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Fombitz answered: 13805 problems
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logarithm/108088: So lost can anyone help me? find k in the exponential function N(t)=N base0e^kt, given that N(0)=1 and N(3)=7. thanks in advance. 1 solutions Answer 78826 by Fombitz(13828)   on 2007-11-05 15:05:24 (Show Source): You can put this solution on YOUR website! where N(0)=1 and N(3)=7 Use your two values to solve for and k~0.649 Check your answers. These values match your original values.

Radicals/108172: Would you please help me with this problem The questions is to simplify and combine like radicals. All variables represent positive numbers. sqrt2 - sqrt8 My results sqrt2 = 1*2 sqrt8 = 2*2*2 answer -sqrt4 ( I was told that this is the wrong answer) Please help!!! 1 solutions Answer 78825 by Fombitz(13828)   on 2007-11-05 14:57:34 (Show Source): You can put this solution on YOUR website! Let's start from your results sqrt2 = 1*2 sqrt8 = 2*2*2 Your right hand side should still include the square root. sqrt2 = sqrt(1*2) sqrt8 = sqrt(2*2*2) Then sqrt2 = sqrt(2) sqrt8 = sqrt(2*2)*sqrt(2) and you can substitute since sqrt(2*2) = 2 Your equations then become sqrt2 = sqrt(2) sqrt8 = 2*sqrt(2) Now your subtraction can take place. sqrt2 - sqrt8 = sqrt2 - 2*sqrt(2) sqrt2 - sqrt8 = -sqrt(2)

logarithm/108166: can anyone help me?:determine the horizontal asymptote of the graph of B(t)=1200/1+34e^-0.125t. i have no idea how to solve this. 1 solutions Answer 78824 by Fombitz(13828)   on 2007-11-05 14:51:27 (Show Source): You can put this solution on YOUR website! You can do it two ways. Graphically or by analysis. Let's do analysis. As t gets large, since there is a -.125 coefficient to multiply t in the exponential, the exponential function drops quickly to zero. Then function then looks like for large positive t. Example: At t=100, B(t)=1199.848 I'm not sure of the context of this function, that is if t is always positive, like time. If not, we can look at what happens when t becomes large in the negative direction. In that case (-.125t) becomes very large, and the exponential function becomes very large. for large negative t. Example: At t=-100, B(t)=.000132 There is a horizontal asymptote at y=1200. And if it makes sense in your problem, there is also one at y=0. Graphically it's easier to find the asymptotes,

logarithm/108167: what is the domain of f(x)=x+log(base)3(x-5). not sure if it is x>5 or x>0 of course i could be wrong for both . can someone help. 1 solutions Answer 78822 by Fombitz(13828)   on 2007-11-05 14:24:59 (Show Source): You can put this solution on YOUR website! No, you're on the right track. Then, using the definition of the logarithm function,

Trigonometry-basics/108065: Find the least common multiple (LCM) for each of the following groups of numbers. Use whichever method you wish. 12, 20 and 35 1 solutions Answer 78820 by Fombitz(13828)   on 2007-11-05 14:20:28 (Show Source): You can put this solution on YOUR website! Prime factors are 2,3,5,7 with highest powers of 2,1,1,1 respectively.

logarithm/108165: can anyone help me solve this: find the balance(to the nearest cent) if $24,000 is invested at an annual interest rate of 6.8% for 10 years compounded continuously. I have tried to solve 5 times but cannot come up with a reasonable answer. 1 solutions Answer 78819 by Fombitz(13828)   on 2007-11-05 14:16:35 (Show Source): You can put this solution on YOUR website! After 10 years, you'll have $47373.07.

Linear-equations/108162: HI please help me with this.THankyou The equation 9C-5F+160=0 describes the relationship between tempreature,C, in degrees Celsiu, and the tempreature , F, in degrees fahrenheit. a) express the equation in the form C=mF+b b) Graph this relation c) Identify the slope and the C intercept and explain what they mean 1 solutions Answer 78817 by Fombitz(13828)   on 2007-11-05 14:03:35 (Show Source): You can put this solution on YOUR website! Add (5F-160) to both sides. Simplify. Divide both sides by 9. a) Simplify. b) c.) The slope is the number is the coefficient of F in equation a or 5/9. It relates the rate of change in each temperature system. For a change of 9 degrees Fahrenheit, you get a 5 degrees change in Celsius. The C intercept is where the graph crosses the y axis. The value of C when F=0. C(0) is the equivalent temperature in Celsius to 0 F. In this case,

Graphs/108115: 5 ______> 0 x-2 1 solutions Answer 78815 by Fombitz(13828)   on 2007-11-05 13:49:06 (Show Source): You can put this solution on YOUR website! If the left hand expression is positive, the denominator needs to be positive since the numerator is always positive.

