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Exponential-and-logarithmic-functions/447735: 2^(5/2)- 2^(3/2)= ?
1 solutions

Answer 308196 by Gogonati(809) on 2011-05-10 19:02:33 (Show Source):

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= 2%5E%283%2F2%29%282%5E1-2%5E0%29=2%5E%283%2F2%29%2A%281%29=2sqrt%282%29

Polynomials-and-rational-expressions/447736: (x^6-x^5+x^4)/x^2
1 solutions

Answer 308192 by Gogonati(809) on 2011-05-10 18:54:31 (Show Source):

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= x%5E6%2Fx%5E2-x%5E5%2Fx%5E2%2Bx%5E4%2Fx%5E2=x%5E4-x%5E3%2Bx%5E2

Numbers_Word_Problems/446477: The sum of the squares of two consecutive natural numbers is 85. Determine the number.
1 solutions

Answer 307482 by Gogonati(809) on 2011-05-08 08:16:20 (Show Source):

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Solve the equation: x%5E2%2B%28x%2B1%29%5E2=85

. Set the equation to zero:
2x%5E2%2B2x-84=0

The solution is: x=-7 which is rejected because it is not natural number, and
x=6 which is the right solution.
Answer:Two consecutive natural numbers are 6 and 7.

Permutations/446479: A cow costs seven times as much as goat for 84000 i can buy 18 more goats than cows,How much does a goat cost?
1 solutions

Answer 307480 by Gogonati(809) on 2011-05-08 08:00:15 (Show Source):

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Let x the price of a goat, then the price of a cow is 7x.
With $84000 we can buy 84000%2Fx

goats or

cows
Now write the equation; 84000%2Fx=84000%2F7x%2B18

, solving this equation find:
7%2A84000-84000=7%2A18x

Answer:The price of a goat is $4000.

Square-cubic-other-roots/446475: hey my name is farah i want help in my homework i want to know how can you solve those square root cubic y^3-64 and 1000x^3-27
1 solutions

Answer 307477 by Gogonati(809) on 2011-05-08 07:47:04 (Show Source):

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y%5E3-64=y%5E3-4%5E3=%28y-4%29%28y%5E2%2B4y%2B16%29

1000x%5E3-27=%28%2810x%29%5E3-3%5E3%29=%2810x-3%29%28100x%5E2%2B30x%2B9%29

Sequences-and-series/445978: simplify : 2i+7/8-3i

1 solutions

Answer 307153 by Gogonati(809) on 2011-05-06 15:33:03 (Show Source):

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2i%2B7%2F8-3i=-i%2B7%2F8

Rational-functions/446018: The asymptotes of the function g(x)= x+2/x^2+2x-3 are?
1 solutions

Answer 307152 by Gogonati(809) on 2011-05-06 15:30:43 (Show Source):

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g%28x%29=%28x%2B2%29%2F%28x-1%29%28x%2B3%29

, and its asymptotes are: x=1 and x=-3, because
lim%28x-%3E1%2C+g%28x%29%29=infinity

and

Triangles/446020: A 15 ft ladder is leaning against a house at a 60 degree angle with the ground. How far is the ladder from the house
1 solutions

Answer 307148 by Gogonati(809) on 2011-05-06 15:22:20 (Show Source):

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The leg of the right triangle opposite to the angel 30 degree is half of the
length of hypotenuse. In our case the distance of the ladder from the house is
15/2 ft=7.5 ft.

