TayB

Most popular questions and responses by TayB
1. 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

2. 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

3. Calc 1

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

4. Math

lim x→−12 sqrt(x^2 +25 −13)/x+12

5. 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

6. 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.

7. 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

8. 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

9. 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

10. 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

11. 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

12. Calculus 1

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

13. 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)

14. 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)}=?

15. 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.

16. 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.)

17. 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

18. History

The 1964 Civil Rights Act did all of the following except: a. ban discrimination on the grounds of sex b. prohibit racial discrimination in employment c. prohibit racial discrimination in privately owned businesses that provided public accommodations

19. 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

20. 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.

21. Calculus 1

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 7 ft

22. Calculus 1

The rate (in mg carbon/m^3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = (120I)/(I^2 + I + 4) where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a

23. 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).

24. Calc 1

Use l'Hospital's Rule to find the exact value of the limit. lim x→∞ (1+4/x)^x

25. 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

26. 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

27. 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

28. 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?

29. Calculus 1

Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) (x − 9)^2 =ln x

30. 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

31. Calc 1

Related Rates: Two cars approach the intersection of two highways. The one coming from the west is traveling at 60mph and the one traveling from north is traveling at 50 mph. At what rate is the distance between the cars changing when the car from the west

32. 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)}=?

33. 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.

34. 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

35. Calculus 1

Related Rates: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the

36. 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=

37. 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.

38. 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

39. Calc 1

Of the infinitely many lines that are tangent to the curve y = −6 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.

40. Philosophy

According to James Rachels, your personal identity in the numerical sense is: Select one: a. Your personality b. Your physical appearance c. Your moral beliefs d. Your personal identity in the literal sense e. Your family background I think maybe d or c

41. 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.)

42. 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

43. 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 = x^−3, 1 ≤ x ≤ 5

44. Calc 1

Of the infinitely many lines that are tangent to the curve y = −6 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.

45. 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.

46. Calculus 1

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

47. Calc 1

A rectangular storage container with an open top is to have a volume of 10 m3. The length of the base is twice the width. Material for the base is thicker and costs \$13 per square meter and the material for the sides costs \$10 per square meter. Find the

48. 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)

49. calculus 2

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

50. 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

51. Philosophy

According to Rachels, which of the following supports the truth of determinism? Select one: a. Studies that show that social conditions influence behavior b. Discovery of genetics c. Experiments in psychology such as the Milgram and Stanford Prison

52. 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

53. 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.

54. Calculus 1

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 32 ft, express the area A of the window as a function of the width x of the window.

55. 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)

56. 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.

57. 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

58. 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.

59. 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

60. 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

61. Calc 1

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

62. 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

63. 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.

64. calc 3

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

65. 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

66. 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^4/5(x − 1)^2

67. 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"

68. philosopy

Do you agree with Bruce Hinrichs (in Kessler) that there is no good reason for people to feel "threatened or dehumanized" if scientific studies showed that the human mind is nothing more than the physical brain - and, more generally, that humans are

69. 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

70. 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

71. Philosophy

According to James Rachels, personal identity in the qualitative sense refers mainly to: Select one: a. Important parts of your personality b. Parfit's split brain theory c. Family background d. Hume's bundle theory e. All of the listed I think e or a

72. 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 = cube root(x) , 0 ≤ x ≤ 27

73. Calc 1

A rectangular garden is to be enclosed by a fence and divided into 5 regions as shown below. Find the values of L and W for which the total area is as large as possible assuming that only 120 ft. of fencing is available.

74. 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

75. 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]

76. 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

77. History

1.What is popular culture? 2.How was post WWII popular culture affected by the Cold War? Did the Cold War “narrow” postwar popular culture and/or “distort and enfeeble” cultural expression? If so, how and in what ways?

78. History

The Progressive movement primarily drew its strength from: Select one: a. big business b. farmers c. middle class reformers d. military leaders e. socialists I think a. If not a then I think c

79. 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

80. math

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

81. 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.

82. 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,

83. Calculus 1

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 16 cos t + 8 sin 2t, [0, π/2]

84. Calculus 1

Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) 7/x = 1 + x^3

85. Calculus 1

Related Rates: 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

86. english or philosophy- came up with it myself

Those who are happy (I thought) who have their minds fixed on some object other than their own happiness; on the happiness of others, on the improvement of mankind, even on some art or pursuit, followed not as a means, but as itself as an ideal end. Aiming

87. Calc 1

The acceleration function (in m/s^2) and the initial velocity are given for a particle moving along a line. a(t) = t + 6, v(0) = 4, 0 ≤ t ≤ 11 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval

88. 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

89. Calculus 1

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

90. History

During the 1930s New Deal, African-Americans: a. worked in segregated CCC camps b. were mostly excluded from Social Security benefits c. were discriminated against by the Federal Housing Administration d. All of the above *I think D for this. What ended

91. 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)

92. 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

93. Philosophy

Based on your understanding of the different theories of personal identity, which of the following philosophers is most likely to have said: "The mind is a kind of theatre, where several perceptions successively make their appearance; pass, re-pass, glide

94. Philosophy

Rachels's Prince and Cobbler story presents a counterexample to the Same-Body Theory of personal identity. Select one: True False I think true

95. Philosophy

Which of the following is a direct objection to the Same-Body Theory of personal identity? Select one: a. Parfit's split brain theory b. Hume's bundle theory c. Causal determinism d. Locke's prince and the cobbler story e. Compatibilism I think d or a?

96. calc 3

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

97. 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

98. 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.

99. Calculus 1

Related Rates: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.