Square-cubic-other-roots/108155: Please help me solve this equation the square root of x+6 = x+4 1 solutions Answer 78813 by Fombitz(13828)   on 2007-11-05 13:34:40 (Show Source): You can put this solution on YOUR website! Square both sides. Expand right hand side. Group all terms on one side. Factor. x=-2,-5 Check your answers. True statement. Good answer. True statement, since . Good answer.

Polynomials-and-rational-expressions/108148: please help solve this i keep coming up with different answers. (6*10^12)(3.2*10^8)divide by (1.6*10^7)(3*10^2) 1 solutions Answer 78811 by Fombitz(13828)   on 2007-11-05 13:16:16 (Show Source): You can put this solution on YOUR website! Break it up into the numbers and exponents. x x x

Complex_Numbers/108152: (7+2i)-(3+3i) 1 solutions Answer 78808 by Fombitz(13828)   on 2007-11-05 12:58:46 (Show Source): You can put this solution on YOUR website! Complex number addition and subtraction is done by separately working on the real and imaginary parts of the expression.

Linear_Equations_And_Systems_Word_Problems/108124: Stan invested $17,000, part at 18% and part at 4%. If the total interest at the end of the year is $1,380, how much did he invest at each rate? 1 solutions Answer 78802 by Fombitz(13828)   on 2007-11-05 11:11:05 (Show Source): You can put this solution on YOUR website! Let's call the part he invested at 18%, E, and the part he invested at 4%, F. Then you know that, 1. 2. Use 1. to solve for E in terms of F. 1. Now substitute that into equation 2 and solve for F. 2. From 1. Verify your answer using equation 2. Close enough, round off error. Good answer. $4571.43 at 18%, $12428.57 at 4%.

Inequalities/108126: please help me solve this equation x+3_>4 and -4x<20 1 solutions Answer 78801 by Fombitz(13828)   on 2007-11-05 11:01:13 (Show Source): You can put this solution on YOUR website! x+3_>4 and -4x<20 First equation Subtract 3 from both sides. Second equation Divide both sides by (-4), change direction of inequality. Since you must satisfy both conditions and , then the solution is

Polynomials-and-rational-expressions/108145: Will you please help me with this equation x^2-7x+12 over x^2-16 1 solutions Answer 78799 by Fombitz(13828)   on 2007-11-05 10:53:20 (Show Source): You can put this solution on YOUR website! Factor both numerator and denominator. Simplfy.

Age_Word_Problems/108129: I am trying to help my daughter but we cannot set up this problem can you please help us thank you. For six consecutive years a man's age was a multiple of his granddaugters age. How old was each during the sixth year? 1 solutions Answer 78798 by Fombitz(13828)   on 2007-11-05 10:49:52 (Show Source): You can put this solution on YOUR website! Let's call the Grandfather's age, X, and the Grandaughter's age Y. The first year X=mY where m is an integer (1,2,3,4,..) and for the next 5 years, X+1=n(Y+1) X+2=o(Y+2) X+3=p(Y+3) X+4=q(Y+4) X+5=r(Y+5) where n,o,p,q,and r are also integers. Using this method you have 6 equations, but you have 8 unknowns, so it doesn't help. Another method is to look at the list of prime numbers, that is numbers that are divisible only by themselves and 1. You need to find 6 consecutive non-prime or composite numbers. The list of primes under 100 is 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 The first time you have six consecutive divisible numbers starts at 90. 90=3x3x10 91=7x13 92=2x2x23 93=3x31 94=2x47 95=5x19 96=2x2x24 The issue is that 93,94,95 have only prime factors and the factors are not consecutive, so they can't be the daughter's age. The next 6 consecutive composite numbers start at 114 to 126. The same issue exists as before 115,118,119,122,123,124 have large prime factors in them and cannot be the daughter's age. I don't believe there's a solution to this problem, as stated.

Expressions-with-variables/108139: p=ad divided by e, solve for e 1 solutions Answer 78788 by Fombitz(13828)   on 2007-11-05 09:35:18 (Show Source): You can put this solution on YOUR website! Multiply both sides by e. Divide both sides by p.

