AzizHusain

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.

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.

You can convert a fraction to a percentage by:

fraction --> decimal --> percentage

For the fraction --> decimal stage: Example - 3/4 = 0.75 (Divide to get the decimal) 

For the decimal --> percentage stage: 0.75 = 75% (Multiply 0.75 by 100 to get the % / move the decimal place to the right two times [0.75 is the same as 75/100 or 75%]).

You could also try converting 3/4 to something _ / 100 --> multiply both the numerator and denominator by 25 --> (3*25)/(4*25) = 75/100 (100's make things much easier.) From there, you know that 75/100 --> 75% since the denominator is 100. By doing this, you can avoid the intermediate decimal step and directly head from fraction --> percentage since a denominator of 100 is present.

y -5y+3(y+6)=32

Our goal is to get one term with "y" on one side and a number on the other side:

First, distribute the 3 by multiplying it to both 'y' and '6': y - 5y + 3y + 18 = 32.

Second, combine like terms (the terms with "y") and subtract 18 from both sides to get a number on the right side: 

(1)y - 5y + 3y = -1y = -y

32 - 18 = 14

Therefore, we have -y = 14 --> divide both sides by "-1" to obtain y = -14.

Do a check to see if the equation makes sense.

y -5y+3(y+6)=32; plug in y = -14:

-14 - 5(-14) + 3(-14 + 6) = 32 --> 

-14 + 70 +3(-8) = 32 -->

56 - 24 = 32 -->

32 = 32 --> Yes.

No problem and yes, they do change results dramatically sometimes.

I believe you need to upload the image, but to do that, you need to become a member first by registering first on the website before you can upload attachments/files when you post questions.

Perform the FOIL method:

First - 2*4sqrt(5) = 8sqrt(5)

Outside - 2*(-2) = -4

Inside - 4sqrt(10)*4sqrt(5) = 16sqrt(50)

Last - 4sqrt(10)*(-2) = -8sqrt(10)

Adding all the terms: 8sqrt(5) - 4 + 16sqrt(50) - 8sqrt(10)

16sqrt(50) can be converted to: 16*sqrt(25*2) = 16*sqrt(25)*sqrt(2); we can take out the 25 from the square root as a 5 since sqrt(25) = 5 --> 16*5sqrt(2) = 80sqrt(2)

Now, we have 8sqrt(5) - 4 + 80sqrt(2) - 8sqrt(10)

8[sqrt(5) - sqrt(10) + 10sqrt(2) - (1/2)]*

*I have just done the distributive property backwards so that when you distribute it, you get the same result: 8sqrt(5) - 4 + 80sqrt(2) - 8sqrt(10)

For 80sqrt(2), since 8 is a common term that can be taken out, we can make it 8(10sqrt(2)).

For -4, we know that 8*(-1/2) = -4; therefore, we can make it 8(-1/2).

Now, combining like terms for the 8sqrt(5) and - 8 sqrt(10) is easy since both have an 8. 

That is how we end up with 8[sqrt(5) - sqrt(10) + 10sqrt(2) - (1/2)] as the final answer.