Polynomials-and-rational-expressions/446027: please help me.
2(3-x)<4x+8
1 solutions

Answer 307144 by Gogonati(809) on 2011-05-06 15:15:12 (Show Source):

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6-2x%3C4x%2B8

.
Answer:The solution set for this inequality is:(-1/3, infinity

Rational-functions/446023: Solve:
(x^2 - 1)^1/2 + (x^2 - 1)^-1/2 = 2
Any help would be very much appreciated.
Thank you
1 solutions

Answer 307141 by Gogonati(809) on 2011-05-06 15:11:01 (Show Source):

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%28x%5E2-1%29%5E%281%2F2%29%2B1%2F%28x%5E2-1%29%5E%281%2F2%29=5%2F2

,multiply both sides by %28x%5E2-1%29%5E%281%2F2%29

%28x%5E2-1%29%2B1=%285%2F2%29%28x%5E2-1%29%5E%281%2F2%29

x%5E2=%285%2F2%29%28x%5E2-1%29%5E%281%2F2%29

. Raise to the
second power both sides of equation: x%5E4=%2825%2F4%29%28x%5E2-1%29

, set the equation to
zero: 4x%5E4-25x%5E2%2B25=0

, substitute x%5E2=y

and get a quadratic equation:
4y%5E2-25y%2B25=0

, solving this equation we find:y=5 and y=5/4.
Knowing that, x%5E2=5

, get

and

Also from

, we get

and

Thus, the solution set is:[ sqrt%285%29

]

Quadratic_Equations/445946: 6^2+3x-18=0
1 solutions

Answer 307073 by Gogonati(809) on 2011-05-06 09:21:37 (Show Source):

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6x%5E2%2B3x-18=3%282x%5E2%2Bx-6%29=3%282x-3%29%28x%2B2%29=0

You easy can solve the equivalent
equation: 3%28x%2B2%29%283x-2%29=0

and find the solution: x=-2 and x=2/3.

Points-lines-and-rays/445924: The equation of a circle is (x - 3)2 + (y + 2)2 = 25. The point (8, -2) is on the circle.
What is the equation of the line that is tangent to the circle at (8, -2)?

1 solutions

Answer 307072 by Gogonati(809) on 2011-05-06 09:11:11 (Show Source):

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First we find the slope of the line which passes through the (8, -2) and
center of the circle (3,-2). This line contains the radius and is perpendicular to the tangent line at (8, -2).
The slope is: m=%28-2%2B2%29%2F%288-3%29=0

, since its slope is zero the line is parallel
to the x-axis, and its equation is: y=-2. The equation of the tangent line at
(8, -2) will be: x=8.
Answer:The equation of the line is x=8.

Polynomials-and-rational-expressions/445940: Can someone please help me with the problem below? Thank you very much.
Solve
(2+ √5) (2-√5)

1 solutions

Answer 307070 by Gogonati(809) on 2011-05-06 08:47:30 (Show Source):

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%282%2Bsqrt%285%29%29%282-sqrt%285%29%29=2%5E2-%28sqrt%285%29%29%5E2=4-5=-1

Polygons/445920: The measures of 5 of the interior angles of a hexagon are: 130°, 120°, 80°, 160°, and 155°. What is the measure of the largest exterior angle?

1 solutions

Answer 307069 by Gogonati(809) on 2011-05-06 08:44:12 (Show Source):

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The sum of interior angels of hexagon is 720 degree, the measure of the unknown angel of hexagon will be:720-645=75 degree. The supplement of 75 degree will be the largest exterior angle of our hexagon thus,180-75=105 degree.

expressions/445911: Given that 8^x-1/3^2x = 2^3x+1/54^x , evaluate 6^x .
1 solutions

Answer 307068 by Gogonati(809) on 2011-05-06 08:33:33 (Show Source):

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Dividing both sides by: -3%5E%28-2x%29

, we get:

1=-3%5E%28-3x%29%2F%282%5Ex%2A3%5E%28-2x%29%29

Polygons/445841: the shape is a pentagon. if you have an apothem of 6 and your area of the the shape is 130.8 cm 2[ squared ] how would you find the perimeter?
1 solutions

Answer 307063 by Gogonati(809) on 2011-05-06 07:32:46 (Show Source):

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The area of a regular pentagon is given by formula: A=%281%2F2%29%2Ap%2Aa

, where p is
the perimeter and a the apothem.Substituting in our formula we have:
130.8=%281%2F2%29%2A6%2Ap

cm.

