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Numbers_Word_Problems/451121: absolute value of y2-3y is equal to 4.
1 solutions

Answer 310233 by Gogonati(809) on 2011-05-18 08:51:26 (Show Source):

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Base on the absolute value deffinition the equation abs%28y%5E2-3y%29=4

is
equivalent to the equations: y%5E2-3y=4

and

. We solve these
two equations:1) y%5E2-3y-4=0

, where y=-1 and y=4.
2) y%5E2-3y%2B4=0

, which has not real solution because the discriminant is
negative number.
answer: The solution of original equation is the set; {-1, 4}.

Equations/451119: Find the product.....
(4x+3)(6x^2)
1 solutions

Answer 310229 by Gogonati(809) on 2011-05-18 08:38:01 (Show Source):

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Using the distributive property we get:
%284x%2B3%296x%5E2=4x%2A6x%5E2%2B3%2A6x%5E2=24x%5E3%2B18x%5E2

Equations/451090: (4sqrt(3)-5)(2sqrt(3)+5)
(2sqrt(5)-6sqrt(7))(3sqrt(5)+sqrt(7))
Simplify
Thank you
1 solutions

Answer 310228 by Gogonati(809) on 2011-05-18 08:34:46 (Show Source):

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The first is for me the second is for you;
1)

Exponential-and-logarithmic-functions/451117: (a^4b^3)2/3
1 solutions

Answer 310227 by Gogonati(809) on 2011-05-18 08:27:10 (Show Source):

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Using the properties of power we can write:

Complex_Numbers/451113: (3+5i)/(8i)
1 solutions

Answer 310226 by Gogonati(809) on 2011-05-18 08:17:24 (Show Source):

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To divide complex numbers we multiply the nominator and denominator by the conjugate of the denominator:(Don't forget i%5E2=-1

)

Quadratic_Equations/451111: 10x^2= -100x
Please tell me how to solve this problem by factoring and doing 2 checks.
Thanks. SAL
I think the answer is x=0, x= -10. But, how do you do it?
1 solutions

Answer 310224 by Gogonati(809) on 2011-05-18 08:06:28 (Show Source):

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First set the equation to zero; 10x%5E2%2B100x=0

, factor 10x out and get:
10x%28x%2B10%29=0

. Use the fact that if ab=0 then a=0 or b=o to find the roots:
10x=0=> x=0 and x+10=0 => x=-10
Answer:The solution is x=0 and x=-10.
Check:1)10*0^2=-100*0 => 0=0; 2)10*10^2=-100*(-10)=> 1000=1000.

Rectangles/449977: If a tv is 24 inches in length and 18 inches wide, how big is the screen?

1 solutions

Answer 309553 by Gogonati(809) on 2011-05-16 08:26:51 (Show Source):

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The screen will be 30 inches: 24%5E2%2B18%5E2=30%5E2

Miscellaneous_Word_Problems/449981: The sum of the base and the height of a parallelogram is 24 in. Find the base and the height for which the area is a maximum.
1 solutions

Answer 309551 by Gogonati(809) on 2011-05-16 08:22:25 (Show Source):

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Let the base of parallelogram x inches, then the height will be 24-x inches, and
the area is A=x%2824-x%29=-x%5E2%2B24x=-%28x-12%29%5E2%2B144

A=x%2824-x%29=-x%5E2%2B24x=-%28x-12%29%5E2%2B144

, which represent a downward
parabola with vertex (12, 144), and the maximum area is 144 square inches.
If you have knowledges about derivatives, find the maximum value of the function
A=-x%5E2%2B24x

. Its derivative is -2x+24, and the maximum value
will be: -2x+24=0 for x=12.
Answer:The maximum area of the parallelogram will be, where the base and height are equal with 12 inches.

Equations/449983: IF x+y=4 y=x-8, what is the value of x?
1 solutions

Answer 309545 by Gogonati(809) on 2011-05-16 07:57:50 (Show Source):

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To find the value of x, substitute in the first equation y=x-8, and solve for x:
x%2Bx-8=4

Quadratic-relations-and-conic-sections/449974: whats the graphing form for this equation Center(-3,-6) Directrix x=-9
1 solutions

Answer 309544 by Gogonati(809) on 2011-05-16 07:54:01 (Show Source):

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First you need to find the equation of the parabola, where based on the data is
in the standard form: %28y-y%5B0%5D%29%5E2=4c%28x-x%5B0%5D%29

, and directrix x=-c or c=9.
Since its vertex is (-3, -6) the equation will be: %28y%2B6%29%5E2=36%28x%2B3%29

This parabola opens right because c=9>0, the vertex is (-3, -6), the axis is the
line y=-6 , the focus is (9, -6) and the directrix x=9.

