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$480 invested at 12% compounded quarterly after a period of 7years.

480(1+0.12/4)^(4*7) = 1098.205284353885345

$1098.21

Hi Rosala,

It is great to see you.

Come back and visit often.   :)

Yes, I get x=5, y=49, z=97

There is another triple that results in 19/97, namely x=5, y=97, z=1; however, this doesn't satisfy the condition x<y<z

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its weird you know?i mean when i am on a vacation then that is the period when i spent almost my whole day on this forum and these kinds....theyre so different..well not everybody is like me...funless.....anyway..i gotta run..i have my maths tuition at 12..so i should go...okay bye! 

ill return..soon!!

.34 - .31=.03 the cost in 1917

.34/.03 =11.3333..... - 1 =10.3333 x 100 =1033.33% increase since 1917.

CPhill: If you use the method of subtracting the old from the new and dividing by the old, such as you have done, you do not subtract 1 or 100%. You do that only if you use the method I used above.

So, in your calculation: 31/3 X 100=1,033.33%.This is the increase since 1917.

Proof: 933.33/100 +1=10.3333 X 3=31 cents- current price of stamp (your method.)

           1,033.33/100 +1 =11.3333 X 3 =34 cets-current price of stamp (my method.)

It's quieter now that the US students are on break.......but.....it was pretty busy around the end of April, or so....!!!!!

Bummer that we can't go back and see individual posts.....!!!!!

Assuming that all 4 sides are fenced.......we have....

Total perimeter  =  2(Width + Length)  .....so.....

308  = 2(Width + Length)      divide both sides by 2

154  = Width + Length       subtract the Length from both sides

154 - Length = Width

And...... Area  = Length * Width   ........so we have

Area  =  Length * (154 - Length)

What are the zeros of f(x)=x^3+3x^2-4x-12?

\(\begin{array}{lrrl} x^3+3x^2-4x-12\\ & & 12 = 2\cdot 2 \cdot 3\\\\ (x-x_1)\cdot (x-x_2)\cdot (x-x_3) & \Rightarrow & -12 = (-x_1)\cdot(-x_2)\cdot(-x_3)& \\ & \Rightarrow & \boxed{ \begin{array}{rcll}12 = \underbrace{x_1}_{=2}\cdot \underbrace{x_2}_{=2} \cdot \underbrace{x_3}_{=3}\end{array} } & (\text{sign} \ ?)\\\\ (x-x_1)\cdot (x-x_2)\cdot (x-x_3) & & = x^2\cdot(-x_1)+x^2\cdot(-x_2)+x^2\cdot(-x_3) \\ & \Rightarrow & 3x^2= x^2\cdot(-x_1-x_2-x_3) \\ & & 3 = -(x_1+x_2+x_3) \\ & & -3 = x_1+x_2+x_3 \\\\ & & & \text{sum} \\ & & 2+2+3 & =7~ (\text{no})\\ & & 2+2-3 & =1~ (\text{no})\\ & & 2-2+3 & =3~ (\text{no})\\ & & 2-2-3 & =-3~ (\text{yes})\\ & & -2+2+3 & =3~ (\text{no})\\ & & -2+2-3 & =-3~ (\text{yes})\\ & & -2-2+3 & =-1~ (\text{no})\\ & & -2-2-3 & =-7~ (\text{no}) \end{array}\)

\(\boxed{ \begin{array}{lrrl} x_1 = 2\\ x_2 = -2\\ x_3 = -3\\ x^3+3x^2-4x-12 = (x-2)\cdot(x+2)\cdot(x+3) \end{array} }\)

Yes.....the same conversion would still apply, no matter the angle....

Your teacher's method is basically the same as mine.

