All Answers 358150 Answers

1 - The smallest integer ==2 * 3 ==6>>>>>1.846757322198614016e+18 = 2^48 * 3^8

2 - The next smallest ==24 = 2^3 * 3

3 - The next smallest ==54 = 2 * 3^3

4- The next smallest==96 = 2^5 * 3

If  the circle is tangent to the y axis at (0,2)  the center must be (c , 2)  where c is the radius

Using the squares of the  distance formula

(c- 0)^2  +  ( 2 - 2)^2  = (12 - c)^2 + (2 - 0)^2

c^2 =  c^2 - 24c  + 144 + 4

24c =  148

c = 148/24 =  37/6  =  the radius

basically L=16

Let \(l\) be the side length of the square. 

So, \(l^2=4 \times 4l\). Simplified: \(l^2=16l\)

Equation's solution is ans

Let P = the perimeter = 4S

Area of square =   S^2

S^2  =  4 (4S )

S^2  =  16S

S^2 - 16 S =  0

S (S - 16)  = 0

S =  16

7A + 5A = 90 deg

12A =90

A = 7.5 deg.

Diameter of 10  = radius of 5

pi ( 20^2 - 5^2)  = 

375 pi    (in^2)

2^3 *  4^5  * 6^7  * 8^9 =

2^3 * (2^2)^5  * 2^7 * 3^7 * (2^3)^9  =

2^3 * 2 ^10 * 2^7  * 2^27 * 3^7  =

2^47 * 3^7

We need  2 * 3    =  6

CORRECTED  !!!!

Volume of 8 steel balls =   

8 * pi (5)^2  =  200pi

200 pi =  pi (r^2)

200 = r^2

10sqrt (2) in   =  r

Also.....notice that if angle AOB = 60

Then angle  AOX = 30  = angle BOX

And angle  OAB  = Angle BOA  =  60

So triangle   AOB is equilateral with AB  = 20

hmm...are you sure that's correct?

gracias.

Thx, BB.....I didn't read this one correctly !!!!

Taking this from

x^2 =  3y^2 + 2xy

x^2  - 2xy  - 3y^2  = 0

(x - 3y) ( x + y) = 0

x + y = 0    not possible

x - 3y = 0

x = 3y

y / x =   1 /  3

First, we need to convert 13 pounds to ounces: \(13 \times 16 = 208\)

Now, we can form a ratio table:

\(130 = 208\)

\(\text{?} = 11\)

Multiplying both sides by \({11 \over 208}\), we find that \(6.875 = \color{brown}\boxed{6 {7\over 8}}\) pounds of cheese are needed to make 11 ounces of cheese. 

Using the Law of Cosines on \(\triangle AOB\) gives us \(AB = \sqrt{20^2 + 20^2 - 2\times 20 \times 20 \cos 60} = \color{brown}\boxed{20}\)

Note that we have a \(30-60-90\) triangle with the longer leg being \(\sqrt 3\). This means that the other leg is 1, and the hypotenuse is 2. 

This means that the length of the longer base is \(5 + (2 \times 1) = 7\). 

So, the total perimeter is \(7 + 5 + (2 \times 2) = \color{brown}\boxed{16}\)

NVM  !!!

maybe check your question before posting 

We have the equation \({n +1\choose 3} \geq 365\)

Note that \({14 \choose 3} = 364\), so there are 15 members in the group, making for \(\color{brown}\boxed{14}\) people. 

There are \({5 + 7 \choose 5} = 792\) ways to get from the origin to \((5,7)\)

Now, we need to subtract this from the number of ways to get form the origin to \((4,4)\). 

There are \({4 + 4 \choose 4} = 70\) ways to get from the origin to \((4,4)\).

So, there are \(792 - 70 = \color{brown}\boxed{722}\) ways. 

Here is a link that explains this better: https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/

(3/4)N  -10  = 14

(3/4)N =  24

N = 24 (4/3)  =  32

2x > 3x - 3                8x - a > -6 + 2x

3 > 3x - 2x                8x -2x  > -6 + a

3 > x                            6x > -6 + a

If x = 2  then  

6(2) > -6 + a

12 + 6 >  a

18 > a

17 positive integers

We have \(10^n = 10^{-6}\times \sqrt{\frac{10^{46}*10^{18}}{0.01}}\)

Recall that when you multiply exponents with the same base, you add the exponents, and when you divide exponents, you subtract the exponents. 

Simplifying the square root gives us \(\sqrt{10^{64} \over {10^{-2}}}\), which can be simplified to \(\sqrt{10^{66}} = 10^{33}\).

Now we have \(10^n = 10^{-6} \times 10^{33}\).

Can you take it from here?

Let Fred and Gwynn  occupy any two chairs....and they can be seated in 2 ways

The other 4 people can  be  seated in 4! =  24 ways

So

2 * 24  = 

48 ways