Polynomials-and-rational-expressions/108141: I can't seem to figure this one out can you help me please? 4n^2 + 20n=0 I have to solve the equation. 1 solutions Answer 78787 by Fombitz(13828)   on 2007-11-05 09:33:12 (Show Source): You can put this solution on YOUR website! Two solutions Check your answers. True statement. Good answer. True statement. Good answer.

Complex_Numbers/107653: 2x²+26=-10 1 solutions Answer 78448 by Fombitz(13828)   on 2007-11-02 17:00:00 (Show Source): You can put this solution on YOUR website! or or where

Polynomials-and-rational-expressions/107656: This question is from textbook Intermediate Algebra PLease help me simplify: r^2/r-s + s^2/s-r 1 solutions Answer 78447 by Fombitz(13828)   on 2007-11-02 16:54:51 (Show Source): You can put this solution on YOUR website! Get the same denominator, (r-s). Subtract numerators. Factor the quadratic.

Graphs/107699: A television is marked down from $350 to $308. What is the discount rate? 1 solutions Answer 78446 by Fombitz(13828)   on 2007-11-02 16:47:43 (Show Source): You can put this solution on YOUR website! Discount Rate = (0ld Price-New Price)/Old PriceX100 The TV has a 12% discount applied to it.

Polynomials-and-rational-expressions/107689: This question is from textbook Please help me with this problem: Simplify the expression: sqrt (x) times ^3 sqrt (x) 1 solutions Answer 78445 by Fombitz(13828)   on 2007-11-02 16:43:29 (Show Source): You can put this solution on YOUR website! Exponent rules that are important here. The square root is another way to say to the 1/2 power.

Radicals/107625: Multiply: (8√[6] + 3√[2])(4√[6] – 5√[2]) I believe FOIL is used here. I also think the answer should have no decimals. Thanks for helping!!! 1 solutions Answer 78401 by Fombitz(13828)   on 2007-11-02 11:32:37 (Show Source): You can put this solution on YOUR website! Yes FOIL Method (First Outer Inner Last) (8√[6] + 3√[2])(4√[6] + (-5√[2])) Original Equation First (8√[6]*4√[6])=32√[36] First (8√[6]*4√[6])=32*6 First (8√[6]*4√[6])=192 Outer (8√[6]*-5√[2])=-40√[12] Outer (8√[6]*-5√[2])=-80√[3] Inner (3√[2]*4√[6])=12√[12] Inner (3√[2]*4√[6])=24√[3] Last (3√[2]*-5√[2])=-15√[4] Last (3√[2]*-5√[2])=-15*2 Last (3√[2]*-5√[2])=-30 (8√[6]+3√[2])(4√[6]+(-5√[2]))=192+(-80√[3])+24√[3]+(-30) Combine all of the terms (8√[6]+3√[2])(4√[6]+(-5√[2]))=162-56√[3] Final answer.

Equations/107634: Determine whether the equation is an identity, a conditional equation, or an inconsistant equation. 1/(x+5) + 2/(x+3) = -2/(x^2 + 8x +15) 1 solutions Answer 78398 by Fombitz(13828)   on 2007-11-02 11:11:51 (Show Source): You can put this solution on YOUR website! Since (x+5) is in the denominator on the right hand side of the equation, we made the assumption that x=-5 and x=-3 were not solutions to avoid division by zero. Since we derived that x=-5, there is no solution(inconsistent).

Graphs/107633: This question is from textbook Blitzer f(X)=2x+3 ---- x+2 Find the Horizontal and Vertical asympotes. 1 solutions Answer 78392 by Fombitz(13828)   on 2007-11-02 10:56:03 (Show Source): You can put this solution on YOUR website! The vertical asymptote occurs when the denominator goes to zero, that is, f(x) goes to and . The horizontal asymptotes occur as x goes to and . As x goes to , f(x) looks like or 2. As x goes to , f(x) looks like or 2. The horizontal asymptote is y=2.

