# Pre- Calculus

21,321 results, page 11

### Pre-Calculus

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression 2lnx - 6lny + 1/3ln e^12 as a simplified logarithm. Is this 2lnx - 6lny + 4, or can it be simplified further?

### Pre-calculus

Derive an identity that transforms sin(α+β+γ) into a sum of products of sines and/or cosines of the individual numbers α, β, γ.

### pre calculus

write the slope-intercept form of an equation for a line that passes through A(3,4)and is perpendicular to the line that passes through e(4,1) and F(-2,4)

### Pre-Calculus

Verify: 1/(1-sintheta) * 1/(1+sintheta) = sec^2theta sec^2theta is the answer, it would be great if someone can do the steps for me. thank you.

### Pre-Calculus

Composition of Functions If f(x) = 2x+1 find A. f o f(x) f(f(x)) = f(2x+1) f(2x+1) = 2(2x+1) f(f(x)) = 4x +2 B. f o f o f o f(x) ^ I don't get how to solve this one C. f o f o f o f o f ...o f(x) n functions of f ^ I also don't get how to solve this one given f(x) = ax+b and g...

### pre-calculus

form a polynomial f(x) with real coefficients having the given degree and zeros. degree 5; zeros -7; -i;-9+i enter the polynomial. f(x)=a(?)

### Math

Is IB Math Studies the same as Pre-Calculus? I heard that IB Math Studies is for students who have a low background in math. Is that right?

### math: pre-calculus

Let u=ln and v=ln y. Write the expression ln(5√(x3√y)) in terms of u and v. for example, lnx^3y = lnx^3+lny = 3lnx+lny = 3u+v

### pre calculus

In the rectangular coordinate system, each point (x, y) has a unique representation. Explain why this is not true for a point (r, Θ) in the polar coordinate system.

### Pre-Calculus

Verify the identity. cos x - sec x = -sin x tan x So far I have applied a reciprocal identity =cos x - 1/cos x I know I must combine using the least common denominator but I don't know how it would be written.

### Pre-Calc

I'm stuck on a pre-calc problem. I need to find y as a function of x, where the constant c is a positive number for In(y-1)+In(y+1)= -x+c express your question as ln[(y-1)(y+1)] = -x+c change that to exponential form e^(-x+c) = (y-1)(y+1) e^(-x+c) = y^2 - 1 y^2 = e^(-x+c) + 1 ...

### Pre-Calculus

How do you factor this completly 7x*(4x-5)^3+(4x-5)^4 I am confused by the different power of exponets and the 7x in front Can you please help me? 7x*(4x-5)^3+(4x-5)^4 factor out the common term: (4x-5)^3 * (7x+4x-5) Then simplify the second term. what general equation will ...

### Pre-Calculus

One model for the population P of bacteria in a sample after t days is given by P(t) = 1000 - 19.75t + 20t² - 1/3t³ Whoops accidently hit post question a)what type of function is P(t) b)when is the bacteria population increasing c) When is it decreasing

### Pre calculus

bit strings of a fixed length are needed to form a code. what is the minimum length of the string is one string is needed to represent each letter of the alphabet and each decimal digit?

### College Pre Calculus

anne and nancy use a metal alloy that is 19.3% copper to make jewelry. how many ounces of a 19% alloy must be mixed with a 20% alloy to form 110 ounces of the desired alloy?

### Pre-calculus

The terminal side of theta lies on a given line in the specified quadrant. Find the values of the six trigonometric functions of theta by finding a point on the line. y= -3/2x in quadrant 4

### Pre-calculus

The terminal side of theta lies on a given line in the specified quadrant. Find the values of the six trigonometric functions of theta by finding a point on the line. y= -3/2x in quadrant 4

### Pre-calculus

The terminal side of theta lies on a given line in the specified quadrant. Find the values of the six trigonometric functions of theta by finding a point on the line. y= -3/2x in quadrant 4

### Pre calculus

A window is made up of a circle embedded in a rectangle so that the diameter of the circle is a side of the rectangle. Find the demensions that will admit the most light if the perimeter ofthe window is 44 meters.

### pre- calculus

consider the collection of all rectangles that have lengths 2in. less than twice their widths. find the possible widths(in inches) of these rectangles if their perimeters are less than 200 in

### Pre-Calculus

A rectangular window is topped with a semicircle. The height of the rectangular part is 1 more than 3 times its width, w meters. Which function represents the total area, A, of the window in terms of the width?

