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how many years it will take for the two accounts to reach the same balance. 1000 investment with a rate of 5.25% compounded continuously and 800 investment with a rate of 6.25% compounded continously. i got this far
1000e^.0525=800e^.0625
----------------------
1000e^.0525t=800e^.0625t You need the time in the exponents
--------------
Take the ln of both sides
ln(1000) + 0.0525t = ln(800) + 0.0625t
0.0625t - 0.0525t = ln(1000) - ln(800)
0.01t =~ 0.223144
t =~ 22.3144 years (assuming the int rates are annual)

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Hello,
There are 100 centimeters in meter. There are 1000 meters in 1 kilometer. Do you know from this data how to solve the problem? Try it and see. Good luck.
RJ Toftness
www.math=unlock.com

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(Note: A solution provided by another tutor has some very serious errors in it. The solution is not correct. The first part was correct. You do want to factor the denominators, use the factored denominators to find the lcd and you do want to write each fraction with the lcd for the denominator. But after that it goes very wrong. This is where I will start.)



lcd:

To avoid some common errors with subtractions, I am going to rewrite the expression as additions:

The first fraction already has the lcd as a denominator. The denominator of the second fraction is missing (x-2) so we will multiply its numerator and denominator by (x-2). The denominator of the third fraction is missing (3x+1) so we will multiply its numerator and denominator by (3x+1):

Multiply out the numerators but leave the denominators factored for now:

Now that the denominators are the same we can add:


At this point we should try to reduce the fraction. To reduce the fraction we have to factor the numerator and denominator. (We didn't multiply out the denominator earlier so that we would not have to factor it again now.) The only factoring that can be done on the numerator, however, is to factor out a -1:

As we can see, there are no common factors to cancel. So all we can do is simplify (i.e. multiply out):

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Perform the indicated operations and simplify.
[x^2/3x^2-5x-2]-[2x/3x+1]∙[1/(x-2)]
-----------------------------
Factor where you can:
[x^2/(x-2)(3x+1]-[2x/3x+1]∙[1/(x-2)]
---
lcd = (x-2)(3x+1)
---------------------------
Write each fraction with the lcd as its denominator:
[x^2/lcd] - [2x/lcd]
----
Combine the numerators over the lcd:
(x^2-2x]/[(x-2)(3x+1)]
---
(x(x-2))/[(x-2)(3x+1)]
---
x/(3x+1)
=================
Cheers,
Stan H.

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Hello,
The wording of the problem seems but let's see what I can to help you. Let x represent the smaller angle and 7x+36 be the larger angle. We know supplementary s 180 degrees.
so here's the equation we can set up.
7x+36+x=180 Combine like terms:
8x+36=180 Subtract 36 from both sides gives us:
8x=144 Now divide both sides by 8 gives us:
x=18 So now we know the smaller angle is 18 degrees.
The larger angle is 162 degrees.
RJ Toftness
www.math-unlock.com

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(9/8)^-2
----------
= (9/8)^-2/1
It's a fraction. Multiply NUM and DEN by (9/8)^2
= (9/8)^0/(9/8)^2
= 1/(9/8)^2 anything with exponent 0 = 1
--------------
Moving a term from NUM to DEN (or v.v.) changes the sign of the exponent.
(9/8)^-2 = 1/(9/8)^2
1/(9/8)^2 = (1/(9/8)^2 = (8/9)^2
1 over a fraction is the inverse of the fraction.
= 64/81

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when doing systems of equations and graphing, i have a problem that reads
4x - 20 = 5y
8x - 10y = 12
--------------------------
Solve each for "y"
y = (-4/5)x - 4
Plot points: (0,-4)(5,0)

-----------------------------------------------
y = (4/5)x-(6/5)
Plot points: (-1,-2)(4,2)

--------------------------
Both together:

====================================
Cheers,
Stan H.

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three times one number plus -7 times another number equals 21
:
3x + -7y = 21
:
3x - 7y = 21
:
-7y = -3x + 21
:
Multiply by -1
7y = 3x - 21
:
y = x -
y = x - 3
:
Some integer values, ignoring 0;
x=14, y=3
x=21 y=6
x=28 y=9
x=35 y=12
note as x increases by 7, y increase by 3

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2/5 = 5/10n + 2
Do you want to solve for n? You didn't say.
Multiply thru (all terms) by 10 n
4n = 4 + 20n
0 = 4 + 16n
16n = -4
n = -1/4
---------
The second one is: 7/10 = 3/8k + 1
Multiply by 40k
28 = 15 + 40k
40k = 13
k = 13/40

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I'm unsure how to solve log2(square root of xy to the 3rd power)
------------
It's not an equation, so there's no solving to do.
Is it
---------
= all logs base 2

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Whenever a Trig problem refers to "exact values" you will end up using angles that are multiples of 30 or 45 degrees (or or radians).