Exponents/107638: problem: divide and simplify: (a^-2)^3(a^4)^2 / (a^3)^-3 this^and a number is the exponet please show how you come to your answer. 1 solutions Answer 78390 by Fombitz(13828)   on 2007-11-02 10:45:46 (Show Source): You can put this solution on YOUR website! Remember the exponent rules Now for your equation,

Polynomials-and-rational-expressions/107636: This question is from textbook Please help: One of my homework problems involves the following expression (-8/27)^-2/3 The expression needs to be simplified. I think the answer is 4/9, but I want to make sure I'm on the right track. Thank you 1 solutions Answer 78389 by Fombitz(13828)   on 2007-11-02 10:39:09 (Show Source): You can put this solution on YOUR website! Let's look at numerator and denominator separately. Now back to the equation,

Exponents/107628: x^3y^2=t^4/w solve for y 1 solutions Answer 78387 by Fombitz(13828)   on 2007-11-02 09:40:34 (Show Source): You can put this solution on YOUR website! Divide both sides by . Take the square root of both sides. or

Exponents/107570: 3^(2x)+3^x=20 1 solutions Answer 78385 by Fombitz(13828)   on 2007-11-02 09:10:04 (Show Source): You can put this solution on YOUR website! Let u=-5 and u=4 Since , the negative solution is not possible. Check your answer, True statement. Good solution.

Linear_Algebra/107512: I am trying to help my daughter with her homework, but since I have no idea what I am doing I hope that having the answer will help me out: Cricket Problem: Based on information in Deep River Jim's Wilderness Trailbook, the rate at which crickets chirp is a lenear function of temperature. At 55 degrees F they make 70 chirps per minute and at 69 degrees F they make 126 chirps per minute. a) Write the equation expressing chirping rate as a function of temperature. b) Predict the chirping rate at 90 degrees F. c) How warm is it if they are chirping 120 chirps per minute? d) Calculate the temperature-intercept. What does this tell you about this numbeer in the real-world? e) Calculate the chirping-intercept. What does the chirping-intercept tell you about the real-worl? f) Shetch and label the graph. Thank you for any help. Brian 1 solutions Answer 78289 by Fombitz(13828)   on 2007-11-01 17:05:09 (Show Source): You can put this solution on YOUR website! Linear equation means you need two points to calculate the equation. You have two points. Let C=chirp rate and T=temperature. The equation of a line is given by, where m is the slope of the line and b is the intercept. The slope is given by Using the two data points, you gave, and the units are chirps per minute/degree F. You can solve for b by using m you just calculated and one data point. The equation of your line is then You can verify with your two points. 70 chirps at 55 degrees F. That checks out. 126 chirps at 69 degrees F. That checks out. Your equation matches the data. a.)C(T)=4T-150 where C is chirps per minute, T is degrees F. Chirping rate at 90F. C(90)=4(90)-150 C(90)=360-150 C(90)=210 b.)210 chirps per minute at 90 degrees F. C(T)=4T-150=120 4T-150=120 4T-150+150=120+150 4T=270 T=270/4 c.)T=67.5 degrees F for 120 chirps per minute. d.) The temperature intercept is where the chirping rate is equal to zero. 4T-120=0 4T-120+120=120 4T=120 T=30 degrees F. In the real world, that says chirping doesn't start until 30 degrees. The birds are probably conserving their energy because its so cold. e.) The chirping intercept is where the temperature is equal to zero. C(0)=4(0)-120=-120. This doesn't really have a real world interpretation since there is no such thing as a negative chirp. Chirps need to be positive, that is not defined below T=30 degrees F.

Rational-functions/107484: Solve the inequality 21/15-3x<0 and express the solution as an interval. a. (5, ∞) b. (7, ∞) c. (–∞,5) d. (–∞, 7) 1 solutions Answer 78286 by Fombitz(13828)   on 2007-11-01 16:39:10 (Show Source): You can put this solution on YOUR website! If then (15-3x)<0 since the numerator is positive. Add 3x to both sides. Divide both sides by 3. or Check your answer. Pick a number greater than 5. Let's pick 10. The inequality should hold true since 10>5. True statement. Good answer. a. (5, ∞)

Rational-functions/107480: If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be f (t) = 50,000(1.05t ) . According to this model, by how much will the value of this piece of property increase between the years 2007 and 2008? a. $2500 b. $3140 c. $3880 d. $31,400 1 solutions Answer 78283 by Fombitz(13828)   on 2007-11-01 16:30:11 (Show Source): You can put this solution on YOUR website! First, a correction. If the property appreciates 5% every year, then after the first year,1999. F(1)=50000(1.05) After the second year, 2000. F(2)=F(1)*(1.05)=50000(1.05)(1.05)= The equation should be then 2007 would be the 9th year and 2008 would be the 10th year. and or and The difference between the 10th year and the 9th year would then be C.3880, close enough. If you used the original equation, the house value increases only $2500, after the first year but then increases value by $52,500 every year after. At the end of the 10th year, the house would be worth $525,000. That would be a great profit.