### Pre Calculus

I have tried and tried to understand double angle identities but it just won't stick. if sin x = -0.6 and 180 (degrees) < x < 270 (degrees), find the exact value of sin 2x

### Math (pre-calculus)

Hi! I have a question! I forgot how to do these two problems, and I need some help in solving them! Thanks so much! 1.) Find the first 5 terms of the sequence given by a1=2, an=3an-1 -1. (It's: a sub 1 =2, a sub n= 3a sub n-1 -1) Does that make sense? If not, that's ok. I'll ...

### Pre-Calculus-Trig

A lighthouse keeper 100 feet above the water sees a boat sailing in a straight line directly toward her. As watches, the angle of depression to the boat changes from 25 degrees to 40. How far has the boat traveled during this time?

### Pre-Calculus ( Trigonometry)

The point P(k, 24) is 25 units from the origin. If P lies on the terminal arm of an angle, theta, in standard position, 0 < theta < 360,determine the measure of theta. Unsure how to go on from here. I'd appreciate if someone can guide me through the first few steps Thank...

### Math (pre-calculus)

Hey! I have a domain and range question! I don't remember how to get these, can you help? How do you calculate the domain and range of these? What's the domain and range of each? a. f(x)= 1/x=3 b. g(x)= [square root of] (x+6) c. h(x)= x^3+2x+5 Thanks for help!:)

### Pre-calculus

Find the interquartile range and the semi-interquartile range of the following data: 42 51 53 53 59 61 75 100 mean=61.75=62 median=56 mode=53 interquartile range=87.5-52=35.5?

### math: pre-calculus

Let u=lnx and v=lny. Write the expression ln3√x/2y in terms of u and v. For example, lnx^3y=lnx^3+lny=3lnx +lny= 3u+v.

### pre calculus

The base of an Isosceles triangle is half as long as the two equal sides. Write the area of the triangle as a function of the length of the base. the answer is: A=a^2times the square root of 15 ------------------------------ 4 How did they get this answer? Thanks!

### pre-calculus

A man who can row in still water at 3 mph heads directly across a river flowing at 7 mph. At what angle to the line on which he is heading does he drift downstream and at what speed does he drift downstream?

### Pre-Calculus

A salesman's monthly commission is 15% on all sales over $12000. If his goal is to make a commission of at least $3000/month, what minimum monthly sales figures must he attain?

### Pre-Calculus

The angle of depression from the top of a 75 ft. lighthouse to a ship out in the ocean is 40*. How far out is the ship from the lighthouse? I've been stuck on this problem for an hour, I know the answer but don't know how to set it up/enter it in a calculator.

### pre-calculus math

A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i; degree 3

### pre-calculus

the function f(x)=4/x-7 is one to one a. find the inverse of f b. graph f, f^-1, and y=x on the same set of axes find the inverse of f f^-1(x)=

### pre calculus

A airplane is 145 miles North and 85 miles west of an airport. What is the compass direction from the airport to the airplane?

### pre-calculus 11

-x/(x-3) + 2x/(x+2) (x-1) x (x-2) (x+2)/(x-3)(x-3) my question is should i multiply first and then do the adding or subtracting through a LCD or should i do the adding first?

### pre calculus

A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x < 2

### pre calculus

A small fast food restaurant invests $4000 to produce a new food item that will sell for $3.50. Each item can be produced for $2.15. How many items must be sold in order to break even? Round to the nearest item.

### pre alg

How do u find the GCF with exponets in a 7th gr. pre alg. class?

### pre-Algebra

Sorry, struggling through pre-Algebra .. :-( .. How do i figure out 5x = -20 ?

### Pre Calculus 12

permuations an orchestra has 2 violinsts, 2 cellisst, and 4 harpists. Assume that the players of each instrument have to sit together, but they can sit in their own group. In how many ways can the conductor seat the members of the orchestra in a line? I just went 4*3*2 and got...

### pre-calculus 11

abs x^2/2 -1 =x+3 solve algebraically so if I divide through by 2 i get x^2 -2= 2x+3 simplifying x^2-2x-5 =0 solve by quadratic formula to get =3.449 and -0.445 both of which are extraneous roots if I take negative then I get -x^2 +2=2x+6 simplify to x^2 +2x +4 if taking using...

### Pre-Calculus

Sue is building a triangle out of sticks. The length of the first side is "a" and the second side is of length "b". The length of the third side must be between 8 and 26 units. Find the product of "a" and "b".

