### Writing trigonometric functions as algebraic expressions

Write cos(arccosx + arctany) as an algebraic expression in x and y.

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Write cos(arccosx + arctany) as an algebraic expression in x and y.

Write sec(arcsinx) as an algebraic expression in x.

Solve the open sentence. If there are no solutions or if it is true for all real numbers then indicate so. x + 11 < -1 or -1/2x < -4

(a) Let F = { (matrix with first row; a 0, second row is 0 a) : a is an element of R Show that F is a field and that F ~= R (b) Give the definition of a cyclic group Prove that every subgroup H of a cyclic group G =<a> is itself cyclic

Pretend the paper is 1/1000 of an inch thick and suppose we could fold the paper 50 times. How many miles tall would it stand?

Problems related to exponential and Logarithmic Functions

If x times 5 gives the same result as x less than 5, what is the value of x? (A)5 (B)6 (C)4/5 (D)5/6 (E) -5/4

The number of bacteria N in a culture is given by the model N=250e^kt, where t is the time in hours, with t=0, corresponding to the time when N=250. When t=10, there are 280 bacteria. How long does it take the population to double in size? To triple in size?

Determine the price index for a product that sold for $8.99 in 1999, compared to $6.99 in 1996. a. 77.75 b. 122.25 c. 128.61 d. 177.75

A manufacturer reports the production of 120,000 units in the third quarter of the year. This is an increase of 15,000 units over production in the second quarter. What was the rate of increase for the period? a. 11.11% b. 12.5% c. 14.29% d. 15%

A jetliner has completed 225 miles of a 3000-mile flight. At an airspeed of 475 mi/h, how long will it take the jetliner to reach its destination?

A state college has a total freshman enrollment of 2,200 students, of whom 42% are male. If the remainder of the total school enrolment of 6,800 students is divided evenly between male and female, determine the total male enrollment in the school.

A start-up firm's sales increased by 350% from its first year of operation to its third year total of $1.68 million. What were its total sales in its first year of operation?

A car has a tank that holds 12 3/8 gallons of gasoline. Mr. Brown fills his tank and drives along the highway until he runs out of gas. If his car averages 19 2/5 mpg, how far has he traveled?

Four partners, A,B,C,D, invest in the ratio of 5:3:3:1 in their firm. If partner A invests $20,000, what is the total invested?

A firm's sales for the month total $30,000. If the ratio of cash to credit sales is 2:3, cash sales total = ?

7:x = 9:27; x = ?

Pick a number from 1 to 9 (0<x<10). Multiply it by 2. Then add 3 to the result. Now multiply this number by 50, then add 1853 and subtract the year of you birth. You now should have a 3 digit number. The first digit is the number you picked above, and the last 2 digits are your age after your birthday this year (2003). How is t

Solve for t: 1.) 7*(4^t)=9 2.) 2^(t+1)=5^(t-3)

Square root of 100 plus the square root of 200 plus the square root of 300 multiplied by the square root of 400 equals ?

-4x+3=0 What are the roots?

Solve for X:LOG2X=8 Write as a single logarithm:5LNX-1N(X+1)

This is a day to day problem which can be taken mathematically: There are 23 school buses each carrying 41 kids and teachers on a picnic to the Niagara Falls. How many total number of people are going in this trip? Mathematically, the problem is 41 X 23 = ?

Q. Three whole numbers, greater then zero can be used to form a trio. example: (1,2,2) is a trio whose sum is 1+2+2=5 And (2,1,2) is a different trio whose sum is also 5 How many trios can you find with a sum of 5?

The equations of two lines are 4x-5y = -15 and y = 4/5x -6 Which of the following describes their point of intersection? A) (5,-2) B) (-5,1) C) (10,-5) D) (No intersection)

Factor the following: a) 3y^2-3 b) 25-16x^2y^2 c) (x+y)^2-z^2 d) (x-3)^2-9 e) t^2-2t-3

1)We wish to measure a wavefront u(x,y) on a 3X3 grid (see the attached file). The sensor how ever provides us only with differences between grid points. There is sensor noise, so the difference measurements may not be consistent. Number the grid points linearly and set up a set of linear equations (matrix form) relating the

Solve, find the solution set, solve for the real values - see attachment Solve for x: x + 1 - x > 1 2 5 a. { x _ x > 5 } 3 b. { x _ x > 3 } c. { x _ x > - 4 } 3 d. { x _ -2 < x < 5 } Find the solution set for x = 2 + __1___ 1 + x

Use elementary row operations to write the matrix in echelon form.

Lnx+ln(x+2)=4 3^x=45 x=log17 96 I did not know how to put the 17 lower than the log lnx for x=e^x f(6) for x^2+3x-2/x^2-6x=f(x)