All Answers 358083 Answers

 [ 1 - sin^2 (x) ] / cot^2 (x)  =

[ cos ^2 (x) ] /  [ cos^2 (x) / sin^2(x) ]

sin^2 (x) =   sqrt (3)  / 3         take both roots

sin (x)  =   ± sqrt ( 1/ √ 3) 

So.....      arcsin (  sqrt ( 1/ √ 3)  )  ≈  0.8631       and    pi - 0.8631 ≈  2.2785

And   arcsin ( -  sqrt ( 1/ √ 3)  )  ≈   5.4201    and   pi + 0.8631  ≈  4.0047

The first answer is correct

I'm assuming that the question is asking for the roots of the expression \((9x+1)(x-1)\).

Finding the roots simply means to set the expression equal to zero and solve for any variables. Let's do that!
 

Therefore, the roots are the following:
 

\(x_1=-\frac{1}{9}\)

\(x_2=1\)

10 years ago  he was  t - 10  years old....so.....

His current age   =   3 times his age 10 years ago

t  =   3 ( t - 10)

(6,1)   (5,4)

Find the slope

[ 4 - 1 ] / [ 5 - 6 ]   =   3 / -1  =  -3

So....using  (6, 1)  we have

y =  -3 (x - 6)  + 1      simplify

y =  -3x +  18  + 1

y = -3x +  19         add 3x to both sides

In standard form we have    3x + y  =  19

(6, -7)  =  (x, y)

In polar coordinates we will have    (x , y)  =  ( r , θ)

r =  sqrt ( x^2 + y^2)         θ =  arctan (y /x)   ....this is in rads

r = sqrt ( 6^2 +  (-7)^2 )  =  sqrt (36 + 49)  =  sqrt ( 85)

θ =  arctan (y /x)   =    arctan ( -7/6)  ≈  -0.862 

So   (6, -7)   =   ( sqrt (85), -0.862 )   in  polar form

See if you can do the second one....

15*5=75yd

1 = 1 X 1 True

1 + 9 = 2 X 5 True

1 + 9 + 17 = 3 X 9 True

1 + 9 + 17 + 25 = 4 x 13 True

1+ 9 + 17 + 25 + 33 = 5 x 17 True

1+ 9 + 17 + 25 + 33 + 41 = 6 x 21 True............etc.

Notice the pattern. The LHS forms an arithmetic sequence with a common difference of 8. The RHS forms a pattern of: 1, 2, 3, 4, 5.....etc., each is multiplied by the PREVIOUS multiplicand + 4. So you have: 1 x 1, 2 x (4 + 1),  3 x (4+5), 4 x (4 + 9), 5 x (4 + 13), 6 x (4 + 17).......etc. 

welcome

dang thanks

Playground 
256 yd^2 
P least perimeter 

1. 
All except b satisfy the model. However from the wording of the playground c is probably the most appropriate. 

2. 
Step 7. It should have read x(1/2*P - x) = 256 though I don't see what it proves. 

3. 
x(x + 8) = 256 
x^2 + 8x - 256 = 0 

By quadratic formula 

x = [-b ± √(b^2 - 4ac)]/(2a) 
= [-8 ± √(8^2 + 4*256)]/2 
= (-8 ± √1088)/2 
= [-8 ± √(64*17)]/2 
= (-8 ± 8√17)/2 
= -4 ± 4√17 ….. minus in ± does not apply in this case 
x = -4 + 4√17 
≈ 12.49 
x + 8 = 20.49 

_12.49_ yards and _20.49_yards 

4. 
x^2 = 256 
x = √256 
= 16 

_16_ yards and _16_yards 

5. 
A = x(P/2 - x) 
= -x^2 + Px/2 

Taking the derivative 

A' = -2x + P/2 

Setting it to zero 

-2x + P/2 = 0 
x = P/4 

So 

A = (P/4)(P/2 - P/4) 
= (P/4)^2 

Therefore it is a square 

256 = (P/4)^2 
P/4 = √256 
= 16 
P = 4*16 
= 64 

The least fencing is 64 yards 

im pretty darn sure im correct

nvm i got it.

