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The answer is 2.34 seconds

The expression \(\dfrac{\sqrt{x+8}}{x^2+x+16}\) is defined if:

\(x+8\ge 0 \implies x\ge -8\)

AND

 \(x^2+x+16 \neq 0 \\ \text{Which, in real numbers, is already satisified; as it only equals 0 if x is a complex number.}\)

So the smallest x for which this expression is defined is -8.

S = [(3 ζ(3))/32] 

T =  [π^3/32]

S / T = [(3 ζ(3))/32] / [π^3/32]

S / T = (3 ζ(3)) / π^3

ζ(3) - This is called "Riemann zeta function" = 1.202056903159594285...etc.

Note: If you don't understand it, consult your Math Teacher.

CPhil is RETIRED! He may or may not come in, because he did this job as a volunteer.

\(k = x + y(1 - x) + z(1 - x)(1 - y)\\ k = x + y-xy + z(1-x-y+xy)\\ k = (x + y-xy) - z(x+y-xy)+z\\ k = (x + y-xy) (1- z)+z\\\)

The maximum of x+y-xy is 1 when x=1 and y=1 

You can prove that by considering the case where  x=1-t   and y=1-m   where t and m are (0,1]

If z=0 then we have  1*1+0 = 1

So I get a max of 1 when  x=1,y=1 and z=0

There is also be a max of 1 when x=0, y=0 and z =1

I do not think that k can be bigger than 1

Like so:

Answered just a few days ago.

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The answer is 2*sqrt(17)

See here:  https://web2.0calc.com/questions/counting_17272

60 = 2^2 * 3 * 5

[942! + 120!] = 2^116 × 3^58 × 5^28 × 7^19 × 11^10 × 13^9 × 17^7 × 19^6 × 23^5 × 29^4 × 31^3 × 37^3 × 41^2 × 43^2 × 47^2 × 53^2 × 59^2 × 61 × 67 × 71 × 73 × 79 × 83 × 89 × 97 × 101 × 103 × 107.....etc. 

Since 5 is the largest prime factor of 60, therefore 28 would be the largest exponent of 60, or 60^28.

In how many seconds will the ball hit the ground?

Hello Guest!

\(y = -16t^2 + 28t + 180\)

\(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ t = {-28 \pm \sqrt{28^2-4\cdot (-16)\cdot 180} \over 2\cdot (-16)}\\ \color{blue}t=4.341 \)

In 4.341 seconds will the ball hit the ground.

  !

If the ratio of the perimeter of the squares is  5:2

Then .. What is the ratio of the sides of the squares.  Draw a pick and think about it.   I'll continue after you answer.

Hint:

5:2 is the same as   20:8    Do you see why?

20:8 is easier to work with.  

Let the squares have a perimeter of  20 and 8 respecively.  How long are the sides.?

You are welcome.

Method 1

16 - 5 =11 days' work remains by the original 60 bricklayers

[60  x  16] / 55 =17.4545.....days that would have taken 55 bricklayers to finish the entire work.

But 5/16 of the work is already done and 11 /16 remains.

So: 17.4545...  x  11/16 =12 days for the remaining 55 bricklayers to finish the work

12  +  5  days =17 days, or 1 extra day for the 55 bricklayers to finish the work.

Method 2

Since 60 / 16 =3.75 old rate  and 55 / 11 =5 new rate 

Therefore: 3.75 / 5  x  16 days =12 days, or 1 extra day for 55 bricklayers to finish the work.

12  +  5 ==17 days, or 1 extra day.

Method 3

55 / 60 = 0.9166667 of the original 60 bricklayers remain on the job. Therefore the number of days to finish the work will go up to: [1 / 0.9166667]  x 11 days = 12 days.

It's about to get better.

All of the values of x from [-25, -sqrt 5) would get squared and turned positive, and outside of the domain. So they don't work.

All of the values of x from (sqrt 5, 5] would get squared outside of the domain of f(x). So they don't work.

Everything inside those still works, so the width of the interval is \(2\sqrt5\).

ab has to be a perfect square.

b has to be a perfect square.

(4 + sqrt(4b) + b)/3 = (4 + 2sqrt(b) + b)/3 = an integer

And from there you just plug values in.

9 doesn't work.

16 doesn't work.

25 works.

So the value of b that answers this problem is 25.

800 - 7m ==1200 - 12m, solve for m

m=80 minutes before they equalize

800 - [7 * 80] ==1200 - [12 * 80]

240 = 240 Liters remaining in the 2 containers.

sam and ella more like salmonella.

of course, Sam saves more gas in total because she starts with a car that gets 26 and ends with one that gets 36 while Ella starts with one that gets 12 and ends with one that gets 34. We were never told how many miles they actually drove in each car so we cannot really do any math here and we can only assume.