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Solve:(i)(dy/dx-1)^2(d^2y/dx^2+1)^2y=sin^2(x/2)+e^x+x
(ii)2x^2y(d2y/dx2)+4y^2=x^2(dy/dx)^2+2xy(dy/dx)
(ii)2x^2y(d2y/dx2)+4y^2=x^2(dy/dx)^2+2xy(dy/dx)
The diagram shows a sector of a circle of radius r cm containing angle Ө radians. The area of the sector is Acm2 and the perimeter of the sector is 50 cm.
a. Find Ө in terms of r.
b. Show that A = 25r – r2
a. Find Ө in terms of r.
b. Show that A = 25r – r2
A manufacturer of guitar amplifiers markets one of its models, Vagabond, at a power rating of 45 watts. GuitarGod magazine suspects that this rating is inaccurate for this year's model of the amp. In a random sample of 32 units of this year's version of the Vagabond the mean output power is 42 watts, with a standard deviation of 8 watts.
Assuming a confidence level of 95%, which of the following statements do these data support?
A. This year's Vagabond's output power is 45 watts.
B. This year's Vagabond's output power is 42 watts.
C. This year's Vagabond's output power is not 45.
D. None of the above
Assuming a confidence level of 95%, which of the following statements do these data support?
A. This year's Vagabond's output power is 45 watts.
B. This year's Vagabond's output power is 42 watts.
C. This year's Vagabond's output power is not 45.
D. None of the above
Table 1
Male Female Male Female Male
A A A A E
C E C C A
A A C B E
A C A D D
A A B A A
C D E B B
D A D D A
D A
A survey was administered to a random sample of 37 students and recorded in Table 1:
A – Ironic dance B – Pro dance C – Sway dance
D – Dad-dance E – Twerk dance
Prepare a summary table for dance preferences. Calculate percentage and sectarian angle of each type of dance preferred. Represent these figures on a pie chart. Draw a bar chart to represent the dance preferences.
Male Female Male Female Male
A A A A E
C E C C A
A A C B E
A C A D D
A A B A A
C D E B B
D A D D A
D A
A survey was administered to a random sample of 37 students and recorded in Table 1:
A – Ironic dance B – Pro dance C – Sway dance
D – Dad-dance E – Twerk dance
Prepare a summary table for dance preferences. Calculate percentage and sectarian angle of each type of dance preferred. Represent these figures on a pie chart. Draw a bar chart to represent the dance preferences.
A bag contains 3 black balls and 5 white balls. Samuel picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag. Construct a probability tree of the problem and calculate the probability that Samuel picks two black balls and a black ball in his second draw.
Table 1
18 15 17 22 12 20
19 15 20 25 16 13
Calculate the mean, the median, the mode, the standard deviation, the Pearson coefficient of skewness of assembling time.
18 15 17 22 12 20
19 15 20 25 16 13
Calculate the mean, the median, the mode, the standard deviation, the Pearson coefficient of skewness of assembling time.
The angle of depression is 20° for a yacht and the barge is 12° 30'. Are they less than 300' apart?
Consider the Cantor-Lebesgue function F : C → R, where C is the Cantor set.
a) Show that F is continuous and actually F can be extended to the whole R so that it is continuous (to do
this, note that if (a, b) is an interval from the complement of C, then F(a) = F(b)).
b) Using (a), show that if f : R → R is continuous function and A is a measurable subset of R, then f(A) may
not be measurable.
c) Show that the inverse image of a measurable set under a continuous function is not always measurable
(compare with Problem 2).
Hint: For (c), notice that F is increasing, thus the function F(x) +x is strictly increasing (and continuous).
Therefore, F(x) + x has a continuous inverse...
a) Show that F is continuous and actually F can be extended to the whole R so that it is continuous (to do
this, note that if (a, b) is an interval from the complement of C, then F(a) = F(b)).
b) Using (a), show that if f : R → R is continuous function and A is a measurable subset of R, then f(A) may
not be measurable.
c) Show that the inverse image of a measurable set under a continuous function is not always measurable
(compare with Problem 2).
Hint: For (c), notice that F is increasing, thus the function F(x) +x is strictly increasing (and continuous).
Therefore, F(x) + x has a continuous inverse...
In 2013, there were 19,767 Starbucks stores world- wide. This is approximately 4551% more stores than in 1994. How many Starbucks stores were there in 1994 ? (Round to the nearest whole number.)
Three of the best-selling albums of 2013 were Justin Timberlake's The 20120 Experience, Eminem's The Marshall Mathers LP2, and Imagine Dragons' Night Visions. Eminem's album sold 0.33 million more copies than Imagine Dragons'. The number of Justin Timberlake albums sold was 0.37 million less than twice the number of Imagine Dragons' sales. The three recording artists sold a total of 5.56 million albums. How many albums did each artist sell?