Frequently, especially in trigonometry, the unit circle is thecircle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere.

http://www.geteasysolution.com/e*x+2=0

Simplifying e * x + 2 = 0 Multiply e * x ex + 2 = 0 Reorder the terms: 2 + ex = 0 Solving 2 + ex = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + ex = 0 + -2 Combine like terms: 2 + -2 = 0 0 + ex = 0 + -2 ex = 0 + -2 Combine like terms: 0 + -2 = -2 ex = -2 Divide each side by 'x'. e = -2x-1 Simplifying e = -2x-1

i think its right.

Well, let's say the list price is x. 

And if the price was 1/4 off the list price (this is discount, right?), then it would be the price would be x*0.75

But we know Saidhari bought the toaster oven for $90.00 (dollars, right?). 

So the equation would be 90.00 = x*0.75

Divide both sides by 0.75 and get 120 = x.

So the list price was $120.00.

Correct me if I'm wrong. 

2 = 1 X 2 True

2 + 6 = 2 X 4 True  

2 + 6 + 10 = 3 X 6 True 

2 + 6 + 10 + 14 = 4 x 8 True

2 + 6 + 10 + 14 + 18 = 5 x 10 True 

2 + 6 + 10 + 14 + 18 + 22 = 6 x 12 True

2 + 6 + 10 + 14 + 18 + 22 + 26 = 7 x 14 True............etc.

Notice the pattern. The LHS is an arithmetic sequence with a common difference of 4. The RHS forms a pattern of 1, 2, 3, 4, 5........ each multiplied by its double. 1 x 2, 2 x 4, 3 x 6, 4 x 8, 5 x 10......etc.

Well, if it's a square background, then the length of two sides must be the same. So we can square root 256 to get the length of one side.  You can plug that into a calculator, but it's easy to memorize that it is 16.

I don't really know what you want to know...but here are some possible answers: 

Length of one side: 16 meters

The total length of fence needed: 64 meters

Correct me if I'm wrong. (Getting a lot of questions wrong these days...)

with what?

Given t ≈ 9.4 is a solution to cot t = –40.35, use the period of the function to name three additional solutions.

tan is negative in  the second and forth quadrants. 

Since cot is the reciprocal of tan, it is negative in the second and 4th quadrants too.

So the solutions for t will be at pi radian intervals

t cannot be measured in degrees because cot of 9.4 degrees would be positive so t must be measured in radians.

So the general solution for t must be 

\(t=9.4-n\pi \qquad n\in z\)In other words n is in the set of integers

so here are 3 more solutions

\(t=9.4-\pi\\ t=9.4-2\pi\\ t=9.4-\pi\\\)

Use the formula S​ = n2 to find the sum of

1​ + 3​ + 5​ + ...​ + 861 = ?

​(Hint: To find​ n, add 1 to the last term and divide by​ 2.)

\(\begin{array}{|rcll|} \hline n &=& \frac{861+1}{2} \\ &=& \frac{862}{2} \\ &=& 431 \\ \hline \end{array} \)

\(\begin{array}{rcll} sum &=& n^2 \\ &=& 431^2 \\ &=& 185761 \\ \end{array}\)

\(\begin{array}{rcll} 1\ + 3\ + 5\ + 7\ + \ ... \ + 859\ + 861 &=& 185761 \\ \end{array}\)

There is nothing in the original expression to indicate that 5(7-5) has been factored from (35 - 25).  If it had been the correct way to express the result would have been 60/(5(7 - 5))

60/5(7 - 5) has an implied multiplication so should be read as 60/5*(7-5)

To avoid ambiguity either use parentheses or write as \(\frac{60}{5}(7-5)\text{ or}\frac{60}{5(7-5)}\) as appropriate.

No wait. I'll leave my answer. People can learn by my mistake too. 

Always think positively. 

Oops. Sorry Alan. Sorry. I'll delete my answer. Sorry guest.

What's wrong with me these days?

It says 

60 ÷ 5 ( 7 - 2 )

60 ÷ 5 ( 2 )

60 ÷ 10

6

But that's a typo. Meant 

60 ÷ 5 ( 7 - 5 )

60 ÷ 5 ( 2 )

60 ÷ 10

6

Was thinking ahead to the answer.

Remember that the term 5(7-5) is a monomial term that has been simplified from (35-25) and that you need to DISTRIBUTE the 5 back into the brackets to solve the brackets.