Quadratic-relations-and-conic-sections/449665: write an equation of the given conic section with the givin informaton.
ellipse with center (1,-3) and vertices (1,2) and (1,-8) and co verticies (4,-3)and (-2,-3)
Thank you so much for all your help i really appreciate it!
1 solutions

Answer 309315 by Gogonati(809) on 2011-05-15 16:26:30 (Show Source):

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The equation of the ellipse with center (1, -3) is:
+%28x-1%29%5E2%2Fa%5E2%2B%28y%2B3%29%5E2%2Fb%5E2=1+

Since we have the endpoints of major and minor axis we can find their lengths:
2a=sqrt%28%281-1%29%5E2%2B%28-8-2%29%5E2%29=sqrt%28100%29=10

, thus a=5
2b=sqrt%28%28-2-4%29%5E2%2B%28-3%2B3%29%5E2%29=sqrt%2836%29=6

, thus b=3
The equation of ellipse is: %28x-1%29%5E2%2F25%2B%28y%2B3%29%5E2%2F9=1

Quadratic-relations-and-conic-sections/449573: Find the equation of the parabola with its vertex at the origin if its directrix is y=3
1 solutions

Answer 309310 by Gogonati(809) on 2011-05-15 16:05:51 (Show Source):

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As you know the directrix of the parabola x%5E2=4cy

is y=-c, since y=3, we get
3=-c or c=-3, and the equation of parabola will be: x%5E2=-12y

graph%28300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+%28-1%2F12%29%2Ax%5E2%29

test/449609: 2zy over y2 =14 over y
1 solutions

Answer 309306 by Gogonati(809) on 2011-05-15 15:50:04 (Show Source):

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2yz%2Fy%5E2=14%2Fy

,reducing the first term we get: 2z%2Fy=14%2Fy

=>
=>

, substituting z=7 we find y=1.

Polygons/449626: How many sides does a regular polygon have if the measure of an exterior angle is 24.
1 solutions

Answer 309301 by Gogonati(809) on 2011-05-15 15:39:32 (Show Source):

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As you know the sum of exterior angels of a regular polygon is 360 degree.
Let n the number of angels of polygon, then 24%2An=360

.
Answer:The polygon has 15 sides.

logarithm/449645: which of the following is equivalent to log base 4 of 64^x ?
1) 4^3x 2) 3^x 3) 4x 4) .25x 5) 3x
1 solutions

Answer 309298 by Gogonati(809) on 2011-05-15 15:32:06 (Show Source):

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Based on the definition of logarithmic and exponential functions we write:
log%284%2C+64%5Ex%29=y

.
Answer: log%284%2C+64%5Ex%29

, is equivalent to 3x.

Polynomials-and-rational-expressions/449634: simplify by removing factors of 1 z^2-9z+20/z^2+z-30
1 solutions

Answer 309295 by Gogonati(809) on 2011-05-15 15:24:13 (Show Source):

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First we factor the nominator and denominator of the rational expression and after reduce the same factors:
= %28z-5%29%28z-4%29%2F%28z-5%29%28z%2B6%29=%28z-4%29%2F%28z%2B6%29

%28z-5%29%28z-4%29%2F%28z-5%29%28z%2B6%29=%28z-4%29%2F%28z%2B6%29

Trigonometry-basics/449325: solve for theta in teh intervals 0 - 360
sin x cos x = cos x
1 solutions

Answer 309102 by Gogonati(809) on 2011-05-14 16:09:17 (Show Source):

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Dividing both sides by cosx we get sinx=1

, and its solution is x=pi%2F2

Polynomials-and-rational-expressions/449321: Find the volume of a cube if its surface area is 6x^2 + 36x + 54 square meters
1 solutions

Answer 309101 by Gogonati(809) on 2011-05-14 16:05:50 (Show Source):

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First we factor the polynomial of the surface area:
6x%5E2%2B36x%2B54=6%28x%5E2%2B6x%2B9%29=6%28x%2B3%29%5E2

, from this expression we conclude that the
dimension of the cube is (x+3) m, because the area of one side of the cube is
%28x%2B3%29%5E2

square meter, and the volume will be:
V=%28x%2B3%29%5E2%2A%28x%2B3%29=%28x%2B3%29%5E3m%5E3

Trigonometry-basics/449320: Prove that it is an identity
1) tan (1/2) A = csc A - cot A
1 solutions

Answer 309100 by Gogonati(809) on 2011-05-14 15:48:26 (Show Source):

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We know from trigonometry that tan%28x%2F2%29=%281-cosx%29%2Fsinx

, assuming x=A and
transforming the right side of the identity we get the left side:
cscx-cotx=1%2Fsinx-cosx%2Fsinx=%281-cosx%29%2Fsinx=tan%28x%2F2%29

Trigonometry-basics/448398: verify sinx+cotxcosx=cscx
1 solutions

Answer 308572 by Gogonati(809) on 2011-05-12 07:05:01 (Show Source):