Since you are looking for the exact value of we have to find a way to express in terms of multiples of and/or . This expression can be a sum or a difference. The expression can be twice or half a special angle. And this expression can be some combination of any of these.

So what expression of multiples of and/or equals ? There are probably others but the one that is most obvious to me is: . SO we will be using half-angle formulas.

There is no half-angle formula for sec, so we will find and then find its reciprocal to get the sec:

(The formula has a "+-" in front of the square root. However, since , is in the first quadrant. And since is in the first quadrant where all Trig functions are positive, we will discard the "-" and use the positive square root.)

Now we just find , substitute and simplify. is in the second quadrant where cos is negative. And its reference angle is . Together this makes . Substituting this into our equation we get:

To simplify this we will start by eliminating the fraction within a fraction. We can do this my multiplying the numerator and denominator of the "big" fraction by the LCD of the "little" fraction(s). Since there is only one "little" fraction, we will use its denominator, 2:

which simplifies to:

Using the property, :

which simplifies to:

Now we can find the sec by finding the reciprocal of cos:

This may be an acceptable answer. However, the denominator is not rational. If you want rationalized denominators:







I'll leave it up to you to multiply this out.

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Assume it should read:
A 67,500 estate is to be split among four children and a grandchild.
Each child gets the same amount, and the grandchild gets half the amount.
How much will each receive?
:
Let x = amt received by the grandchild
then
2x = amt received by the children
:
x + 4(2x) = 67500
x + 8x = 67500
9x = 67500
x =
x = $7500 received by the grandchild
then
2(7500) = $15000 received the the children
:
:
Check 4(15000) + 7500 = 67500

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To estimate the size of the bear population on the Keweenaw Peninsula,
conservationists captured, tagged, and released 50 bears.
One year later, a random sample of 100 bears included only 2 tagged bears.
What is the conservationist’s estimate of the size of the bear population?
:
let x = estimation of no. of bears
;
=
cross multiply
2x = 100 * 50
2x = 5000
x = 2500 bears

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The product of two consecutive integers is 5 more than their sum. Find the integers
------------
x*(x+1) = x + x+1 + 5
x^2 + x = 2x+6
x^2 - x - 6 = 0
(x-3)*(x+2) = 0
x = 3 --> 3 and 4
x = -2 --> -2 and -1

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1. Graph the equations by completing the tables and plotting the points. You may use Excel or another web-based graphing utility.
a). y = -½ x + 3
Use the table; find at least 3 points using any values for x.
Sub each x and find y
x....y
-2...4 --> (-2,4)
0....3 --> (0,3)
4....1 --> (4,1)
Plot the points and draw a straight line thru them.
------------------
b). Use the values of x provided in the table.
Is this the same equation?
x y
0 3
1 2.5
2 2
3 1.5
4 1
----------

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the probability that 2 men in a group of 5 will still be working in 30 years is 3.5
------
The probability cannot be 3.5. Probabilities are always between 0 and 1.
Cheers,
Stan H.

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+ =
do some factoring here
+ =
The common denominator is (a+3)(a+1) multiply thru by this
:
(a+3)(a+1)* + (a+3)(a+1)* = (a+3)(a+1)*
:
Cancel out the denominators, leaving:
(3a - 5) + (a+1)*2(a+1) = (a+3)(a-3)
:
FOIL
3a - 5 + 2(a^2 + 2a+ 1) = a^2 + 3a - 3a - 9
:
3a - 5 + 2a^2 + 4a + 2 = a^2 - 9
:
combine like terms on the left
2a^2 - a^2 + 3a + 4a - 5 + 2 + 9 = 0
:
a^2 + 7a + 6 = 0
Factor
(a + 6)(a + 1) = 0
Two solutions
a = -6
a = -1
;
:
Check in original equation using x=-6
+ =
+ =
+ =
+ = ; confirms our solution
;
:
You can check it using x=-1

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The second angle of a triangle is 30(degrees)less than the first angle.The third angle is twice the second angle. How large are the angles? This problem i really struggled on because i dont know how to write it out and solve it.
-------------
The 1st angle is d degrees
The 2nd angle is d - 30
The 3rd angle is 2*(d-30)
---------------
The sum is (always) 180º
d + d-30 + 2(d-30) = 180
4d - 90 = 180
4d = 270
d = 67.5º
2nd angle = 37.5º
3rd angle = 75º

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A rational number is an integer divided by an integer. The root of the word "rational" is "ratio"

John

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Use the distance formula to calculate the measure of a side.



where and are the coordinates of the given points, so:









A radical is just another number. Just because it looks funny doesn't mean you should treat it any differently than any other number. Would you want people to laugh at you if you had a big wart on your nose?