Polynomials-and-rational-expressions/445447: The area of a triangle is 270. It has a base of 15 and a height of 12x. What is the area of a circle with a radius of 2x?
1 solutions

Answer 306923 by Gogonati(809) on 2011-05-05 14:59:13 (Show Source):

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The area of triangle is half of the base and height product.
270=%281%2F2%2915%2A12x

, solving this equation we get: 2x=270%2F45=6+cm

The area of the circle with radius 6cm is: A=pi%2Ar%5E2+=pi%2A6%5E2=36%2Api

cm^2.

Trigonometry-basics/445499: find all solutions on the interval 0 ≤x≤2pi : sin^(2)x-3cos^(2)x=0
1 solutions

Answer 306919 by Gogonati(809) on 2011-05-05 14:47:33 (Show Source):

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%28sinx%292-3%28cosx%29%5E2=0

, substitute %28sinx%29%5E2=1-%28cosx%29%5E2

, and get:
1-%28cosx%29%5E2-3%28cosx%29%5E2=0

.
The last equation is equivalent with two equations:
cosx=1%2F2

and

. The solution for the first equation is:
x=pi%2F3

and

. The solution for the second equation is:
x=2pi%2F3

and

Polynomials-and-rational-expressions/445519: (2s^2 - 9y)(2s^2 + 9y)
1 solutions

Answer 306913 by Gogonati(809) on 2011-05-05 14:28:59 (Show Source):

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%282s%5E2-9y%29%282s%5E2%2B9y%29=4s%5E4-81y%5E2

Expressions-with-variables/445526: 125x^3+216
1 solutions

Answer 306911 by Gogonati(809) on 2011-05-05 14:25:52 (Show Source):

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125x%5E3%2B216=%285x%29%5E3%2B6%5E3=%285x%2B6%29%2825x%5E2-30x%2B36%29

Volume/443127: A sphere and a cube have same volume. Find the ratio of the lenght of the side of the cube to the radius of the sphere.
1 solutions

Answer 305692 by Gogonati(809) on 2011-05-01 08:28:24 (Show Source):

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As you know the volume of the sphere with radius r is: V%5B1%5D=%284%2F3%29%28pi%29r%5E3

, and
the volume of the cube with length a is: V%5B2%5D=a%5E3

.
To find the ratio a%2Fr

, we know that V%5B2%5D=V%5B1%5D

, substituting:
a%5E3=%284%2F3%29%28pi%29r%5E3

, and,
a/r=cubed root of 4%2A%28pi%29%2F3

a%2Fr=%284%2A%28pi%29%2F3%29%5E%281%2F3%29=1.66

Surface-area/443139: Sean drew a circle with an area of 254.34 square centimeters.What is the diameter of Sean's circle.
1 solutions

Answer 305689 by Gogonati(809) on 2011-05-01 08:05:28 (Show Source):

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As you know the area of the circle given by the formula: A=%28pi%29r%5E2

, where r
is the radius of the circle.Substitute and get: 254.34=3.14%2Ar%5E2

, and

, where D is the
diameter of the circle.

Volume/443142: what is the length and width of a square prism that`s volume is 0.5L
1 solutions

Answer 305683 by Gogonati(809) on 2011-05-01 07:51:47 (Show Source):

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As you know 1+L=1+dm%5E3=1000+cm%5E3

and

.
The volume of square prism is: V=a%5E3=500cm%5E3

, where a is the dimension of
square prism: a=cubed root of 500, a=7.94 cm.

Quadratic_Equations/443133: What is the domain and sketch the graph of the reducible function.
f(x) = (x^2 -25) / (2x -10).