### Pre Calculus

Identify the x-intercept of the function f(x) = 2 ln(x-3). a. x=3 b. x=0 c. x=2 d. x=4 e. The function has no x-intercept

### pre-calculus

sin theta = 1/4, find sin (-theta)

### Pre-Calculus-check answers

Find the sixth term in the geometric sequence: sqrt3y^3, -3y^5, 3sqrt3y^7 Answer: -27y^13 2) Find three geometric means between -sqrt2 and -4sqrt2. Answer: -2, 2sqrt2, -4 Thanks

### Pre calculus

Find all roots f(x)- x^3+2x^2-15x+30 Factor f(x) completely. I can't find any roots and always get a remainder with 1, -1, 2, -2 What do you do if you cannot find a root?? Using Calc button on ti84 I got X= -5.619 Y=1.4E-11 Still can't find zeros...

### Pre-Calculus

a jet, in calm air conditions, travel with velocity vector (389, 389). the wind velocity (in mph) at the plane's cruising altitude is given by (0, 50). how fast is the plane's true speed

### pre-calculus

R(x)=x^2+x-6 ________ x-3 1. find the domain and y-intercepts 2. find the x-intercepts 3. find the real solution of the equation 4. find the horizontal or oblique asymptotes 5. find the x-axis 6. plot the points

### Pre-Calculus

Solve. Express your answer as exact roots. (s+6)^2 = 3/4 Sq root (s+6)^2 = +-sq root 3/4 (s+6) = sq root 3/ 2 s = -6 +- sq root 3 ----------------- 2 (The answer according to the textbook is (-12 +- sq root 3)/2. What error have I made?) Thank you

### PRE - CALCULUS

Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π A. x2 - y2 = 6; -6 ≤ x ≤ 6 B. x2 - y2 = 36; -6 ≤ x ≤ 6 C. x2 + y2 = 6; -6 ≤ x &#...

### Pre-Calculus

One walker was sponsored $100 plus $5 for the first kilometre, $10 for the second kilometre, $15 for the third kilometre, and so on. How far would this walker need to walk to earn $150? (I know it is 4 km, but I can't figure out how to write the general term.)

### college pre calculus

A kite frame is to be made from 6 pieces of wood. The four border pieces have been cut 5 and 12. The long center piece is 13. what should the length of the cross pieces be in order to maximize the area of the kite.

### Pre-Calculus

Find the equation in standard form for the hyperbola that satisfies the given conditions: transverse axis has endpoints (5,3) and (-7, 3) and conjugate axis has a length of 10. I found the distance of the transverse axis to be 12. For the formula, I have a=6 b=5. I just need ...

### Pre-Calculus

determine the projection of u = 1.6 vector i + 3.3 vector j in the vector v = -2.1 vector i - 0.5 vector j direction

### Pre Calculus

Determine the quadrant in which an angle, θ, lies if θ = 8π / 7 a. 3rd quadrant b. 1st quadrant c. 4th quadrant d. 2nd quadrant

### Pre Calculus

Determine the quadrant in which an angle, θ, lies if θ = 5.40 radians. a. 4th quadrant b. 3rd quadrant c. 2nd quadrant d. 1st quadrant

### Pre Calculus

Determine the quadrant in which an angle, θ, lies if θ = 5.40 radians. a. 4th quadrant b. 3rd quadrant c. 2nd quadrant d. 1st quadrant

### Pre-Calculus

Two sides of a triangle are x units and y units in length. The angle between them is theta. Prove that the area of the triangle is 1/2xysin(theta). I'm not sure how to do this question, I tried drawing a picture but I'm still not understanding it.

### Pre-Calculus

Two sides of a triangle are x units and y units in length. The angle between them is theta. Prove that the area of the triangle is 1/2xysin(theta). I'm not sure how to do this question, I tried drawing a picture but I'm still not understanding it.

### pre calculus

A box with a square base and no top is to be made from a square piece of carboard by cutting 5 in. squares from each corner and folding up the sides. The box is to hold 23805 in3. How big a piece of cardboard is needed?

### pre calculus

Create systems of equations in two variables that have (a) no solution, (b) one distinct solution, and (c) infinite solutions. Show that each system has the indicated number of solutions by using a graph or solving the system.

### pre calculus

Environmental Concerns: The spread of oil leaking from a tanker is in the shape of a circle. If the radius r (in feet) of the spread after t hours is r(t) = 200sqrt t, find the area A of the oil slick as a function of the time t. I don't get this at all. could someone please ...

