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Travel_Word_Problems/594447: If you are going 80 kilometres per hour how fast are you going in miles per hour? 1 solutions Answer 376727 by Alan3354(30993)   on 2012-04-02 14:54:52 (Show Source): You can put this solution on YOUR website! If you are going 80 kilometres per hour how fast are you going in miles per hour? ---------- 1 mile =~ 1.609 km

expressions/594429: |x + 4| = x² – 26 1 solutions Answer 376724 by Alan3354(30993)   on 2012-04-02 14:45:03 (Show Source): You can put this solution on YOUR website! |x + 4| = x² – 26 ----------------- That makes 2 quadratics. x + 4 = x² – 26 and -(x + 4) = x² – 26 ----- Solve for x

Polynomials-and-rational-expressions/594383: If a stone is tossed from the top of a 330 meter building the height of the stone as a function of time is given by h(t)=-9.8t^2-10t+330 where is it in seconds and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredths place; include units in your answer. 1 solutions Answer 376721 by Alan3354(30993)   on 2012-04-02 14:26:45 (Show Source): You can put this solution on YOUR website! If a stone is tossed from the top of a 330 meter building the height of the stone as a function of time is given by h(t)=-9.8t^2-10t+330 --------------- That might be true somewhere, but on Earth, it's h(t)=-4.9t^2-10t+330 ------------ -4.9 m/sec/sec, negative falling, approximate value.

Trigonometry-basics/594430: hello this is my first time here can please help me solve this problem im not entirely sure how to do it. find all values of theta in the interval 0°≤θ≤360° 1.)sin^2θ-sinθ=0 thankyou. 1 solutions Answer 376720 by Alan3354(30993)   on 2012-04-02 14:19:52 (Show Source): You can put this solution on YOUR website! find all values of theta in the interval 0°≤θ≤360° 1.)sin^2(t) - sin(t) = 0 sin(t)*(sin(t) - 1) = 0 sin(t) = 0 t = 0, 180, 360 degs ------------- sin(t) = 1 t = 90 degs

