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# Recent problems solved by 'nerdybill'

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 Pythagorean-theorem/205196: Measure the distance of the diagonal (corner to corner) of the screen on your computer monitor to the nearest tenth of a centimeter or six tenths of a inch. Measure the height of the screen the vertical as well. Use the pythagorean theorem to find the horizontal. 13in diagonal and 8 in. high? I cannot get this. Ty in advance judy 1 solutions Answer 154894 by nerdybill(7003)   on 2009-08-02 23:16:26 (Show Source): You can put this solution on YOUR website! Measure the distance of the diagonal (corner to corner) of the screen on your computer monitor to the nearest tenth of a centimeter or six tenths of a inch. Measure the height of the screen the vertical as well. Use the pythagorean theorem to find the horizontal. 13in diagonal and 8 in. high? . The "vertical" and the "horizontal" measurements represents the sides while the "diagonal" is the hypotenuse. . Let h=horizontal then h^2 + 8^2 = 13^2 h^2 + 64 = 169 h^2 = 105 h = 10.25 inches (horizontal length)
 Radicals/205095: Hi. I am having trouble with this problem: Expressed in a + bi form, 5/ 3 + i is equuivalent to... A) 15 - 5i, B) (3/2) - (1/2i), C) (5/3) - 5i, D) (15/8) - (5/8i) 1 solutions Answer 154813 by nerdybill(7003)   on 2009-08-02 10:06:12 (Show Source): You can put this solution on YOUR website!Answer is B . Multiply by (3-i)/(3-i): 5/(3+i) * (3-i)/(3-i) = 5(3-i)/(3+i)(3-i) = 5(3-i)/(9-3i+3i+1) = 5(3-i)/(9+1) = 5(3-i)/10 = (15-5i)/10 = 15/10 - 5i/10 = (3/2) - (1/2)i
 Radicals/205096: I am having trouble with this equation: 5/ (3 + i) is equivalent to what in a + bi form. 1 solutions Answer 154812 by nerdybill(7003)   on 2009-08-02 10:04:20 (Show Source): You can put this solution on YOUR website!5/ (3 + i) is equivalent to what in a + bi form. . Multiply by (3-i)/(3-i): 5/(3+i) * (3-i)/(3-i) = 5(3-i)/(3+i)(3-i) = 5(3-i)/(9-3i+3i+1) = 5(3-i)/(9+1) = 5(3-i)/10 = (15-5i)/10 = 15/10 - 5i/10 = (3/2) - (1/2)i (this is the form they want)
 Square-cubic-other-roots/205049: I need help figuring out (2+the square root of 3)(3-the square root of three) Calculators did not help solve the answer. I tried the foil method but I am getting stuck on how to foil square roots.. Please help me. I would appreciate it very much.1 solutions Answer 154775 by nerdybill(7003)   on 2009-08-01 17:30:42 (Show Source): You can put this solution on YOUR website! . Your first instinct with FOIL is correct:
 Pythagorean-theorem/204918: The diagonal of a square is 42.5 cm. Calculate the perimetre and area of the square.1 solutions Answer 154670 by nerdybill(7003)   on 2009-07-31 08:52:28 (Show Source): You can put this solution on YOUR website! The diagonal of a square is 42.5 cm. Calculate the perimetre and area of the square. . Let x = length of one side of the square then from Pythagorean theorem we have: x^2 + x^2 = 42.5^2 2x^2 = 1806.25 x^2 = 903.125 x = 30.052 . Perimeter = 4x = 120.208 cm Area = x^2 = 903.125 sq cm
