Pre Calculus
21,880 results, page 13

PreCalculus
Could someone check my answers? 25. 32^(2x3)=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^(x2)=25 Answer x= 7/2 33. 81^(x... 
math: precalculus
The Department of Commerce estimated that there were 53 million internet users in the country in 1999 and 90 million in 2002. Find an exponential function that the models the number of Internet users in year x, with x=0 corresponding to 1999. 
PreCalculus
An open box is to be made from a piece of cardboard 11 in by 17 in, by cutting out a square of length x from each corner and turning up the sides. Express the volume V of the box as a function of the length x of the side of the square cur from each corner. 
Precalculus
a triangular shelf is to be placed in a curio cabinet whose sides meet at an angle of 105 degrees. If the edges of the shelf along the sides measures 56 centimeters and 65 centimeters, how long is the outside edge of the shelf? Round to the nearest tenth. Thanks for any help... 
Pre Calculus
The burial cloth of an Egyptian mummy is estimated to contain 56% of the carbon14 it contained originally. How long ago was the mummy buried? (the halflife of carbon14 is 5730). Please round the answer to the nearest tenth. I have figured that: m(t) = Moe(ln2/5730) is a ... 
PreCalculus
The exponential function y(x)=Ce^ax satisfies the conditions y(0)=6 and y(1)=7. (a) Find the constants C and a. Enter the exact value of a. (b) Find y(2). Enter the exact answer. Simplify the answer so it does not contain any logarithms. 
PreCalculus
A town has a population which is growing linearly. In 1970 its population was 36,000 while in 1985 its population was 63,000. Find a formula for its population P(t), where t=0 corresponds to the year 1970. 
pre calculus
Candy and Tim share a paper route. It takes Candy 70 min to deliver all the papers, and it takes Tim 80 min. How long does it take the two when they work together? 
Precalc
Are exponential equations the same as exponential functions? I am writing a summary of this year's PreCalculus lessons and one of the topics on the outline is "Exponential Equations", but on the lesson Power Points on my teacher's website there is only one labeled "... 
precalculus
Callaway golf Company has determined that the marginal cost C of manufacturing x Big Bertha Golf clubs may be expressed by the quadratic function: C(x) = 4.9^2  617.4x + 19,600 How many clubs should be produced to minimize marginal cost? 
precalculus
At a selling price of $ 54 , a lamp company breaks even on total sales of $ 3564 . If the company's overhead is $ 396 , find the marginal production cost per lamp and find the profit on sales of 145 lamps. 
PreCalculus
A gardener has 72' of edging. She wants to use it to enclose a 125 square foot rectangular area; she does not have to use up all of the edging. What are the possible lengths that a side of the rectangle can have? Answer using interval notation. Hint: If the length of the ... 
math: precalculus
You have 5 grams of carbon14; whose halflife is 5730 years. a)Write the rule of the function that gives the amount of carbon14 remaining after x years. b)How much carbon14 will be left after 4,000 years? c)When will there be just 1 gram left? 
PreCalculus
A gardener has 100' of edging. She wants to use it to enclose a 130 square foot rectangular area; she does not have to use up all of the edging. What are the possible lengths that a side of the rectangle can have? Answer using interval notation. Hint: If the length of the ... 
precalculus 11
I have the question what is the equation of the function in the form f(x) = 1/xc for the function with a vertical asymptote at x=1? sketch the graph. I am uncertain how I plug this into a graphing calculator. Could I substitute 1 for x and then put an x in for c to input this... 
PreCalculus
It is well known that superman can withstand as much as 3 grams of Green Kryptonite indefinitely. However, exposure to more than 3 grams for more than 13 hours is fatal. Assume that Kryptonite decays at an hourly rate of 5.35% If superman is trapped in a room with 6 grams of ... 
pre calculus
Which is worth more after 5 years, an investment of $1000 at 5% interest compounded semi  annually(twice a year). or an investment of $1000 at 5% interest compounded continuously? 