Inequalities/594419: 1. Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first. A. B. C. D. 2. Solve 2x = 5x2 for x. A. 2.322 B. 0 and 2.322 C. 0 and 0.431 D. 0.431 3. Which of the following is not a property of logarithms? A. B. C. D. 4. A falling object has velocity 37(1 − e–0.4t) meters per second after t seconds of free fall. Which of the following statements is true? A. Its initial velocity was 0 meters per second and its velocity after 10 seconds is –12.2 meters per second. B. Its initial velocity was –1 meter per second and its velocity after 10 seconds is –36.3 meters per second. C. Its initial velocity was 0 meters per second and its velocity after 10 seconds is 36.3 meters per second. D. Its initial velocity was 1 meter per second and its velocity after 10 seconds is 12.2 meters per second. 5. How many roots does x6 = 3x5 + 1 have? A. 6 B. 5 C. 11 D. 1 6. If 2 − i is a root of 3x3 − 11x2 + 11x + 5, then what are its other roots? A. B. C. D. 7. On which interval does the Intermediate Value Theorem guarantee that the polynomial x4 + 7x2 − 9x − 1 has a root? A. B. C. D. 8. If 1 and –6 are two of the roots of 6x4 + 31 x3 − 33x2 − 16x + 12, then what are the other two? A. B. C. D. 9. Which of these graphs could be the graph of y = ex + 1? A. B. C. D. 10. Why do we use the Intermediate Value and Bisection Theorems to find only the irrational roots of polynomials? A. It is the only method available for finding irrational roots of any polynomial. B. The Rational Roots Theorem is better for finding the rational roots. C. Those theorems are unable to find rational roots. D. No polynomial has rational roots. 11. A population of 2000 snakes is released into a marshland and grows according to the formula P = 2000 • 1.5t, where t is the number of months after the release. Find the population 10 months after the release. A. 63,246 B. 115,330 C. 5.9 x 1034 D. 30,000 12. Write in terms of ln a, ln b, and ln c. You may assume that all variables are positive. A. B. C. D. 13. Which of these is the result of (x5 − x3 + 2x2 − 9x + 5) χ (x + 2)? A. B. C. D. 14. Evaluate . A. 2 B. 4 C. Ό D. ½ 15. Find the point (x, y) on the parabola y = 9 − x2 such that the shaded rectangle in the figure below has area 20 square units. A. B. C. D. 16. Solve ln t = log 50 for t. A. t = 5.47 B. t = 8166.3 C. t = 13.6 D. t = 50 17. Which of the following is the conclusion you can draw using Descartes' Rule of Signs applied to 2x4 − 6x3 + x2 + 7x − 4? A. Zero is not a root. There are either 1 or 3 positive real roots. There are 3 negative real roots. There are either 0 or 2 complex roots. B. Zero is not a root. There are either 1 or 3 positive real roots. There are 3 negative real roots. No information is available about the number of complex roots. C. Zero is not a root. There are either 1 or 3 positive real roots. There is 1 negative real root. There are either 0 or 2 complex roots. D. Zero is not a root. There are either 1 or 3 positive real roots. There is 1 negative real root. No information is available about the number of complex roots. 18. Which of these is the remainder when 4x4 − 5x3 + 9 is divided by x − 3? A. B. C. D. 19. Which of these could be the graph of y = 7x − 2? A. B. C. D. 20. Simplify . A. B. 216 C. D. is already in simplified form. 21. Which of the following is a reason for why the trace function on a graphing calculator can sometimes be better than the Bisection Theorem for finding roots? A. The trace function always finds an exact root. B. The Intermediate Bisection Theorem applies only to continuous functions, and not all polynomials are continuous. C. Some roots aren't surrounded by one positive and one negative value of the polynomial D. The Bisection Theorem can't find roots to more than 3 decimal places. 22. If a cubic polynomial has roots –5 and 6 − 2i, what is its third root? A. 1 − 2i B. –30 + 10i C. 6 + 2i D. 5 23. Which of the following is a correct description of the expression logbx? A. It is the power to which b must be raised to yield x. B. It is the xth power of b. C. It is the bth power of x. D. It is the power to which x must be raised to yield b. 24. Which of the following is equal to log6(t + 1) − log6(t2 − 1)? A. log6(t + 1) B. log6t − log6t2 C. log6t D. –log6(t − 1) 25. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0? A. –3 and –1, 1, and 3 B. –2 and 2 C. –2 and –1, 1, and 2 D. 0 and 3 1 solutions Answer 376718 by Alan3354(30993)   on 2012-04-02 14:02:11 (Show Source): You can put this solution on YOUR website! 1. Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first. Hint: Try the factors of 1. --------------------- No one's gonna do all these problems. Post them separately, you might get some of them.

�t�e�s�t/594364: (3-2i)^6 Im not looking for the answer just the how to get to the answer. 1 solutions Answer 376708 by Alan3354(30993)   on 2012-04-02 11:23:52 (Show Source): You can put this solution on YOUR website! (3-2i)^6 Im not looking for the answer just the how to get to the answer. ------------ One way is to multiply it. Square it, then cube the result. ------ If it's a larger exponent, that's not practical, so use DeMoivre's Theorem. --- Angle = arctan(-2/3) sin(A) = -2/sqrt(13) cos(A) = 3/sqrt(13) ---- --> z = sqrt(13)*cis(A) z^6 = (sqrt(13))^6*cis(6A) = 13^3*cis(6A) = 2197*(-0.92626 + i*0.37688) = -2035 + 828i ======================= It's the same answer I get using an Excel sheet I made to do these.

Linear-systems/594354: how do I solve than graph?Is there a graph calculator I can plug into? y=1/2x+5 y=6x-6 1 solutions Answer 376706 by Alan3354(30993)   on 2012-04-02 09:20:15 (Show Source): You can put this solution on YOUR website! how do I solve than graph?Is there a graph calculator I can plug into? y=1/2x+5 y=6x-6 ----------- To solve: Both RH sides = y, so the equal each other. (1/2)x + 5 = 6x - 6 x + 10 = 12x - 12 11x = 22 x = 2 ------- y = 6 ============ To graph: They're straight lines, so you need 2 points. y=1/2x+5 Pick 2 values for x and find y x = 0, y = 5 --> (0,5) x = 6, y = 8 --> (6,8) Plot the 2 points, draw a line thru them. ----- Do the same for the other one.