John

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Find the slope,if possible,of the line passing through each pair of points.
(2,-1)and(6,3)
-------------
The slope, m, is the diff in y over the diff in x
m = (-1-3)/(2-6)
m = -4/-4
m = 1
------
You try the other 2, email me to check your work or for assistance at
gsihoutx@aol.com

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,

So:





Using the Rational Root Theorem

http://en.wikipedia.org/wiki/Rational_root_theorem

To determine the possible rational roots. You can also use your graphing calculator to find a root of the equation. You could also realize that x + 1 will probably be very close to the cube root of 504. Use your calculator to find a numeric approximation of cube root of 504, then take the nearest integer as x + 1.

John

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x*(x+1)*(x+2) = 504

It's likely to be integers, so look for integer roots.
504 = 2*2*2*3*3*7 so it's likely a root will be 7 or a multiple of 7. Plus, the dimensions are 3 sequential numbers.
504 = 7*8*9, so that's the answer.

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A cylindrical container has 3 inches of water in it and is being filled at a rate of 1/2 inch per minute.
The volume, V, of the water in the container is given by the function: V(h)=(π/4)h^3.
Write a formula for the volume in terms of the time in minutes.
:
The formula appears to be the volume of a cylinder with a radius of 1/2 inch
V(h) =
which is
V(h) =
or
V(h) =
:
let t = time in minutes, h = 3 inches to start with, therefore the height:
(3+.5t)
V(t) =
:
Then, calculate the amount of time that will take to fill the container to 70 cubic inches.
Replace V(t) with 70, solve for t
= 70
Multiply both sides by (reciprocal gets rid of on the left)
3 + .5t = 70 *
:
3 + .5t =
3 + .5t = 89.126
.5t = 89.126 - 3
.5t = 86.126
t =
t = 172.25 min to reach 70 cu/inches
;
:
Check this in the volume equation: t=172.25
V(t) =
V(t) =
V(t) =
V(t) = 69.9986 ~ 70
;
:
Two hrs is a long time, hope this has helped!

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c

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Solve for . Exclude the negative root. Subtract 2x from 9 for one dimension, subtract 2x from 12 for the other dimension.

John

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x+5x=90
6x=90
x=15 degrees
5x=75 degrees

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x+.79x=109675
1.79x=109675
x=$61,270.95 husband
.79x=$48,404.05 Lucy

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r=D/t
r=18/3
r=6 mph

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Presuming equal bases:
1. The sum of the logs is the log of the product.

2. The difference of the logs is the log of the quotient.

3. If the logs are equal, the arguments are equal.









Solve the quadratic. The quadratic does not factor over the rationals, so you will need to use the quadratic formula. (or complete the square, if you prefer -- though I would recommend against it in this case). You must then exclude any root that would cause either of the log arguments containing the variable to be negative.

John

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It's -1.

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For example, If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together?
----------------
Use the shortcut, product/sum
3*5/(3+5) = 15/8

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If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together?
:
Let t = time required when they work together (assuming two lawn mowers)
let the completed job = 1
:
+ = 1
clear the denominators, multiply by 15:
15* + 15* = 15(1)
cancel the denominators:
5t + 3t = 15
8t = 15
t =
t = 1.875 hrs or 1 + .875(60) = 1 hr 52.5 min
;
:
Check solution in the original shared work equation:
1.875/3 + 1.875/5 =
.625 + .375 = 1
:
:
:
The larger hose can fill the pool by itself in 10 hours,
The smaller hose can fill the pool in 15 hours.
Unfortunately, I left the drain open in the pool and it can drain the pool in 20 hours.
How long will it take before the pool is filled with both hoses running and the drain open
:
Let t = time required to fill the pool with this situation
Let the full pool = 1
Use + for filling and - for draining
:
+ - = 1
Clear the denominator by multiplying by 60
:
Use the 1st one as an example, you should be able to do this by yourself.

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If the ratio is 7:4, then one of them did of the work and the other did . One should get of the money and the other should get of the money.


John