to find the derivative of the function. y = x^(8cosx)

69. ## History

A cause not widely championed by Progressives was: Select one: a. regulating industry b. women's suffrage c. prohibiting alcohol d. equal rights for blacks I think c or d

70. ## History

At times, the Populists made remarkable efforts to unite black and white small farmers on a common political and economic program. Select one: True False I think true

71. ## History

The Supreme Court's decision in Plessy v. Furguson (1896): Select one: a. Was a unanimous decision b. Sanctioned racial segregation c. Voided (undid) the Thirteenth Amendment to the Consititution d. Limited the hours that women could legally work. I think

72. ## History

By the 1890s, through a network of women's clubs, temperance associations, and social reform organizations, women were exerting a growing influence on public affairs. True False I think true

73. ## calc 3

Find a unit vector that is parallel to the line tangent to the parabola y = x^2 at the point (4, 16).

74. ## Calc 2

Determine whether the series is convergent or divergent series symbol n=1 to infinity (n^2/(e^(3n))

75. ## Calc 2

Find the solution of the differential equation that satisfies the given initial condition. du/dt= (2t + sec^2(t))/(2u), u(0) = −4

76. ## calculus 2

The birth rate of a population is b(t) = 2000e^0.022t people per year and the death rate is d(t)= 1460e^0.017t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)

77. ## Calculus 1

Consider the function below. f(x)= (x^2)/((x-4)^2) Find the interval where the function is concave up. (Enter your answer using interval notation.) Find the intervals where the function is concave down. (Enter your answers using interval notation.) For

78. ## Calculus 1

Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.

79. ## Calculus 1-Optimization

A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used. sides of base cm height cm

80. ## Calculus 1

The curve with the equation y^2=5x^4-x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (-1,2).

81. ## Calc 1

If a function is continuous, then it is differentiable.

82. ## Calc1

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = sec^2 x, 0 ≤ x ≤ π/4

83. ## Philosophy

Do you believe abortion is morally permissible? Why or why not?

84. ## Calc 1

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=x^3+x-4 [0,2]

85. ## Calc 1

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (e^9x−1−9x)/(x^2)

86. ## History

Can anybody help me figure out what is progressive and considered progressivism in this video. American Experience TR, The Story of Theodore Roosevelt Part4 4 PBS Documentary

87. ## Calculus 1

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+4y^2−x)^2 (0, 0.25) (cardioid)

88. ## Philosophy

If you were to sum up the Stanford Prison and Milgram experiments in a phrase that encapsulates the findings of the experiments, which of the following would it be? Select one: a. "Only the strong survive." b. "Evil acts are performed by inherently evil

89. ## History

Theodore Roosevelt's taking of the Panama Canal Zone is an example of: Select one: a. his ability to "speak softly". b. his belief in intervening with the sole purpose to "uplift" the peoples of Central America. c. his belief in "liberal internationalism"

90. ## Calculus 1

Find an equation of the tangent line to the curve y = 6/(1+e^−x)at the point (0,3).

91. ## History

Compare and contrast the ideas and policies, domestic and foreign, of Roosevelt, Taft and Wilson. Where can I find information that compares their domestic policies? -My Answer so far: Roosevelt, Taft, and Wilson were all progressive reformers, but their

92. ## Calculus

Find an equation of the normal line to the parabola y=x^2−8x+1 that is parallel to the line x−6y =7.

93. ## Math

Find an expression for the function whose graph is the given curve. The top half of the circle x^2+(y-4)^2=4

94. ## calc 3

Find the exact length of the curve. x = 1 + 9^t2, y = 7 + 6^t3, 0 ≤ t ≤ 2

95. ## Law and ethics

On Sunday I was rear ended while waiting in line at a McDonald’s drive thru. I got out right after it happened while still in line to see if I could see any damages because I did hear and feel the impact. The person who hit me yelled at me that there was

96. ## Matrices

Solve the system using matrices. Show all the row operations that you use. 3x-9y=30 2x+5y= -2

97. ## calculus 2

Use Euler's method with a step size of 0.2 to estimate y(1), where y(x) is the solution of the initial value problem y' = 6x+y^2, y(0)=0. Round your final answer to 4 places, but keep more places on the intermediate steps for accuracy.

98. ## calc 2

Find the orthogonal trajectories for the family of curves y=(kx)^6.

99. ## Calc 2

Find the center of mass for the region bound by y= -2x+6, x=0, and y=0