Quadratic_Equations/594223: Solve by using quadratic formula: (r-4)(r+12)=16 1 solutions Answer 376676 by Alan3354(30993)   on 2012-04-01 22:04:22 (Show Source): You can put this solution on YOUR website! Solve by using quadratic formula: (r-4)(r+12)=16 ------- ------- Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=320 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.94427190999916, -12.9442719099992. Here's your graph: ---------

Surface-area/594278: How do you find the surface area of a regular octagon 1 solutions Answer 376675 by Alan3354(30993)   on 2012-04-01 21:58:53 (Show Source): You can put this solution on YOUR website! How do you find the surface area of a regular octagon --------- What info you're given determines the method.

Travel_Word_Problems/594277: If Angela runs at a steady pace of mph for 3 hours and 20 minutes, how far will she run? 1 solutions Answer 376673 by Alan3354(30993)   on 2012-04-01 21:58:01 (Show Source): You can put this solution on YOUR website! If Angela runs at a steady pace of mph for 3 hours and 20 minutes, how far will she run? ------------ It depends on how fast she runs. d = r*t

Functions/594275: If a ball is dropped from the top of a 256-ft building, then the formula h(t)= 256-16t^2 expresses its height h(t) in feet as a function of the time t in seconds. 1.Find h(2), the height of the ball 2 seconds after it is dropped. 2.Find h(4). 1 solutions Answer 376672 by Alan3354(30993)   on 2012-04-01 21:57:03 (Show Source): You can put this solution on YOUR website! If a ball is dropped from the top of a 256-ft building, then the formula h(t)= 256-16t^2 expresses its height h(t) in feet as a function of the time t in seconds. 1.Find h(2), the height of the ball 2 seconds after it is dropped. Sub 2 for t h(2) = 256 - 16*2^2 = 256 - 64 h(2) = 192 ft ------ 2.Find h(4). Do the same as above.

Polynomials-and-rational-expressions/594273: what is the answer to the math equation 9x squared + 6xy divided by 3x 1 solutions Answer 376670 by Alan3354(30993)   on 2012-04-01 21:55:11 (Show Source): You can put this solution on YOUR website! what is the answer to the math equation 9x squared + 6xy divided by 3x ---------- It depends on the question. PS There's no equal sign, so it's not an equation.

Trigonometry-basics/594182: prove the identity. 1+sin(a)/1+csc(a)=tan(a)/sec(a) 1 solutions Answer 376647 by Alan3354(30993)   on 2012-04-01 19:39:18 (Show Source): You can put this solution on YOUR website! prove the identity. 1+sin(a)/1+csc(a)=tan(a)/sec(a) ------ Change everything to sines and cosines. Eliminate fractions.

Exponents-negative-and-fractional/594120: supposed to be this, keeps putting my fractional powers in the wrong space: 2x^(-7/4)/4x^(4/3) I have been stuck trying to work this out all day, it says the answer is: or x^(11/12)/2x^4 I can't seem to get it to this, have been trying to use the rule: or moving the negative exponent down and applying the: But with no success. :( please give me all the steps in the answer, many thanks Jim. 1 solutions Answer 376623 by Alan3354(30993)   on 2012-04-01 16:37:30 (Show Source): You can put this solution on YOUR website! supposed to be this, keeps putting my fractional powers in the wrong space: 2x^(-7/4)/4x^(4/3) ------------------ = x^(-7/4)/2x^(4/3) Multiply NUM and DEN by x^(7/4) = 1/2x^(4/3 + 7/4) = 1/2x^(37/12) --------------- Multiply NUM and DEN by x^(11/12) to eliminate fractional exponents in the DEN. = x^(11/2)/2x^4 ------------------ I have been stuck trying to work this out all day, it says the answer is: or x^(11/12)/2x^4

Quadratic_Equations/594106: 5x^2-3=0 solve by quadratic formula without imaginary numbers. 1 solutions Answer 376621 by Alan3354(30993)   on 2012-04-01 16:32:42 (Show Source): You can put this solution on YOUR website! 5x^2-3=0 solve by quadratic formula without imaginary numbers. ---------- Sometimes the answer is an imaginary or complex number. Saying to find the answer without them is silly. The answer is the answer.