Precalculus
prove the identity sin2xsin2y/sin2x+sin2y=tan(xy)/tan(x+y) 
Pre Calculus
How are the factors of a polynomial related to the xintercepts of a polynomial? How do you find the xintercepts given the factors? 
Pre Calculus
Prove that the equation is an identity. sec x/(sec x tan x)=sec^2 x +sec x tan x 
PreK lesson plan
I am a prek summer school teacher, and the theme for this week is "my neighbors." Can you suggest any lesson plans or art and craft activities that connects to the "my neighbor" theme.... or do you know a particular website that could help me.... thanks alot 
prealgebra
I am actually in 6th grade but I really want to learn more about pre algebra. I was given a task to solve the question of y=9x+3*7 and i don't get what to do. Should I graph? Or solve for y? 
PreK class needs your help
I noticed that someone posted this question before but I wanted to see if there were anymore ideas...... I am a preK teacher, as well, and my class will be doing a unit on Community History.... what activities and worksheets could I give my students (prek) that connects to ... 
Honors Pre Calculus
Verify the trigonometric identity:￼ ￼(1+sin x)/ (1sinx)^2=￼(1+sin x)/[cos x] Hint: [cos x] means the absolute value of cos x 
Honors Pre Calculus
Verify the trigonometric identity:￼ ￼(1+sin x)/ (1sinx)=￼(1+sin x)/[cos x] Hint: [cos x] means the absolute value of cos x 
Honors PreCalculus
You are traveling in a car toward a certain mountain at a speed of 80km/hr. The apparent size of the mountain is .5degrees. Fifteen minutes later the same mountain has an apparent size of 1 degree. About how tall is the mountain? I believe you must convert the degrees to ... 
PreCalculus
translate this polar equation into a rectangular form: rsin(2theta)=sin(theta) My answer: r2sin(theta)cos(theta)=sin(theta) 2rcos(theta)=1 2x=1 x=1/2 This is the only answer I can get and someone told me it's wrong. Would someone please help me with this 
Pre Calculus
You have been hired by the Humane Society to construct six 2 by 3 animal cages using 1400 feet of chain fence. Express the length and width using function notation. Include a graph with the area function with explanation of significance. Find the dimensions that maximize the ... 
PreCalculus
You have been hired by the Humane Society to construct six animal cages using 1400 feet of chain fence. Express the length and width using function notation. Include a graph with the area function with explanation of significance. Find the dimensions that maximize the total ... 
PreCalculus
Solve the triangle. Round to the nearest tenth. B=54deg a=42 c=6.5 1. I found length of b using law of cosine and got 36.2 2. Using side of b, I used the law of sine to get angle A = 28.2 3. I added B+A and subtracted from 180 to get angle C = 127.8 which DOES NOT make sense ... 
precalculus
A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a greenbelt of uniform width along two adjacent sides. The greenbelt must be 10 times the area of the development. find the ... 
Pre calculus
Log base 10(log base 8 8)=x 
Precalculus
1. The graph of the equation y = x2 – 3 is symmetric with respect to which of the following? The answer is the yaxis . why? 2.The graph of an odd function is symmetric with respect to which of the following? the origin is the answer, why ? 
PreCalculus
A.Verify the identity. B.Determine if the identity is true for the given value of x. Explain. [cot(x) – 1] / [cot(x) + 1] = [1 – tan(x)] / [1 + tan(x)], x = π/4 I solved A and I believe it's true; however, I need help with B. 
precalculus
the path of a ball is given by y=.05+3x^2+3x+5, where y is the height (in feet) of the ball and x is the horizontal distance (in feet) from where the ball was thrown. Find the maximum height of the ball. 
Precalculus
I am having difficulty with two problems: 1) Evaluate (1+i)^12 by using DeMoivre's Theorem. Express the result in rectangular form. So far I have: r=sqrt(1)^2+(1)^2 which simplified is sqrt2. Don't know how to proceed. 2) Write the polar equation theta = 45 degrees in ... 