 Percentage-and-ratio-word-problems/204919: Paolo's monthly salary is 1 3/7 that of Francesca's. Francesca's monthly salary is 7/5 of Dante's. What fraction of Paulo's earnings is Dante's?1 solutions Answer 154668 by nerdybill(7003)   on 2009-07-31 08:47:49 (Show Source): You can put this solution on YOUR website! Paolo's monthly salary is 1 3/7 that of Francesca's. Francesca's monthly salary is 7/5 of Dante's. What fraction of Paulo's earnings is Dante's? . Let D = Dante's salary and P = Paolo's monthly salary then (7/5)D = Francesca's salary . So, Paolo's monthly salary is: (1+3/7)(7/5)D =P (7/7+3/7)(7/5)D =P (10/7)(7/5)D =P (10/1)(1/5)D =P (2/1)(1/1)D =P (2)D =P D = (1/2)P . So, Dante's salary is 1/2 of Paulo's
 Equations/204912: Please can someone help me solve this problem: Write the standard equation of the circle passing through (2,5) with the center at (-2,-3).1 solutions Answer 154665 by nerdybill(7003)   on 2009-07-31 02:16:14 (Show Source): You can put this solution on YOUR website!Write the standard equation of the circle passing through (2,5) with the center at (-2,-3). . Equation of a circle: (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center r is the radius . The problem gives the center at (2,5) Plugging that into our formula we have: (x-2)^2 + (y-5)^2 = r^2 The only thing we need is the radius. Get this from the distance between (2,5) and (-2,-3): d = sqrt[(x2-x1)^2 + (y2-y1)^2] d = sqrt[(2+2)^2 + (5+3)^2] d = sqrt[(4)^2 + (8)^2] d = sqrt[16 + 64] d = sqrt[100] d = 10 (this is our radius) . so now we finally get: (x-2)^2 + (y-5)^2 = 10^2
 Quadratic_Equations/204830: I am having problems with this question, please could you help me to understand it? I open a bottle of champagne and release the cork vertically from the bottle. The height in metres of the cork above the level of the ground at time (t) seconds is modelled by the equation h = 1 + 8t - 5t^2. a) find the height of the cork after 0.8s....i have the answer of 4.2m for this. b) find the time when the cork is at ground level (h = 0)......i have the answer of 1.72s for this. c) explain what the maximum value of t is for which this function is a plausible model for the height of the cork?....i don't understand this question. hope you can help me by explaining how to do this thank you Dawn 1 solutions Answer 154588 by nerdybill(7003)   on 2009-07-30 09:39:26 (Show Source): You can put this solution on YOUR website!h = 1 + 8t - 5t^2. a) find the height of the cork after 0.8s....i have the answer of 4.2m for this. Correct. b) find the time when the cork is at ground level (h = 0)......i have the answer of 1.72s for this. Correct. c) explain what the maximum value of t is for which this function is a plausible model for the height of the cork?....i don't understand this question. hope you can help me by explaining how to do this . By inspection of: h = 1 + 8t - 5t^2 Rewritten as: h = -5t^2 + 8t + 1 . We see that is is a parabola and it opens downward (upside down U). We can tell by looking at the coefficient associated with the t^2 term (-5) -- since it is negative, think "sad face". Because of this, we now know that the VERTEX of the parabola is your maximum height/time pair. There are several ways to find this vertex. One way is to find the "axis of symmetry" t = -b/2a = -8/(2(-5)) = -8/(-10) = 8/10 = 4/5 = .8 seconds . Height, at that time is: h = -5t^2 + 8t + 1 h = -5(.8)^2 + 8(.8) + 1 h = 4.2m Which is "part a" of this problem.
