Question about Computers & Internet

A boat takes 2 hours to row 24 km downstream and 3 hours to row the same distance upstream.Find the speeds of the boat in still water and of the current.

Posted on Oct 29, 2009

If i am not mistaken you are saying the price was reduced by 20% per room hence here is the answers to your question.

Initially 24 rooms were rented at 28,800 for a total of 691200

AFTER THE 20% discount

You were already able to rent 30 rooms at 23040 for a total of 691200 hence you were able to rent 6 more rooms after the 20% discount

Posted on Oct 27, 2008

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Posted on Jan 02, 2017

Use the identity cos(2x)=2(cos(x))^2-1

cos(2x)+3=5cos(x) becomes 2(cos(x))^2-1+3=5cos(x)

Arrange a bit: 2(cos(x))^2-5cos(x)+2=0

Get rid of the 2-factor

(cos(x))^2-(5/2) cos(x)+1=0

This is a quadratic equation for the unknown U=cos(x)

U^2-(5/2)U+1=0

Solve it by factoring or with the quadratic equation formula. The solutions are** U=2 or U=1/2.**

Since U=cos(x), the root U=cox(x)=2 must be rejected.

What is left is cos(x)=(1/2). The solutions are x=60 or x=-60 plus or minus 360 degrees.

cos(2x)+3=5cos(x) becomes 2(cos(x))^2-1+3=5cos(x)

Arrange a bit: 2(cos(x))^2-5cos(x)+2=0

Get rid of the 2-factor

(cos(x))^2-(5/2) cos(x)+1=0

This is a quadratic equation for the unknown U=cos(x)

U^2-(5/2)U+1=0

Solve it by factoring or with the quadratic equation formula. The solutions are

Since U=cos(x), the root U=cox(x)=2 must be rejected.

What is left is cos(x)=(1/2). The solutions are x=60 or x=-60 plus or minus 360 degrees.

Apr 01, 2014 | SoftMath Algebrator - Algebra Homework...

Calcualte the slope of the line as

a=(7-(-11))/(10-(-5))=18/15=6/5

Use the fact that the line passes through one of the two points, for example (10,7)

7=(6/5)*10+b=12+b

Obtain b as b=7-12=-5

The equation of the line in functional form is y=(6/5)x-5

Multiply everything by 5 to clear the fraction

5y=6x-25 or 0=6x-5y-25

Finally, the equation in general form (standard?) is**6x-5y-25=0**.

Check the calculation by verifying that the point (10,7) lies on the line.

6(10)-5(7)-25=60-35-25=60-60=0 CHECKed!

Check that the second point (-5,-11) lies on the line also (if you want to)

6*(-5)-5*(-11)-25=-30+55-25=0

That checks OK.

a=(7-(-11))/(10-(-5))=18/15=6/5

Use the fact that the line passes through one of the two points, for example (10,7)

7=(6/5)*10+b=12+b

Obtain b as b=7-12=-5

The equation of the line in functional form is y=(6/5)x-5

Multiply everything by 5 to clear the fraction

5y=6x-25 or 0=6x-5y-25

Finally, the equation in general form (standard?) is

Check the calculation by verifying that the point (10,7) lies on the line.

6(10)-5(7)-25=60-35-25=60-60=0 CHECKed!

Check that the second point (-5,-11) lies on the line also (if you want to)

6*(-5)-5*(-11)-25=-30+55-25=0

That checks OK.

Dec 04, 2011 | Super Tutor Pre Algebra (ESDPALG)

**Solve (***x*+ 2)(*x*+ 3) = 12.

- It is very common for students to see this type
of problem, and say:

solve to get x = 10 and x = 9. That was easy!"

So, tempting though it may be, I cannot set each of the factors above equal to the other side of the equation and "solve". Instead, I first have to multiply out and simplify the left-hand side, then subtract the 12 over to the left-hand side, and re-factor. Only then can I solve.

- (

(

Jul 17, 2011 | H. B. Enterprises Quadratic Solver

This equation doesn't have whole number factors so you have to solve it by completing the square or using the quadratic equation. I used the quadratic equation and got the following answers.

[3 + sqrt(209)]/10 and [3 - sqrt(209)]/10

I hope this helps you out.

[3 + sqrt(209)]/10 and [3 - sqrt(209)]/10

I hope this helps you out.

Jul 05, 2011 | SoftMath Algebrator - Algebra Homework...

Definition

A mathematical statement used to evaluate a value. An equation can use any combination of mathematical operations, including addition, subtraction, division, or multiplication. An equation can be already established due to the properties of numbers (2 + 2 = 4), or can be filled solely with variables which can be replaced with numerical values to get a resulting value. For example, the equation to calculate return on sales is: Net income ÷ Sales revenue = Return on Sales. When the values for net income and sales revenue are plugged into the equation, you are able to calculate the value of return on sales.

There are many types of mathematical equations.