PreCalculus
Which one of the following situations would have a graph that is a constant function? (5 points) (Points : 5) The amount of money that someone earning $10.75 per hour would make The total number of days in September each year The amount of rainfall in New York throughout the ... 
pre calculus
find 2 solutions of tan θ=.6524 in both degrees and radians. I know the answer are 33.12 degrees/.578 radians and 213.12 degrees/3.72 radians, but how do you find this? Thanks!!!! 
PreCalculus
A pomegranate is thrown from a ground level straight up into the air at time t = 0 with velocity 67 feet per second. Its height at time t seconds is f(t)=16^2+67t. (a) Find the time it hits the ground and (b) the time it reaches its highest point. (c) What is the maximum ... 
PreCalculus
Approximate the greatest real zero of the function g(x)= x^33x+1 to the nearest tenth. I know that there is a zero between 2 and 1, and another between 0 and 1 but do not know how to find it to the nearest tenth. The only example shown in my book uses a calculator and mine ... 
pre calculus
Use the following conditions to create a sketch of the function by hand. a. vertical asymptote at x=3 b. xintercept of 1 and 5 c. f(2)=f(4)=f(6)=3 d. increasing on [0,3) and [5,infinity) e. decreasing on (3,5] f. f(x) is an odd function I don't know how to graph this. It ends... 
precalculus 11
I have the question y=x^2 9 I am asked for the piecewise function. I have written y={x^2 +9 if x less than equal to 3} { x^2 9 if x is greater than equal to 3} I am wondering if I have my are signs backwards.My reasons for choosing the signs I have is if I plug a ... 
precalculus 11
I have the question y=x^2 9 I am asked for the piecewise function. I have written y={x^2 +9 if x less than equal to 3} { x^2 9 if x is greater than equal to 3} I am wondering if I have my are signs backwards.My reasons for choosing the signs I have is if I plug a ... 
PreCalculus
At 34 degrees north latitude, the longest day of the year has 14.273 hours of daylight, and the shortest day 9.726 hours. If the equinox falls on march 21(day 80), model the hours of the daylight by day? 
precalculus 11
a launch window of 8:00 to 12:00. If t represents the launch time then what is an acceptable range of values for launch times? My thoughts are on this is that the scientist have a window of 4 hours which can include 8:00 and 12:00 but cannot exceed them. So time could be added... 
PreCalculus
Use a graphing calculator to write a polynomial function to model this set of data {(5,2) (7,5) (8,6) (10,4) (11, 1) (12 3) (15,5) (16,9)} A) f(x) = 2x3 + 2.70x2 + 0.09x  65.21 B) f(x) = 2x3  0.09x  65.21 C) f(x) = 0.09x3  2.70x2 + 24.63x  65.21 D) f(x) = x4  5.7x3 + 2... 
precalculus
A plane flies at a speed of 150mph at an angle of 10 degrees, after 6 seconds, the plane keeps the same speed but changes to an angle 18 degrees. How long in minutes would it take the plane to travel to a cruising altitude of 30,000 feet? 
PreCalculus
If you solve the following system of equations by substitution, which statement is true? x = z x  2y + z = 6 2x + y  2z = 1 A. You can substitute z for x into the second and third equations. B. You can substitute x for z into the second and third equations. C. Both methods ... 
precalculus
For groups of 80 or more people, a charter bus company determines the rate per person according to the formula: Rate=80.05(n80),n(greater than or equal to)80 where the rate is given in dollars and 'n' is the number of people. Now, Express the revenue 'R' for the bus company ... 
PreCalculusTrig
A pole tilts 12 degrees from the vertical, away from the sun, casts a 34 foot long shadow on level ground. The angle of elevation from the end of the shadow to the top of the pole is 64 degrees. How long is the pole? 
precalculus
THe sume of 2 positive numbers is 20. Find the two numbers such that 1) the sum of the square is minimum b) the product of one and the square is maximum. c) the product of the square and one and the cube of the other is maximum I will be happy to critique your work on this. 
pre calculus
Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This is the problem I am stuck on: f(x)= x^4... 
pre calculus
Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This is the problem I am stuck on: f(x)= x^4... 