 Polynomials-and-rational-expressions/204815: Factor the polynomial expression. Write each factor as a polynomial in descending order. x2 + 8x + 15 1 solutions Answer 154587 by nerdybill(7003)   on 2009-07-30 09:26:02 (Show Source): You can put this solution on YOUR website!Factor the polynomial expression. Write each factor as a polynomial in descending order. x2 + 8x + 15 . (x+5)(x+3)
 Miscellaneous_Word_Problems/204753: A candy shop mixes nuts worth \$1.10 per pound with another variety worth \$0.80 per pound in order to make 42 lb of a mixture worth \$0.90 per pound. How many pounds of each kind of nut should be used?1 solutions Answer 154528 by nerdybill(7003)   on 2009-07-29 15:39:21 (Show Source): You can put this solution on YOUR website! A candy shop mixes nuts worth \$1.10 per pound with another variety worth \$0.80 per pound in order to make 42 lb of a mixture worth \$0.90 per pound. How many pounds of each kind of nut should be used? . Let x = amount of \$1.10 per pound nuts used then 42-x = amount of \$0.80 per pound nuts uses . 1.10x + .80(42-x) = .90(42) 1.10x + 33.6 - .80x = 37.8 .30x + 33.6 = 37.8 .30x = 4.2 x = 14 pounds (\$1.10 per pound nuts) . \$0.80 nuts: 42-x = 42-14 = 28 pounds (\$0.80 per pound nuts)
 Geometry_Word_Problems/204694: Hi ther thanks again ur a great helppin hand .Here is the question- the volume of a sphere is given by V=4/3TTR^3where R= the radius of the sphere. If the radius is decreased by 25%, find the change in the volume.1 solutions Answer 154483 by nerdybill(7003)   on 2009-07-29 04:30:26 (Show Source): You can put this solution on YOUR website!the volume of a sphere is given by V=4/3TTR^3where R= the radius of the sphere. If the radius is decreased by 25%, find the change in the volume. . Original volume: V=(4/3)(pi)R^3 . If radius = R - .25R = (3/4)R V=(4/3)(pi)[(3/4)R]^3 V=(3/4)^3(4/3)(pi)R^3 V=(27/64)(4/3)(pi)R^3 . Comparing the original to the one above, we find that the change in volume will be 27/64 of the original volume
Quadratic_Equations/204672: Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?

1 solutions

Answer 154480 by nerdybill(7003)   on 2009-07-28 23:48:07 (Show Source):
You can put this solution on YOUR website!
Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?
.
Drawing a diagram of the problem will help you "see" how to approach it.
.
Let w = width of porch
then
"area of house" = "area of porch
120 * 160 = [(120+2w)(160+2w)] - (120 * 160)
19200 = [(120+2w)(160+2w)] - 19200
38400 = (120+2w)(160+2w)
38400 = 19200+240w+320w+4w^2
0 = -19200+560w+4w^2
0 = 4w^2+560w-19200
0 = w^2+140w-4800
Solve for w using the quadratic equation we get:
w = {28.489, -168.489}
Toss out the negative solution leaves us with:
w = 28.489 meters
.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=38800 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 28.488578017961, -168.488578017961. Here's your graph:

 Polynomials-and-rational-expressions/204682: This question is from textbook I need help factoring 12x squared+19x+41 solutions Answer 154478 by nerdybill(7003)   on 2009-07-28 22:47:12 (Show Source): You can put this solution on YOUR website! I need help factoring 12x squared+19x+4 . Apply the "ac method": We get (3x + 4)(4x + 1)
