ADVANCED MATH
Suppose that a+ib is a Gaussian integer and n is a rational integer. Show that n and a+ib are relatively prime if and only if n and b+ai are relatively prime.
LITERATURE
IB character traits
ENGINEERING
Find the fixed points. w=(a+ib)z²
DIFFERENTIAL EQUATIONS
5^-2+3pii in the form a +ib
CALCULUS
In a survey of 400 music downloads, 45 were country music, 16 were religious music, and 16 were jazz, while the remainder were other genres. Calculate the following relative frequencies: a. That a music download was jazz. b. That a music download was either religious music or jazz. c. That a music download was not country music.
COLLEGE ALGEBRA
Suppose that a box containing music CDs has 4 with country music, 6 with rock music, 3 with jazz music, and 7 with rap music. If one CD is selected at random from the box, determine the probability that a. The CD has rap music. b. The CD has jazz music. c. The CD does not have jazz music. d. The CD has classical music.
LINEAR ALGEBRA
(a) Show that every complex matrix Z can be written uniquely in the form Z=A+iB, where A and B are real matrices. (b) If Z=A+iB as in (a), show that Z is hermitian if and only if A is symmetric, and B is skew-symmetric (that is, $$ B^T=-B $$ ).
ENGINEERING
Express $e^{z}$ in the form a + ib. $z=5 i$
ENGINEERING
Find a parametric representation |z+a+ib|=4, clockwise
ENGINEERING
Express $e^{z}$ in the form a + ib. $z=-0.23-i$
CALCULUS
In a survey of 500 music downloads, 160 were rock music, 55 were hip-hop, and 20 were classical, while the remainder were other genres. Calculate the following relative frequencies: a. That a music download was rock music. b. That a music download was either classical music or hip-hop. c. That a music download was not rock music.
ALGEBRA
6 Ib of peanuts which cost $1/lb were combined with 3 Ib of spices which cost$4/lb. Find the cost per lb of the mixture.
COLLEGE ALGEBRA
Knowing that the camping/hiking season has arrived, a nutrition outlet is mixing GORP (Good Old Raisins and Peanuts) for the anticipated customers. How many pounds of peanuts worth $1.29/Ib should be mixed with 50 Ib of deluxe raisins worth$1.89/Ib to obtain a mix that will sell for $1.49/lb?
ENGINEERING
Express $e^{z}$ in the form a + ib. $z=-0.3+0.5 i$
ENGINEERING
Express the given quantity in the form $a + ib$. $\tan (i)$
ENGINEERING
Express $e^{z}$ in the form a + ib. $z=1.5+2 i$
CALCULUS
Fill in the blanks using the named events. 95% of all music composers can read music (M), whereas 99% of all classical music composers (C) can read music. P(___)=___; P(___ | ___)=___
ENGINEERING
Express the given quantity in the form $a + ib$. $\sec (\pi+i)$
ENGINEERING
Express the given quantity in the form $a + ib$. $\csc (1+i)$
CALCULUS
In 2007, total revenues from sales of recorded rock, religious, and classical music amounted to $4 billion. Religious music brought in twice as much as classical music, and rock music brought in$3 billion more than religious music. How much revenue was earned in each of the three categories of recorded music?
LITERATURE
Music Connection: If you were setting these poems to music, what type of music would you choose for each? Explain.
INTERNATIONAL BACCALAUREATE
Write the arguments in symbols and then test its validity. Isaac will pass the Mathematics test or drop out of the IB diploma. He does not drop out of the IB diploma. Therefore he passed the Mathematics test.
QUESTION
Sharing music online (5.2, 5.3). A sample survey reports that 29% of Internet users download music files online, 21% share music files from their computers, and 12% both download and share music. Given that an Internet user downloads music files online, what is the probability that this person also shares music files?
PHYSICS
(a) Research the different types of supernova and explain why Types Ia, Ib, and Ic are labeled differently. (b) Why do Types Ib, Ic, and II have more in common with each other than with Type Ia?
ADVANCED MATH
Let $z=a+ib$. Determine $\text{Re}(z^2)$ and $\text{Im}(z^2)$.