Precalculus
Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours. 
Pre Calculus
At a glassware factory, molten cobalt glass is poured into molds to make paperweights. Each mold is a rectanglar prism whose height is 3 inches greater than the length of each side of the square base. A machine pours 20 cubic inches of liquid glass into each mold. What are the... 
Honors Pre Calculus
Tony visits the local fair and sees one of the rides, the ferris wheel. The ferris wheel has a diameter of 50 feet and is on a platform of 4 feet. If it takes 12 seconds to make one full revolution, what is the equation of the height of a person on the ferris wheel at any time t? 
pre calculus
1. a plane has heading of 54 degrees & airspeed of 225mph. The wind is blowing at 33mph from 144 degrees. what are its actua heading & airspeed? Round to one decimal place. A) 61.4deg, 257.1mph B) 7.4deg, 66114.0mph C) 136.6deg, 288mph D) no solution 
Math
darry and nay eat dinner at a restaurant with 6% sales tax. They leave an 18% tip on the pre tax amount of the bill. If they paid a total of 37.20, what was their pre tax bill? 
Precalculus
How do you write an equation of a translated line given the equation of the original line and both the translated and original lines on a graph?? Thanks in advance!! 
Precalculus
How do you write an equation of a translated line given the equation of the original line and both the translated and original lines on a graph?? Thanks in advance!! 
Pre Calculus
Identify the parametric equations that represent the same path as the following parametric equations. x(t)=2cos2t y(t)=sin3t a. x(t)=2cos2t y(t)=sin6t b. x(t)=4cos4t y(t)=sin6t c. x(t)=2cos4t y(t)=sin6t d. x(t)=4cos2t y(t)=2sin3t 
PreCalculus
P= 0.0001x^2+70x350000 By graphing this what would be the number that would produce a maximum profit. I tried grapghing it but my calculator is not working with me! Is There another way to find the maximum number that would produce the maximum profit? 
calculus (PRE)
This may be simple, but I'm not getting it. An open box of maximum volume is to be made from a square piece of material, 24cm on a side, by cutting equal squares from the corners and turning up the sides. The table for it is: Height(x) Volume(V) 1 484 2 800 3 972 4 1024 5 960 ... 
PreCalculus
Not sure what to solve... I tried to solve it but i ended up proving that it worked. a. Find the equations of the tangents at C (2,1) and D (1,2) on the circle x^2+y^2=5 b. Find the point of intersection of the tangents. ~What I did was find the slope and then B, within the ... 
Pre Calculus
Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. (sin x + cos x) ^2 a. 1+2sinxcosx b. sec^2x−tan^2x+2cosxsinx c.sec x + 2 sin x/sec x d. sin^2x+cos^2x e. 1+2cos (pi / 2  x) cos x 
PreCalculus/Trig Check please and help
Could someone please check the first one and help me with the second one. I'm stuckThank you 1.What are theroots of the following polynomial equation? (x+2i)(x5)(x2i)(x+8) = 0 I think the roots are 2i,5,2i,8you take out the roots as opposites of what are in the equaion ... 
pre calculus
2. Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. y= 2 lxl +2 For example, if you were asked to graph y= x^2 + 1 using transformations, you would show the graph of y= x^2 and the graph shifted ... 
PreCalculus
An Alfa Romeo going at 70 mph requires 169 feet to stop. Assuming that the stopping distance is proportional to the square of velocity, find the stopping distances required by an Alfa Romeo going at 35 mph and at 140 mph (its top speed). 
PreCalculus
Find the slope of the tangent line to the curve 2(x^2+y^2)^2=25(x^2−y^2) at the point (−3,−1)? Here's what I did: 2(x^4 + y^4) = 25(x^2y^2) 2x^4 + 2y^4 = 25x^2  25y^2 8x^3 + 8y^3(dy/dx) = 50x  50y(dy/dx) d/dx(8y^3 + 50y) = 50x  8x^3 d/dx = (50x8x^3)/(8y^... 