 Geometry_Word_Problems/204661: Sam is building a cabinet. The materials that he needs cost \$480. To determine the price of the cabinet for his customer, Sam charges 30% more than the cost of the materials. Sam asks for a downpayment of 40% of the total before the work begins. The costumer pays the balance when the job is finished.1 solutions Answer 154477 by nerdybill(7003)   on 2009-07-28 22:42:42 (Show Source): You can put this solution on YOUR website! Sam is building a cabinet. The materials that he needs cost \$480. To determine the price of the cabinet for his customer, Sam charges 30% more than the cost of the materials. Sam asks for a downpayment of 40% of the total before the work begins. The costumer pays the balance when the job is finished. . Price of the cabinet (to the customer) is: "cost of materials" + "30% of cost of materials" 480 + .30(480) = 480(1+.30) = 480(1.30) = \$624 (cost of cabinet) . Down payment (due at start of work): .40(624) = \$249.60 . Amount due at completion: 624-249.60 = \$374.4
 Equations/204564: please help me find the valiue of the letter X: 1 solutions Answer 154412 by nerdybill(7003)   on 2009-07-28 11:36:02 (Show Source): You can put this solution on YOUR website! Begin by multiplying both sides by 5^x Next, multiply both sides by 10: Take log base 5 of both sides:
 Exponents-negative-and-fractional/204535: x^(-2)=161 solutions Answer 154399 by nerdybill(7003)   on 2009-07-28 09:22:48 (Show Source): You can put this solution on YOUR website!x^(-2)=16 Is equivalent to: 1/x^2 = 16 1 = 16x^2 1/16 = x^2 sqrt(1/16) = x +-1/4 = x (that's plus or minus 1/4)
 logarithm/204536: I have been having a really hard problem with these logs 1. Log base 8 X=1/3 2. Log e^x^2=125 3. Solve for X: Log(5-2x)=log (3x+1) 4. Solve for X: Log(x+1)-Log(x-1)=11 solutions Answer 154398 by nerdybill(7003)   on 2009-07-28 09:20:46 (Show Source): You can put this solution on YOUR website!1. Log base 8 X=1/3 x = 8^(1/3) x = 2 . 2. Log e^x^2=125 x^2 = ln(125) x^2 = 4.8283 x = 2.197 . 3. Solve for X: Log(5-2x)=log (3x+1) 5-2x = 3x+1 5 = 5x+1 4 = 5x 4/5 = x 0.8 = x . 4. Solve for X: Log(x+1)-Log(x-1)=1 Log[(x+1)/(x-1)]=1 (x+1)/(x-1)= 10^1 (x+1)/(x-1)= 10 (x+1) = 10(x-1) x+1 = 10x-10 1 = 9x-10 11 = 9x 11/9 = x 1.222 = x
 Geometry_Word_Problems/204538: This question is from textbook In a triangle, the first angle measures 3 times the second and the third measures 20 degress less than the second. find each angle's measure.1 solutions Answer 154396 by nerdybill(7003)   on 2009-07-28 09:14:44 (Show Source): You can put this solution on YOUR website! In a triangle, the first angle measures 3 times the second and the third measures 20 degress less than the second. find each angle's measure. . To answer this question, you need to know that the sum of the interior angles of any triangle is 180 degrees. . Let x = measure of second angle then 3x = measure of first angle 3x-20 = measure of third angle . x + 3x + 3x-20 = 180 7x-20 = 180 7x = 200 x = 28.57 degrees (second angle) . First angle: 3x = 3(28.57) = 85.71 degrees (first angle) . Third angle: 3x-20 = 3(28.57)-20 = 65.71 degrees (third angle)
Rational-functions/204250: How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it occurs.
I started the equation and found h.
a=-2 b=8 c=-5, so using the ormula -b/2a I got -8/2(-2) which gave me -8/-4 which gave me 2. h=2. Where do I go from here?
1 solutions

Answer 154213 by nerdybill(7003)   on 2009-07-26 13:12:57 (Show Source):
You can put this solution on YOUR website!
How do you complete this function equation f(x)=-2x^2+8x-5. I need to find the vertex h,k , compute h and k and graph the quadratic equation. Plus find the max value of f where it occurs.
I started the equation and found h.
a=-2 b=8 c=-5, so using the ormula -b/2a I got -8/2(-2) which gave me -8/-4 which gave me 2. h=2. Where do I go from here?
.
What you found:
-b/2a = 2
is the "axis of symmetry"
.
To find 'k', simply plug 2 back into the equation and solve:
f(x)=-2x^2+8x-5
f(2)=-2(2)^2+8(2)-5
f(x)=-8+16-5
f(x)=3
.
So, (h,k) = (2,3) vertex
.