If you don't want  a decimal answer, leave it as..... 5pi/ 3   rads

thank you, but one quick question why did you switch the signs for +3x to -3x and -12 to +12

Sandra has two credit cards, P and Q. Card P has a balance of $726.19 and an interest rate of 10.19%, compounded semiannually. Card Q has a balance of $855.20 and an interest rate of 8.63%, compounded monthly. Assuming that Sandra makes no purchases and no payments with either card, after four years, which card’s balance will have increased by more, and how much greater will that increase be?

Card P's balance after 4 years will be =$1,080.70

Card Q's balance after 4 years will be =$1,206.28

$1,206.28 - $1,080.70 =$125.58 Card Q's balance over card P's balance.

we can factorize x^3-3x^2-4x+12. in fact: 

x^3-3x^2-4x+12 == x^2(x-3)-4(x-3) == (x^2-4)(x-3)== 
== (x+2) (x-2) (x-3) 

now 
x^3-3x^2-4x+12==0 iff (x+2) (x-2) (x-3)==0 
and 
(x+2) (x-2) (x-3)==0 iff 
(x+2)==0 or (x-2)==0 or (x-3)==0 

then 
the solution set is: 
S=={x1== -2, x2==2, x3==-3} 

hope this helps 
ciao ciao 

Notice that the arc of a circle is just the part of the circumference enclosed by the endpoints of both radians. Because one-fourth of the circle is shaded, we just multiply the area formula of circle c by a factor of ¼ to find the areaof the circle sector. 

So you would use the same equation if the angle was more than 180 degrees?

And why would you do (300/180)*pi?

Wouldn't you originally do this first (this is how my teacher woud do it basically):

*(pi/180) = (x/300) 

*Times each side by 300

*(300pi/180)

Would this get to the same answer?

And I'm also trying to see the answer NOT in decimal form. The decimal is nice, but I would also like to see an equation-like way of the answer...using the idea I have above. 

You can use this coversion for degrees to radians :    pi / 180    ......so we have

300  *  [ pi   / 180 ]  =

[300/ 180]  * pi   =

[5/3   pi]  ≈   5.236 radians

If you got an answer of  exactly 68 cents.......then you wouldn't need to round at all.....this is to the "nearest cent"

3x = 4y = 7z   implies that

y = (3/4)x        and z  = (3/7)x

So....x + y + z  =

x + (3/4)x + (3/7)x      

And, if y and z are integers, x must be divisible by both 4 and 7.....so, the least that x  can be is 28

And  y = (3/4)(28)  = 21

And z = (3/7)(28)  = 12

So, the least possible value for x + y + z  =   28 + 21 + 12 =   61

How did you find that? Could you do those steps for me please?

cot θ +  tan θ  =

cos θ/ sin θ  +  sin θ/ cos θ      get a common denominator  of sin θ  cos θ

[cos^2 θ   + sin^2 θ] /  [ sin θ  cos θ]

1 / [ sin θ  cos θ]  =

[1/ sin θ] * [ 1 / cos θ ] =

csc θ  sec θ   =   the RHS

To prove the other part, we can just reverse the steps above

sec θ  csc θ   =

1/cos θ  * 1/ sin θ       = 

1/ [cos θ sin θ] =

[sin ^2  θ + cos ^2 θ] /  cos θ sin θ]  =

[sin^2 θ]/ [ sinθ cosθ]   + [cos^2 θ]/ [ sin θ cos θ]  =

sin θ / cos θ   +   cos θ / sin θ  =

tan θ   + cot θ   = the LHS

5.23599 

414.55 * .0282 = 11.69 751.81 * . = 23.231 23.23 - 11.69 = 11.54 Card V is $11.54 greater than Card U.

The answer is 23340.7 

The price in 1917 must have been:   34 cents - 31 cents = 3 cents........so....the % increase is given by:

 ([Current cost  - Old cost] / Old cost  x 100 - 100) %   =

( [ 34  - 4]/ 3  x 100 - 100 ) %  =

( [ 31/3] x 100  - 100) %  =    about 933.33%   increase

7690.80+2928.00+4486.40+1383.80+1984+2300+308+2259.70  =   23340.7