All Answers 358090 Answers

What is meant to be between the 3 and the 14?

Undefined (indeterminant).  You cannot divide by 0.

Start by adding 4x to both sides

then

subtract 4 from both sides

then 

think about what you need to do next.  

Add another post onto the end of this one if you need more assistance.

2+5=7  There will be a total of 7 parts.

2/7 of 252 will be one part

and

5/7 of 252 will be the other part.

You can finish it yourself.  If you doubt your answer than you can ask if it is correct.  

I can - All smiles from me.  

CPhill, that sounds absurdly irrational!

I hope you can hear this. 

The cosine = 1/2 at 60 degrees and at 300 degrees.

So we need to divide both angles by two for 2 theta (or 2 sigma).

So we have 30 degrees and 150 degrees.

Using the tangent inverse, we get about 42.61°....But the tangent is also positive in the 3rd quadrant, so this angle may also be 180 + 42.61   =  222.61°

I've not run across the term "surd" before......Simply put, it is a number that cannot be simpified to remove a root (an irrational number is the result).....

How did we get the word "Surd" ?

Well around 820 AD al-Khwarizmi (the Persian guy who we get the name "Algorithm" from) called irrational numbers "'inaudible" ... this was later translated to the Latin surdus ("deaf" or "mute")

BTW......Thanks Aziz, for that answer........

I believe the questioner wants to take the square root of 69......we cannot "reduce" (simplify) this any further, since the only factors of 69 are 23 and 3, and these are both prime..

Aziz's answer is correct..I mistook "loge" as a mispelling of "log"...but I see now that the intent was "ln".....

Rearranging  a little, we have...

4x^2 - 7x - 2 = 0

And factoring produces

(4x + 1 ) (x - 2) = 0

And setting each factor to 0, we obtain that

x = -1/4  and   x  =  2   as Aziz has said...

4x^2 - 7x - 2 = 0

Use the quadratic formula: x = (7 +/- sqrt[49 - 4(4)(-2)]) / 2(4) -->

(7 +/- sqrt(49 + 32)) / 8 -->

(7 +/- sqrt(81)) / 8 -->

(7 +/- 9) / 8 -->

x = (7 + 9) / 8 = 16 / 8 = 2

&

x = (7 - 9) / 8 = -2 / 8 = -1/4 = -0.25

Note: 4(2^2) -2 ?= 7(2) --> 16 - 2 = 14 --> Yes, therefore, x = 2 is a solution.

4((-1/4)^2) - 2 ?= 7(-1/4) --> -1.75 ?= -1.75 --> Yes, therefore, x = -1/4 is a solution, too. 

Each term has 3v^2 available:

3v^2(3v^2 + 8v + 4)

Next, we factor out the (3v^2 + 8v + 4):

(3v^2 + 8v + 4) -->

(3v + 2)(v + 2)

Putting it all together, we have:

3v^2(3v + 2)(v + 2)

Cross multiply:

-30x = -20(x-2) 

-30x = -20x + 40

-10x = 40

x = -4

Compare the cross or diagonal terms first.

9x^5*y^4 & 3x --> we can cross out the 3x entirely and change the 9x^5*y^4 into 3x^4*y^4 by dividing 9 by 3 and crossing out one x in x^5.

4y & 2y --> we can change 4y into 2(2y) and cross out the 2y.

Notice by crossing out the 3x and 2y, we are left with 1 / 1.

Thus, we have: 3x^4*y^4 / 2  * 1 / 1 -->

3x^4*y^4 / 2.

Let's try simplifying each numerator/denominator:

x - 1 is already simplified.

4x - 8 --> 4(x - 2).

x^2 + x - 6 --> What 2 numbers add up to 1 and multiply to give -6? --> (x + 3)(x - 2).

x + 1 is already simplified.

Now, notice we can cross out the (x-2)'s and we end up with:

(x - 1) / 4 * (x + 3) / (x+1) -->

Now, just multiply like normal: (x - 1)(x + 3) / 4(x + 1) -->

Perform the FOIL method for the numerator and distribute the denominator -->

(x^2 + 2x - 3) / (4x + 4)

3v^3*y^4 - 48v^3

1. We can factor out 3v^3 from both terms -->

3v^3(y^4 - 16)

2. We can further factor out (y^4 - 16) -->

3v^3(y^2 + 4)(y^2 - 4)

3. Finally, we can factor out (y^2 - 4) -->

3v^3(y^2+4)(y + 2)(y - 2)

sqrt(96) = sqrt(16*6) = sqrt(16)*sqrt(6) = 4*sqrt(6).

The surface area of a cylinder is: 2pi*r^2 + 2pi*r*h.

We just need to plug in r = 9 and h = 20 -->

Surface area = 2pi*(9^2) + 2pi*9*20 -->

(2*pi*81) + (2*pi*9*20) = 1639.9113651738720705 square inches.

x^2 + y^2 = 36 is the in the form of x^2 + y^2 = r^2 which is a circle with radius, r. In this case, we have a radius of 6 [36 = r^2 --> r = sqrt(36) = 6] and center at the origin (0,0) [since there is only x^2 and y^2 and not 5x^2 and 4y^2)]. 

To graph this, you can solve for y in terms of x:

x^2 + y^2 = 36 --> 

36 - x^2 = y^2 -->

sqrt(36 - x^2) = sqrt(y^2) -->

y = +/- sqrt(36-x^2)

Notice, we have two half-circles since we took both the positive and negative square root of 36-x^2.

This graph is a circle with a center at the origin (0,0) and a radius of 6. The lines of symmetry include the x-axis and the y-axis.

Suppose we have loge(0.25) = x (variable) -->

By properties of logs: e^x = 0.25 -->

Take logs of both sides: log(e^x) = log (0.25) -->

By properties of logs again: x log e = log (0.25) -->

Now, just divide both sides by log e to get log (0.25) / log e = x; x = B, -1.386.

log(.25) = -0.602

C is not a surd.

sqrt(9+7) = sqrt(16) = 4

The rest are decimals since they cannot be simplified to remove the sqrt symbol.

sqrt(9) by itself is not a surd, but with the + / - sqrt(7) [which cannot be simplified like sqrt(4), sqrt(25), etc.] it is a surd.