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To verify this trigonometric identity we transform the left side until reach the
same expression as the right side:
= sinx%2B%28cosx%29%5E2%2Fsinx=%28%28sinx%29%5E2%2B%28cosx%29%5E2%29%2Fsinx=1%2Fsinx=cscx

sinx%2B%28cosx%29%5E2%2Fsinx=%28%28sinx%29%5E2%2B%28cosx%29%5E2%29%2Fsinx=1%2Fsinx=cscx

Trigonometry-basics/448396: simplify 1/(1-cosx) + 1/(1+cosx)
1 solutions

Answer 308570 by Gogonati(809) on 2011-05-12 06:57:29 (Show Source):

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=

Trigonometry-basics/448400: solve 2sin^2x- square root of 3 sinx=0
1 solutions

Answer 308569 by Gogonati(809) on 2011-05-12 06:51:30 (Show Source):

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2%28sinx%29%5E2-sqrt%283%29%2Asinx=0

, assuming sinx≠0 or x≠n*

,
divide both sides by sinx and get: 2sinx=sqrt%283%29

,
where its solution is: x=2n%2Api%2B%28pi%29%2F3

and

Trigonometry-basics/448402: solve sinxtanx-sinx=0
1 solutions

Answer 308568 by Gogonati(809) on 2011-05-12 06:37:41 (Show Source):

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sinxtanx-sinx=0

, assuming sinx≠0 or x≠n*

, divide
both sides of equation by sinx and get: tanx=1

, where its solution
is: x=n%2Api%2B%28pi%29%2F4

Exponents-negative-and-fractional/448461: reduce given fracion to lowest term
15z^(2)/-36z^(8)
1 solutions

Answer 308567 by Gogonati(809) on 2011-05-12 06:16:30 (Show Source):

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= %28-5%29%2F12z%5E6

Numbers_Word_Problems/447881: find the two-digit number whose units' digit is 5 more than its tens' digit and whose value equals 3 times the sum of these digits.
1 solutions

Answer 308316 by Gogonati(809) on 2011-05-11 08:18:05 (Show Source):

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Let the ten's be x, then its units are x+5 and the sum of digits is x+x+5=2x+5 and the value of a number will be:10x+x+5=11x+5. Since its value equals 3 times the sum of the digits we write the equation:
11x%2B5=3%282x%2B5%29

.The units are 2+5=7.
Answer: The two digit number is 27.

Linear-equations/447918: graph
y = -x^2 + 3
1 solutions

Answer 308307 by Gogonati(809) on 2011-05-11 07:55:40 (Show Source):

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graph%28300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+-x%5E2%2B3%29

Inverses/447941: Suppose f(x) = 2^(x^2) - 5, for x >=0.
find f^-1, the inverse of f. Determine the domain of f^-1.
compute f^(-11).
1 solutions

Answer 308305 by Gogonati(809) on 2011-05-11 07:52:30 (Show Source):

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Assume that y=2%5E%28x%5E2%29-5

, solve this equation for x: y-5=2%5E%28x%5E2%29

, interchange x and y and get the
inverse function: f%5E-1%28x%29=sqrt%28ln%28x-5%29%2Fln2%29

. The domain of this function is:
(5, infinity

). The value x=-11 is not included in its domain for this value
the function f%5E-1%28x%29

is undefined.

Inverses/447943: simplify
ln(1/e)^6-4t
1 solutions

Answer 308302 by Gogonati(809) on 2011-05-11 07:34:08 (Show Source):

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= ln%28e%5E%284t-6%29%29=%284t-6%29%2Alne=4t-6

Inequalities/447948: i need your help... can you graph this equation? y=-(x-4)^2+3
*state weather the graph opens upward or downwards?
*is the vertex of the graph a maximum or minimum point?
*find the vertex of the graph of the functon?
*what is the axis of symmetry?
*identify the transformation of the graph (how did you mave the parabola)?
1 solutions

Answer 308301 by Gogonati(809) on 2011-05-11 07:29:53 (Show Source):

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The graph is a downward parabola, its vertex is the point (4, 3) and the axis of symmetry is the line x=4.
To construct the graph we start from y=x%5E2

:1) reflect to the x-axis
y=-x%5E2

,
2)shift 4 units to the right y=-%28x-4%29%5E2%2C%29

shift 3 units up
y=-%28x-4%29%5E2%2B3

. See the graph below:
graph%28300%2C+300%2C+-2%2C+10%2C+-15%2C+5%2C+-x%5E2%2B8x-13%29

logarithm/447732: How do I solve 7^3b = 12^b+2? I don't know how to even start this problem... Thank you!
1 solutions

Answer 308201 by Gogonati(809) on 2011-05-10 19:19:43 (Show Source):

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= 3blog7=%28b%2B2%29log12

=>
=>

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

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Recent problems solved by 'Gogonati'