To plot, looking at the 'a' coefficient (-2), we KNOW it is a parabola that opens downward. Use the "vertex" above and find two additional points to plot. The two additional points could be where the parabola crosses the x-axis:
0=-2x^2+8x-5
.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=24 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.775255128608411, 3.22474487139159. Here's your graph:

 Miscellaneous_Word_Problems/204225: respected sir, plz help me to solve this math prob. If the numbers x and y are added to set K {5, 1, 6, 4}, the mean will increase by 50%. What is the value of xsquare + 2xy+ysquare? ? waiting for yur reply. thanks u.1 solutions Answer 154190 by nerdybill(7003)   on 2009-07-26 08:23:35 (Show Source): You can put this solution on YOUR website!If the numbers x and y are added to set K {5, 1, 6, 4}, the mean will increase by 50%. What is the value of xsquare + 2xy+ysquare? ? . Calculate "mean" in original set {5, 1, 6, 4}: (5+1+6+4)/4 = 16/4 = 4 . From: "the mean will increase by 50%" we get: (x+y+5+1+6+4)/6 = 4 + .50(4) (x+y+5+1+6+4)/6 = 4 + 2 (x+y+5+1+6+4)/6 = 6 (x+y+16)/6 = 6 (x+y+16) = 36 x+y = 20 . If we simply "square" both sides we get: (x+y)^2 = 20^2 (x+y)(x+y) = 20^2 Applying FOIL: x^2 + xy + xy + y^2 = 400 x^2 + 2xy + y^2 = 400 . Solution: 400
 Equations/204227: This question is from textbook Longman Mathematics for IGCSE Lauren is shooting at a target at afair. If she hits the target she recieves 50 pences,but if she misses she has to pay 20 pences for the shot. After 15 shots, Lauren finds she has made a profit of 1.20 pounds. How many hits has she had? 1 solutions Answer 154189 by nerdybill(7003)   on 2009-07-26 08:16:12 (Show Source): You can put this solution on YOUR website! Lauren is shooting at a target at afair. If she hits the target she recieves 50 pences,but if she misses she has to pay 20 pences for the shot. After 15 shots, Lauren finds she has made a profit of 1.20 pounds. How many hits has she had? . Let h = number of hits and m = number of misses . Since we have two unknowns, we'll need two equations. Equation 1 is derived from the fact she took 15 shots: h + m = 15 . Equation 2 is derived from the profit of 1.20 (100 pences is equivalent to 1 pound) (50/100)h - (20/100)m = 1.20 50h - 20m = 120 5h - 2m = 12 . Using the "substitution method", we solve equation 1 for m: h + m = 15 m = 15-h . We substitute the above into equation 2 and solve for h: 5h - 2m = 12 5h - 2(15-h) = 12 5h - (30-2h) = 12 5h - 30 + 2h = 12 7h - 30 = 12 7h = 42 h = 6 . Solution: 6 hits
 Miscellaneous_Word_Problems/204230: three goats eat 6 tin cans in 1 hour . how long should it take six goats to eat 3 tin cans ?1 solutions Answer 154188 by nerdybill(7003)   on 2009-07-26 08:04:53 (Show Source): You can put this solution on YOUR website!three goats eat 6 tin cans in 1 hour . how long should it take six goats to eat 3 tin cans ? . First determine what ONE goat can do: 6 tins per 1 hour per 3 goats For 1 goat 2 tins per 1 hour . Let t = time it takes then 6(2/1)t = 3 (12)t = 3 t = 3/12 t = 1/4 hour (or 15 minutes)