Linear-systems/594111: How do you solve for x and y in this problem. 5x + 2y = 63 and 3x + 2y = 51 1 solutions Answer 376618 by Alan3354(30993)   on 2012-04-01 16:24:06 (Show Source): You can put this solution on YOUR website! How do you solve for x and y in this problem. 5x + 2y = 63 and 3x + 2y = 51 ---------- There's more than 1 way, but You can subtract one equation from the other and eliminate the y terms.

Travel_Word_Problems/594029: Elda walked from her home to her friend Niabi's house at 4.5 km/hr. When Elda returned home along the same route, she strolled at 3.5 km/hr. Elda took a total of 40 min to walk to Niabi's house and back again. a) How many minutes did Elda take to walk from her home to Niabi's house? b) How far is it from Elda's home to Niabi's house? 1 solutions Answer 376581 by Alan3354(30993)   on 2012-04-01 12:15:24 (Show Source): You can put this solution on YOUR website! Elda walked from her home to her friend Niabi's house at 4.5 km/hr. When Elda returned home along the same route, she strolled at 3.5 km/hr. Elda took a total of 40 min to walk to Niabi's house and back again. --------------- Avg speed for the round trip = 2*4.5*3.5/(4.5 + 3.5) = 31.5/8 km/hr RT distance = r*t = 31.5/8 * (2/3) hr = 21/8 km --> 21/16 km each way. -------------------------- a) How many minutes did Elda take to walk from her home to Niabi's house? t = d/r = (21/16)/4.5 = 21/72 hours = 7/24 hours -------------- b) How far is it from Elda's home to Niabi's house? --> 21/16 km each way.

Quadratic_Equations/593997: a rocket is launched from an 18-foot cliff with an initial velocity of 80 feet per second. the height above the ground of the rocket t seconds after launch is given by the equation h= -16^2+80t+18. hjow long after the rocket is launched will it hit the ground? round your answer to the nearest tenth. 1 solutions Answer 376580 by Alan3354(30993)   on 2012-04-01 12:10:56 (Show Source): You can put this solution on YOUR website! a rocket is launched from an 18-foot cliff with an initial velocity of 80 feet per second. the height above the ground of the rocket t seconds after launch is given by the equation h= -16^2+80t+18. hjow long after the rocket is launched will it hit the ground? round your answer to the nearest tenth. ------------- It's when h = 0. h= -16^2+80t+18 = 0 Solve for t. --------------- Why is this called a rocket? It has no engine, doesn't accelerate.

Miscellaneous_Word_Problems/593985: When a screen is placed 3 metres from a projector, the picture occupies 3 square metres. How large will the picture be when the projector is 5 metres from the screen? I have no idea what the answer would be. 5 seems too easy...Maybe they didn't give enough info? 1 solutions Answer 376575 by Alan3354(30993)   on 2012-04-01 11:00:17 (Show Source): You can put this solution on YOUR website! When a screen is placed 3 metres from a projector, the picture occupies 3 square metres. How large will the picture be when the projector is 5 metres from the screen? ------------------ Both sides of the picture will be 5/3 as big. 3*(5/3)*(5/3) = 75/9 = 25/3 sq meters

Travel_Word_Problems/593998: A car traveled 60 kilometers. About how many miles did the car travel? 1 solutions Answer 376574 by Alan3354(30993)   on 2012-04-01 10:54:14 (Show Source): You can put this solution on YOUR website! A car traveled 60 kilometers. About how many miles did the car travel? ------ ~37.3 miles

Angles/593995: If I want to simply Tan 33pi/4 using related acute angle how would I do it? 1 solutions Answer 376573 by Alan3354(30993)   on 2012-04-01 10:33:54 (Show Source): You can put this solution on YOUR website! If I want to simply Tan 33pi/4 using related acute angle how would I do it? ----------- 2pi is a revolution 33pi/4 = 8pi + pi/4 --> pi/4

Linear_Algebra/593991: Use the elimination method to solve the following system of equations 4x – 2y – z = –5 x – 3y + 2z = 3 3x + y – 2z = –5 1 solutions Answer 376569 by Alan3354(30993)   on 2012-04-01 09:46:27 (Show Source): You can put this solution on YOUR website! Use the elimination method to solve the following system of equations 4x – 2y – z = –5 x – 3y + 2z = 3 3x + y – 2z = –5 ------------------- Multiply the 1st eqn by 2, then eliminate the z terms. Then it's only x & y.