### Pre-Calculus

Jake serves a volleyball with an initial velocity of 32 feet per second from 4.5 feet above the ground at an angle 0f 35 degrees. a) Write parametric equations to model the situation. b) How far will the ball travel( if it hits the ground)show work

### Pre-Calculus

Simplify the rational expression and then add or subtract. Express answers in simplest form and identify all non-permissible values. (The non-permissible value is not the issue. It is the simplification) 3x + 15/x^2-25 + 4x^2 -1/ 2x^2 + 9x -5 3(x+5)/(x+5)(x-5) + 4x^2 -1/ (x+5...

### Math (pre calculus)

The population of a certain town grows from 10,000 in 1982 to 35,000 in 1995. At this rate, in what year will the population reach 300,000? Tip* Population growth formula: P = P(subzero)multiplied by e^(k)(t)

### Pre-Calculus

If sin(theta)=15/17 and cos(beta)=(-5/13 (both theta and beta are in quadrant II) find tan(theta+beta)

### Pre-Calculus

Could someone check my answers? 25. 32^(2x-3)=2 Answer- x= 8/5 26. 9^(2x+1)=81 Answer- x= 1/2 27. 1/4=2^3x Answer- x= -2/3 28. 1/27=3^2x Answer- x= -3/2 29. 9^x=27 Answer- x= 3/2 30. 32^x=4 Answer- x= 2/5 31. 27^(x+1)=9 Answer- x= 1/2 32. 125^(x-2)=25 Answer- x= 7/2 33. 81^(x-...

### pre-calculus

A sphere is contained inside of a cube, tangent to all six faces. Find the surface area of the cube as a function of the radius of the sphere. The answer in the back of the book read:A=24r^2...How did they get this answer? Thanks for helping!

### pre-calculus

The suggested retail price for a new car is p dollars. The dealership advertises a 10% discount and a factory rebate of $1500. Write a function S in terms of p, representing the cost of the car after receiving the dealership discount.

### Pre-Calculus

How do I solve these equations? I need to create an equation given the characteristics? I have to be able to graph a parabola but first I need help solving this. 1.Focus (1.5,1); opens right; directrix x=0.5 2.Focus (1,4);opens down; contains (-3,1)

### Pre-calculus-check answers

Find the number of possible negative real zeros for f(x)=6+x^4+2x^2-5x^3-12. Answer: 0 2) Approximate the real zeros of f(x)=2x^4-3x^2-2 to the nearest tenth. Answer: no real roots

### Pre-Calculus-check answers

Find the number of possible negative real zeros for f(x)=6+x^4+2x^2-5x^3-12. Answer: 0 2) Approximate the real zeros of f(x)=2x^4-3x^2-2 to the nearest tenth. Answer: no real roots

### Pre-Calculus-check answers

Find the number of possible negative real zeros for f(x)=6+x^4+2x^2-5x^3-12. Answer: 0 2) Approximate the real zeros of f(x)=2x^4-3x^2-2 to the nearest tenth. Answer: no real roots

### Public High School Pre Calculus HH

Ok I do not know how to do this problem. I know that csc is simply sin^-1 sin (- pi/12) csc ( (37 pi)/12 ok now I know this also sin (- pi /12 ) = - sin ( pi/12) not really sure how that helps I don't know were to go from here ( - sin (pi/12) )/(sin ( (25 pi)/12 ) )

### Pre-Calculus

Find all solutions to the equation in the interval [0, 2pi) cos4x-cos2x=0 So,this is what i've done so far: cos4x-cos2x=0 cos2(2x)-cos2x (2cos^2(2x)-1)-(2cos^2(x)-1) No idea what to do next.

### Honors Pre-Calculus

The prompt says "Graph each function. Determine the interval[s] for which the function is increasing and the interval[s] for which the function is decreasing." The problems that are given in this prompt are: 1. y= x^3+3x^2-9x 2. f(x)=1/(x+1)-4 3. g(x)=(x^2+5)/(x-2) I need mega...

### Pre-Calculus

The equation H(t) = 30 + 24t - 6t^2 describes the height of a ball at any time t. What's the height of the ball after two seconds h = 30 + 24(2) + 6(2)^2 h = 30 + 48 -24 h = 54 units Therefore, the maximum height is 54 units

### Pre calculus

in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates. Thanks :)

### pre-calculus

given that c is the logarithm of x in base a, and d is the logarithm of x in base b, find the general statement that expresses the log of x in base ab, in terms of c and d. [*subscripts not included: a,b,ab] loga_x=c ; logb_x=d ...logab_x = [in terms of c and d]

### Pre calculus

From h a point A that is 10 meters abov level ground, the angle of elevation of the top a building is 42 degrees and the angle of depression of the base of the building is 8 degrees approximate the height of the building

### Pre-Calculus

If θ represents an angle such that sin2θ = tanθ - cos2θ, then sin θ - cosθ = A. -√2 B. 0 C. 1 D. 2√2 What equation can I use to solve this problem?