 Rectangles/204200: The area of a rectangle is 6, and its diagonal is sqrt{37}. Find its dimensions and perimeter1 solutions Answer 154171 by nerdybill(7003)   on 2009-07-25 19:34:47 (Show Source): You can put this solution on YOUR website! The area of a rectangle is 6, and its diagonal is sqrt{37}. Find its dimensions and perimeter . Let x = width and y = length . From Pythagorean theorem x^2 + y^2 = 37 (equation 1) . From the area: xy = 6 (equation 2) Solve equation 2 for y: y = 6/x . Substitute aboe into equation 1 and solve for x: x^2 + y^2 = 37 x^2 + (6/x)^2 = 37 x^2 + (36/x^2) = 37 x^4 + 36 = 37x^2 x^4 - 37x^2 + 36 = 0 (x^2-36)(x^2-1) = 0 x = {1, 6} . Therefore, dimensions are 1 feet by 6 feet Perimeter: 2(6+1) = 14 feet
 Volume/204154: Find the volume. Round to the nearest whole number, if necessary. Cylindrical grain silo with hemispherical top. Where the heighth of the cylinder is 11 ft. and the diameter is 62 ft. I hope this is understandable without the picture. Thank you for your time and consideration of this math problem.1 solutions Answer 154116 by nerdybill(7003)   on 2009-07-25 08:26:47 (Show Source): You can put this solution on YOUR website! Find the volume. Round to the nearest whole number, if necessary. Cylindrical grain silo with hemispherical top. Where the heighth of the cylinder is 11 ft. and the diameter is 62 ft . Volume of cylinder: (pi)r^2h = (3.14)31^2*11 = 33192.94 cubic feet . Volume of hemisphere: (1/2)(4/3)(pi)r^3 = (1/2)(4/3)(3.14)31^3 = (4/6)(3.14)31^3 = 62362.49 cubic feet . Total = 33192.94 + 62362.49 = 95555.43 = 95555 cubic feet
 Volume/204157: Solve the problem. Use 3.14 as an approximation for π where appropriate. Find the volume of a tent having the shape of a rectangular solid of length 15 ft, width 15 ft, and height 9 ft topped by a rectangular pyramid of the same width and length with height 8 ft. (Round to the nearest hundredth unit.) Thank you tutors for all your help and time.1 solutions Answer 154114 by nerdybill(7003)   on 2009-07-25 08:16:40 (Show Source): You can put this solution on YOUR website!Consider the two shapes separately that makes up the tent: - volume of rectangle -- L*W*H - volume of triangular prism -- (1/2)BHL reference: http://www.mathsteacher.com.au/year9/ch14_measurement/19_prism/prism.htm . volume of rectangle: L*W*H = 15*15*9 = 2025 cubic feet . volume of triangle: (1/2)BHL = (1/2)15*8*15 = 900 cubic feet . Total volume = 2025+900 = 2925 cubic feet
 Polynomials-and-rational-expressions/203973: Ok, so I was told to 'factor the trinomial completly' with this problem... x^7-x^6-64x+64 ..... I think I am sapose to combine like terms so it would be in the form x^2+bx+c where x is one. So I combined them and got x-64x+64 and I know I have to factor but I am not sure if I can....because the product is a*c=64 and the sum is -64 and I am not sure what two numbers multiply together that equal 64 that also add together to equal -64. help? 1 solutions Answer 153905 by nerdybill(7003)   on 2009-07-23 06:37:12 (Show Source): You can put this solution on YOUR website!To factor, use "grouping" technique: x^7-x^6-64x+64 = (x^7-x^6)-(64x-64) = x^6(x-1)-64(x-1) = (x^6-64)(x-1) But wait, we still factor left term: = (x^3-8)(x^3+8)(x-1)
Graphs/203984: what 3 techniques can be used tp solve a quadratic equation? demonstrate these techniques on the eqution "x^2 -10x-39 =0"
1 solutions

Answer 153904 by nerdybill(7003)   on 2009-07-23 06:32:20 (Show Source):
You can put this solution on YOUR website!
Three techniques could be:
1. factoring
2. completing the square
.
1. factoring:
x^2 -10x-39 =0
(x-13)(x+3) = 0
x = {-3, 13}
.
2. completing the square
x^2 -10x-39 =0
x^2 -10x = 39
x^2 -10x+25 = 39+25
(x-5)^2 = 64
x-5 = +-8
x = 5+-8
x = {-3, 13}
.