Precalculus
Nathaniel pulls a sled along level ground with a force of 30 newtons on the rope attached to the sled. If the rope makes an angle of 20 degrees with the ground when it is pulled taught, find the horizontal and vertical components of the force. Round to the nearest tenth. ... 
PreCalculus
Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is smaller than ∠B2.) a = 34, c = 43, ∠A = 39... 
Pre calculus
How do I solve this exponent problem? I understand the exponent rules, but I getting 1 but 1 is not the answer! I don't want anyone to solve the problem for me, I want to learn how to solve this type of problem. Thank you! Solve the equation: 8=36 (3sqrtx^2) Thanks again! 
Pre Calculus
Find all $2 \times 2$ matrices $\bold{A}$ that have the property that for any $2 \times 2$ matrix $\bold{B}$, \[\bold{A} \bold{B} = \bold{B} \bold{A}.\] 
PreCalculus
Find the inverse function for the function f(x)=2^(x)+1/2^(x)1 You will need to use some properties of logarithmic functions to find the inverse of this particular function. 
PreCalculus
1) Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes. x+4/ x^2+x6. 2) Use a graphing utility to graph the function and determine the xintercepts and B. set y=0 and solve the ... 
precalculus
Move point (3,50 degrees) according to the following symmetries (keep positive) a. symmetrical to the origin b. symmetrical to theta=0 degrees c. symmetrical to theta= 90 degrees 
pre calculus
1.) If h(x)= (fog)(x) and h(x) = 3 over the square root of x+3 , find g(x) if f(x)= 3 over the square root of x+2. my answer is x+1. Am I right? 2.)If f(x)=3x,g(x)=x3,and h(x)= the square root of x, find (fogox)(X). I really didn't get this will someone please show me how to ... 
Pre Calculus
Find the roots of the function g(x)=x^3 +16x a)0,4i, 4i b)0,4,4i c)0,4,4i d)0,4,4 The equation can be rewritten x(x^2 + 16) = 0 The function is zero if x = 0, OR if x^2 = 16 That should give you a hint of what the roots are. So you take the square root of 16 which gives ... 
precalculuscheck over work
1). change to exponential form: log2^256=8; 2^8=256 log0.0001=4; 10^4=0.0001 2). change to logarithmic form: 5^3=125; log5^125=3 4^3=1/64; log4^1/64=3 3). solve the equation: 3^(x2)=27^(x+1) 3^(x2)=(3^3)^(x+1) 3^(x2)=3^(3x+3) x2=3x+3 5=2x 5/2=x 2^(x^(2)+1)=4^(x+2) 2... 
PreCalculus
A sailboat in a lake travels 4 km due north and then 4 km due west. From there, the boat travels 5 km due north and 4 km due west. How far is the bboat from the starting point? Express your answer as a mixed radical. (How would I use radicals for this??) Thanks! 
PreCalculus
Use applications of exponential functions and logarithmic functions to solve. The halflife of plutonium 241 is 14.4 years.If 100 grams is present now, How much will it take to reach 2 grams of plutonium 241? y=a(1/2)^(t/14.4) How do I solve for t? I'm not sure where to even ... 
PreCalculuscheck answers
Express 52i in polar form. Express your answer in radians to the nearest hundreth. r=sqrt5^2+2i^2 which equals sqrt21.Arctan of 2/5+pi equals 18.7 Polar form=sqrt21 cis 18.7 Is this correct?? 
PreCalculuscheck answers
Express 52i in polar form. Express your answer in radians to the nearest hundreth. r=sqrt5^2+2i^2 which equals sqrt21.Arctan of 2/5+pi equals 18.7 Polar form=sqrt21 cis 18.7 Is this correct?? 
PreCalculuscheck answers
Express 52i in polar form. Express your answer in radians to the nearest hundreth. r=sqrt5^2+2i^2 which equals sqrt21.Arctan of 2/5+pi equals 18.7 Polar form=sqrt21 cis 18.7 Is this correct?? 
pre calculus
If you are driving down a 10% grade, you will always be 10% below where you would have been if you could have driven on flat ground from where you started. Suppose you descend to where you are 20 feet below your starting point. What concept does the “grade” relate to, and ... 