### Pre-Calculus

Laws of logarithms combine, write as a single logarithm Need help on this question please, Im stuck, don't know where to go abouts from here: I did it on paint and uploaded it onto this website because I don't know how to do the subscript numbers, so it probably wouldnt really...

### pre-calculus

Find the number of possible negative real zeros for f(x)=6+x^4+2x^2-5x^3-12. Answer: 0 2) Approximate the real zeros of f(x)=2x^4-3x^2-2 to the nearest tenth. Answer: no real roots

### Pre-calculus

Prove the following identities. 1. 1+cosx/1-cosx = secx + 1/secx -1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(x-y)= cos^2x - sin^2y

### Pre-calculus

Can somebody help me wit this? Find the range and the domain of: f(x)=(1/2)|x-2| The domain is all real numbers (x) from -infinity to infinity The range (of f(x)) is 0 to infinity, since it can never be negative. f(x) has a minimum value of zero when x=2.

### Pre-calculus-check answers

Use the Remainder Theorem to find the remainder of (x^3-5x^2+7x+3)/(x-2). State whether the binomial is a factor of the polynomial. Answer: Remainder = 1, not a factor 2) Determine the slant asympotte for f(x)=(x^2-5x-3)/x Answer: y=x+5

### Pre-Calculus

How do you find the polynomial funtion that best models data givn in a table for x and f(x). The only example in my testbook shows how to do it on a calculator but I cannot find any instructions with my calculator to tell me how to do it. The data for x=-5, -4,-3, -2, -1, 0, 1...

### Pre-Calculus

How do you find the polynomial funtion that best models data givn in a table for x and f(x). The only example in my testbook shows how to do it on a calculator but I cannot find any instructions with my calculator to tell me how to do it. The data for x=-5, -4,-3, -2, -1, 0, 1...

### pre calculus

A wire 10m long is cut into 2 pieces. one piece will be cut into a square the other piece will be shaped into a circle. Graph A= A(x) for what value of x is A smallest?

### pre calculus

use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers: f(x)=x^4+2x^3-7x^2-8x+12 I am totally lost, please help?

### Pre-Calculus

I am having trouble with several problems: 1) Find the coordinates of the center, foci, and the vertices, and the equations of the asymptotes of the graph of the equation (x+1)^2/2 - y^2/8 =1 2) Write the standard form of the equation of the circle that is tangent to x= -2 and...

### Pre-Calculus

I am having trouble with several problems: 1) Find the coordinates of the center, foci, and the vertices, and the equations of the asymptotes of the graph of the equation (x+1)^2/2 - y^2/8 =1 2) Write the standard form of the equation of the circle that is tangent to x= -2 and...

### pre-Calculus

The coffee starts out at 176 degrees, and cools off like this… Min Degrees 1 169 2 162 3 156 5 146 10 125 15 111 20 101 30 90 60 81 If he measured the coffee at 2 hours and 3 hours, what temperature would it be?

### pre-calculus

Could someone please help me with this problem? square root of (2x+1) -5 = 8 I think I take the 5 and add it to the 8 and then I have square root of (2x+1) = 13 then do I square both sides and end up with 2x+1 = 13^2 2x+1=169 2x+1-1=169-1 2x=168 x=84 am I even close on this?

### Pre Calculus

A motorboat travels 48 miles down a river in the same time it takes to travel 32 miles up the river. If the rate of the current is 4 miles per hour that is the rate of the boat still water?

### Pre-Calculus

A.Verify the identity. B.Determine if the identity is true for the given value of x. Explain. Sec(x) / tan(x) = tan(x) / [tan(x) – cos(x)],x = π I already solved A and I believe it's true; however, I need help with B.

### pre calculus

if the cost to to produce 100 cups of coffee is 11.02, while the cost to produce 400 cups is 401.12, what is the linear cost function?

### pre calculus

A bag contains 4 blue marbles, 2 black marbles, and 3 red marbles. If a marble is randomly drawn from the bag, what is probability that it is not black? 1/2 2/9 5/9 7/9 14/19