1 solutions

Answer 305679 by Gogonati(809) on 2011-05-01 07:41:41 (Show Source):

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In my opinion since the function is reducible, first we reduce the function and after find the domain and sketch the graph.
f%28x%29=%28x%2B5%29%28x-5%29%2F2%28x-5%29=%281%2F2%29%28x%2B5%29

f%28x%29=%28x%2B5%29%28x-5%29%2F2%28x-5%29=%281%2F2%29%28x%2B5%29

, which is the linear function on its
slope-intercept form. We know its domain is the set of all real numbers and the graph the line:y=x/2+5/2.
graph%28300%2C+300%2C+-8%2C+5%2C+-5%2C+5%2C+%28x%2F2%29%2B%285%2F2%29%29

graph%28300%2C+300%2C+-8%2C+5%2C+-5%2C+5%2C+%28x%2F2%29%2B%285%2F2%29%29

Quadratic_Equations/443130: Hey guys,
So I was on your website, practicing solving quadratics by completing the square (as you do) and I ran in to a problem. I had done this:
2x%5E2%2B12x%2B20=0

(where the nines are b/2^2)
%28x%2B3%29%5E2=-1+

What do I do now that there's a negative number on the right side? I can't square root both! HELP!!

1 solutions

Answer 305674 by Gogonati(809) on 2011-05-01 07:29:11 (Show Source):

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If you find the determinant of this quadratic equation D=6%5E2-4%2A1%2A10=-4%3C0

.
We answered that this quadratic equation has no real solution.
If you know the complex numbers you can find the complex roots.
x=3%2Bi

and

where

Angles/442472: What values are there of the six trigonometric functions of an angle Q in standard position whose terminal side passes through (1,2)?
1 solutions

Answer 305200 by Gogonati(809) on 2011-04-29 15:05:29 (Show Source):

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Since the terminal side passes through (1, 2), the legs of the right triangle are 1 and 2 and its hypotenuse is sqrt%281%5E2%2B2%5E2%29=sqrt%285%29

.If angel Q=x we get:
sinx=2%2Fsqrt%285%29

;

;

;

;

and

Radicals/442422: 4 sq rt 6/sq rt30 simplfy by rationalizing the denominator
1 solutions

Answer 305192 by Gogonati(809) on 2011-04-29 14:51:34 (Show Source):

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Travel_Word_Problems/442438: How long would it take for a one mile long frieght train going 15 m.ph. to go through a one mile tunnel?
1 solutions

Answer 305191 by Gogonati(809) on 2011-04-29 14:44:24 (Show Source):

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Since the train and the tunnel are respectively one mile long, the train must travel two miles to pass the tunnel. Since its speed is 15 mph to travel 2 miles need 2/15 h or 8 minutes.

Inequalities/442469: -6< 1/4 (3-x)<12

1 solutions

Answer 305185 by Gogonati(809) on 2011-04-29 14:30:01 (Show Source):

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Multiply the double inequality by 4: -24+%3C+3-x+%3C+48

, adding -3 we get:
-27+%3C-x+%3C+45

, multiplying by -1 and reversing the signs of inequalities we
get the solution: -45+%3C+x+%3C+27

Numeric_Fractions/442467: What is the sum of the 7 over 8 and 1 over 4?
1 solutions

Answer 305180 by Gogonati(809) on 2011-04-29 14:19:29 (Show Source):

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Add the fractions: %287%2F8%29%2B%281%2F4%29=%287%2F8%29%2B%282%2F8%29=9%2F8

The sum is an improper fraction 9%2F8=1%2B%281%2F8%29

Graphs/442454: How do you graph
y is greater than x AND
y is less than -x
I have the answer, but I don't get it.
1 solutions

Answer 305176 by Gogonati(809) on 2011-04-29 14:15:06 (Show Source):

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y>x is an inequality, and its boundary line is y=x, which is the bisector of first and third quadrant.
y<-x is also an inequality, and its boundary line is y=-x, which is the bisector
of the second and fourth quadrant.
The solution set of y>x is the region above the line y=x, and the solution set of
y<-x is the region below the line y=-x.

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