PreCalculus
a ferris wheel is elevated 1 meter above ground. When car reaches the highest point of the Ferris wheel, it's altitude from ground level is 31 metres. How far away from the center, horizontally, is the car when it is at an altitude of 25 meters? 
PreCalculus
A photogrpaher points a camera at a windows in a nearby building forming an angle of 42 degrees with the camera platform. If the camera is 52 meters from the building , how high above the platform is the window, to the nearest hundreth of a meter. The answer is 46.82m, i would... 
PreCalculus Math
An amusement park charges $8 admission and averages 2000 visitors per day. A survey shows that, for each $1 increase in admission cost, 100 fewer people would visit the park. Find the admission cost and number of visitors that gives the maximum revenue. 
precalculus
A rectangular box has a perimeter of 50 inches. Find the length and width of the box that would give the maximum area. Find the maximum possible area of the box. 
PreCalculus
Determine the derivative at the point (2,−43) on the curve given by f(x)=7−7x−9x^2. I know that the answer is 43, but I was wondering if it was just a coincidence that the derivative at the point (2,−43) is 43, or is there a reason why 43 is the same... 
pre calculus
if there are initial 2500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours cab n be found using the formula=N=2500(2^t).how long will it take the culture to grow to 75,000 bacteria. 
precalculus
solve the exponential equation. express the solution in terms of natural logarithims. Then, use a calculator to obtain a decimal point approximation for the solution. e^x=12.3 What is the solution in terms of natural logarithims? The solution set is ? 
PreCalculus
Let F1 = 219.5, F2 = 447.3, θ1 = 52.79◦, θ2 = 7.831◦. Find the magnitude of the resultant F1 _\_ θ1 (in quadrant 3 positive)  F2 _/_ θ2 (in quadrant 1 positive)  I know this is probably hard to understand but I cannot draw diagrams on here 
Pre Calculus
Assume that x, y, and b are positive numbers. Use the properties of logarithms to write the expression logb ^8xy in terms of the logarithms of x and y. a. logb^8 + logb x + logb^y b. logb^8+logbx c. logb^8+logby d. logb^8 + log8 x + log8^y e. logb^8+log8xy 
precalculus
solve the logarithmic equation. be sure to reject any value of x that is not in the domain of the orginal logarithmic expression. In square root of x+2=2 (If I try to make the square root sign it will not come out right so I wrote it out instead) What is the exact solution. A... 
Pre Calculus
The number of new accounts opened at a credit union in the years 2001 to 2006 can be approximated by the model N(t)= 80.6t^2+2100t+12000, where 11 <= t <= 16, with t = 11 corresponding to 2001. Using this model and your graphing calculator, determine the year in which ... 
PreCalculuscheck answers
If cos theta = 0.8 and 270<theta<360, find the exact value of sin 2theta a) 0.96 b) 0.6 c) 0.96 d) 0.28 Answer: b 2) If csc theta = 5/3, and theta has its terminal side in Quadrant III, find the exact value of tan 2theta a)24/25 b) 7/25 c) 24/7 d) 7/25 Thanks 
PreCalculus
I want to learn how to find the domain, holes, xintercepts, y intercepts, vertical asymptotes, and horizontal asymptotes of a rational function. I know it is against the rules in jiskha to do the homework for the students but if I have been looking over my notes and I just ... 
precalculus
find the complex zeros of the polynomial function. write F in the factored form. f(X)=x^37x^2+20x24 use the complex zeros to write f in factored form. f(x)= (reduce fractions and simplify roots) 
PreCalculus
After leaving an airport, a plane flies for 1.75h at a speed of 200km/h on a course of 100 degrees. The plane then flies for 2 hours at a speed of 250km/h on a course of 40 degrees. At this time, how far from the airport is the planee?