Quadratic_Equations/593994: Help! I find myself getting confused when working with negative numbers. Can someone help with this problem and also explain it as well. Thanks so much! Write a quadratic equation in the variable x having the given numbers as solutions. Write the equation in standard form, ax^2+bx+c=0. The solutions are; -11,7. 1 solutions Answer 376567 by Alan3354(30993)   on 2012-04-01 09:44:56 (Show Source): You can put this solution on YOUR website! Write a quadratic equation in the variable x having the given numbers as solutions. Write the equation in standard form, ax^2+bx+c=0. The solutions are; -11,7. -------------- (x - (-11))*(x - 7) = 0

Points-lines-and-rays/593992: This is the question that I am having difficulty with. Write the standard form of the equation from the line that passes through points (-6,-8) and (-4,-11). I have found the slope = -3/2 and I can get through the next step in slope intercept form y=-3/2x -17 but then I get stuck. HELP!!! 1 solutions Answer 376566 by Alan3354(30993)   on 2012-04-01 09:39:13 (Show Source): You can put this solution on YOUR website! Write the standard form of the equation from the line that passes through points (-6,-8) and (-4,-11). I have found the slope = -3/2 ----------- Use y = mx + b and either point to find b, the y-intercept --- -8 = (-3/2)*(-6) + b b = -17 ---- The eqn is y = (-3/2)x - 17 3x + 2y = -34 in standard form

Rectangles/593983: A rectangle measures 12cm by 5cm. how long is its diagonal? 1 solutions Answer 376564 by Alan3354(30993)   on 2012-04-01 08:50:03 (Show Source): You can put this solution on YOUR website! A rectangle measures 12cm by 5cm. how long is its diagonal? ------------

Quadratic_Equations/593595: If a stone is tossed from the top of a 230 meter building, the height of the stone as a function of time is given by h(t) = -9.8t^2 – 10t + 230, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer. 1 solutions Answer 376563 by Alan3354(30993)   on 2012-04-01 08:47:31 (Show Source): You can put this solution on YOUR website! If a stone is tossed from the top of a 230 meter building, the height of the stone as a function of time is given by h(t) = -9.8t^2 – 10t + 230, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer. -------------- The other tutor got the right answer, ~ 4.36 seconds, but if you're on Earth, the equation is h(t) = -4.9t^2 – 10t + 230

Equations/593810: 4x-8y=3 4x-8y=4 solve for the elimination method 1 solutions Answer 376478 by Alan3354(30993)   on 2012-03-31 12:42:41 (Show Source): You can put this solution on YOUR website! 4x-8y=3 4x-8y=4 solve for the elimination method ----------- 4x-8y=3 4x-8y=4 -------- Subtract 0 = -1 --> inconsistent, no solution

Polygons/593823: How to find the area of a regular polygon, it is a triangle with side measuring 6 inches? 1 solutions Answer 376477 by Alan3354(30993)   on 2012-03-31 12:40:03 (Show Source): You can put this solution on YOUR website! How to find the area of a regular polygon, it is a triangle with side measuring 6 inches? ------------ Given the side length, for any regular polygon n = # of sides, s = side length

Polygons/593826: What is the slope of a binomial 2x+3? 1 solutions Answer 376476 by Alan3354(30993)   on 2012-03-31 12:38:23 (Show Source): You can put this solution on YOUR website! What is the slope of a binomial 2x+3? -------------- A binomial doesn't have a slope. Lines have slopes.

Numbers_Word_Problems/593829: I am odd I am a 2 digit number The sum of my digits is 8 1 solutions Answer 376475 by Alan3354(30993)   on 2012-03-31 12:37:29 (Show Source): You can put this solution on YOUR website! I am odd I am a 2 digit number The sum of my digits is 8 --------- 71, 53, 35, 17

Linear-equations/593838: (-7, -5) and (-3, 1)? 1 solutions Answer 376474 by Alan3354(30993)   on 2012-03-31 12:36:30 (Show Source): You can put this solution on YOUR website! (-7, -5) and (-3, 1)? ----------- What about them?