1. Linear Equations y= mx + b (standard form of linear equation)

2. Quadratic Equations y= ax^2+bx+c

3. Exponential Equations y= ab^x

4. Cubic Equations y=ax^3+ bx^2+cx+d

5. Quartic Equations y= ax^4+ bx^3+ cx^2+ dx+ e

6. Equation of a circle (x-h)^2+(y-k)^2= r^2

7. Constant equation y= 9 (basically y has to equal a number for it to be a constant equation).

8. Proportional equations y=kx; y= k/x, etc.

Jun 14, 2011 | Computers & Internet

If we assume the width of the frame is X. Then the one dimension of the framed picture will be 2X + 20 and the other dimension of the picture will be 2X + 34. We know the total area of the framed picture should be 640 in^2. Therefore:

(2X + 10) * (2X + 34) = 640

If you multiply this out you get:

4X^2 + 88X + 340 = 640

Subtract 640 from both sides:

4X^2 + 88X - 300 = 0

Divide both sides by 4:

X^2 + 22X - 75 = 0

Use the quadratic equation to solve for X, with A=1, B=22, C=75

X = [-22 +/- sqr(22^2-4*(-75)] /2

This reduces to:

(-22 +/- 48) / 2

The negative solution doesn't make sense in this case. Therefore: X = (-22 + 28) /2 = 6/3 = 3

Therefore the width of the frame should be 3 inches.

(2X + 10) * (2X + 34) = 640

If you multiply this out you get:

4X^2 + 88X + 340 = 640

Subtract 640 from both sides:

4X^2 + 88X - 300 = 0

Divide both sides by 4:

X^2 + 22X - 75 = 0

Use the quadratic equation to solve for X, with A=1, B=22, C=75

X = [-22 +/- sqr(22^2-4*(-75)] /2

This reduces to:

(-22 +/- 48) / 2

The negative solution doesn't make sense in this case. Therefore: X = (-22 + 28) /2 = 6/3 = 3

Therefore the width of the frame should be 3 inches.

Feb 16, 2011 | SoftMath Algebrator - Algebra Homework...

I'm assumeing the problem is 2x^2 - 19x+22 = 0, solve for x.

I don't see any easy to factor this so I'll either need to complete the square or use the quadratic equation.

Using the quadratic equation, where A = 2, B = -19, and C = 22

x = [-(-19) +/- squareroot( 19^2 - 4*2*22)] / (2*2) =

(19 +/- squareroot(185))/4 =

8.150367 or 1.349632

I don't see any easy to factor this so I'll either need to complete the square or use the quadratic equation.

Using the quadratic equation, where A = 2, B = -19, and C = 22

x = [-(-19) +/- squareroot( 19^2 - 4*2*22)] / (2*2) =

(19 +/- squareroot(185))/4 =

8.150367 or 1.349632

Feb 01, 2011 | SoftMath Algebrator - Algebra Homework...

let sqrt of y =x

y to the power negative 1/2 = 1/ sqrt y

so our equation becomes

( 6x + 1 / 6x ) = 37

36x^2 -222 x + 1 =0

the roots of above quadratic equation are

x1=6.1621

and x2 =.0045

therefore y = x^2

y = 6.1621^2 = 37.971

and y=.0045^2 = .00002025

pls rate the solution if it was helpful.post your doubts i f u have any

y to the power negative 1/2 = 1/ sqrt y

so our equation becomes

( 6x + 1 / 6x ) = 37

36x^2 -222 x + 1 =0

the roots of above quadratic equation are

x1=6.1621

and x2 =.0045

therefore y = x^2

y = 6.1621^2 = 37.971

and y=.0045^2 = .00002025

pls rate the solution if it was helpful.post your doubts i f u have any

Apr 21, 2010 | SoftMath Algebrator - Algebra Homework...

For this type of problem, a equals the constant cost of operation (monthly rent..etc) and b equals the cost to manufacture the items.

first equation: 320 = a + b(10)

second equation: 520 = a +b(20)

320 = a + 10b

520 = a + 20b subtract equation 2 from equation 1

-200 = -10b divide by -10

20 = b plug b into one of the equations

320 = a +(20)(10) multiply

320 = a +200 subtract 200

120 = a

Let me know if i need to explain further.

first equation: 320 = a + b(10)

second equation: 520 = a +b(20)

320 = a + 10b

520 = a + 20b subtract equation 2 from equation 1

-200 = -10b divide by -10

20 = b plug b into one of the equations

320 = a +(20)(10) multiply

320 = a +200 subtract 200

120 = a

Let me know if i need to explain further.

Dec 29, 2009 | Mathsoft StudyWorks! Mathematics Deluxe...

Hi there,

Say you have an equation x = 2y.

On a graph, you plot the points representing the values that fit into the equation.

X Y

2 1

4 2

6 3

etc.

And to throw a curve in there:

X Y

-2 -1

-4 -2

-6 -3

If have further questions repost, I'll be around for a while.

Hope it helps

Mike

Say you have an equation x = 2y.

On a graph, you plot the points representing the values that fit into the equation.

X Y

2 1

4 2

6 3

etc.

And to throw a curve in there:

X Y

-2 -1

-4 -2

-6 -3

If have further questions repost, I'll be around for a while.

Hope it helps

Mike

Nov 24, 2009 | The Learning Company Achieve! Math &...

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