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If my teacher explains as you do I would get full marks every time!! Thanks for the time and effort I appreciate that. 

ROF LMFAO!! I’m going to stroke. I’ve just returned from visiting with my grandchildren, now I’m going to keel over from unrecoverable laughter.  I’ve taken a handful tranquilizers with a double scotch, so I think I can hang on until you post the pics of Sister Alice doing her thing. ROF LMFAO I’m going to stroke! ………

Thanks, Daisy...!!!

Here's a pic of the situation :

Could u go a bit further. I’m a little confused. Or can u solve it.

Thanks!

If you assume such a constant exists, then you can solve for it by setting up an equation based on P(x, y, z) = 0 whenever x + y + z = 0. For example, P(2, -1, -1) = 0.

Can any of u guys help the problem that is P(x, y, z) = x^5 + y^5 + z^5 + k(x^3+y^3+z^3)(x^2+y^2+z^2) . It is the only problem posted today not answered. Here is the link: https://web2.0calc.com/questions/heeeeelp-asap-this-is-due-tomorrow

Haha, no problem!

- Daisy

Thank you!!! 

We have that angle \(ABC = 49\), and that \(ACB = 12\), so we can see that \(BAC = 119\). \(FHE = BHE\) and we can find \(FHE\) by calculating the angle degrees in \(FHEA\), by doing \(360 - 90(AFH) - 90(AEH) - 119(FAE) = 61 = FHE = BHC\), so your answer would be \(61\).

- Daisy

\(f(x) = \left\{ \begin{array}{cl} x+2 &\text{ if }x>3, \\ 2x+a &\text{ if }x\le 3. \end{array} \right. \)

Let x  = 3  and set the functions equal.... we have

3 + 2  = 2(3) + a

5  = 6 + a

5 - 6  = a

- 1  =  a

See the graph  here  that shows that this value of a makes the function continuous :

https://www.desmos.com/calculator/ux7xrnhaxi

1)  Note that  25^(17/x)  = ( 5^2)^( 17/x)  =  5^(34/ x)

25^(-2)  =  5^(48/x)  / [ 5^(26/x) * 5^(34/x)  ]

(5^2)^(-2)   =  5^(48/x)  /  [ 5^(60/x)]

5^(-4)  =  5^(48/x - 60/x)

5^(-4)  = 5^(-12/x)

We have the same bases, so we can solve for the exponents

-4  =  -12 /x  multiply through by x

-4x  = -12   divide both sides by -4

x  = 3

Last one

The point  (0, 3) = (x, y)  is in the shaded area

Notice  that  y - x  < 0   is not true so the first and last answers can be eliminated

And  in the third answer  y ≤ 1 is not true, either

So.....the second answer is correct

We will proceed by contradiction and induction.

Assume that there is no loop. If two bridges connect the same pair of islands, then we have a loop. So, we cannot have two bridges connecting the same islands.

Case 1: Assume now that each island has two bridges. Denote the islands as . WLOG,  connects to ,  connects to , and so on. However, this yields a contradiction since  and  both have one bridge. To fix this, we can connect them together, which results in the whole graph being a cycle of length . On the other hand, we now have  islands and  bridges. Uh-oh. Let's try to fix this by adding in an arbitrary bridge connecting  and . Now note that we have a cycle connecting  which is a contradiction. Thus, if each island has at least two bridges, then there must be (at least) a cycle.

Case 2: If there is an island with less than \(2\) bridges, then we can "ignore" the island and all bridges extending out of the island. We can keep performing this operation until all islands have at least \(2\) bridges. Now, by Case 1, we are done.

We need to find the total amount produced per year  and divide this by 365

( 2.6 x 10^2) ( 3.9 x 10^11)  / 365  =

( 10.14  x 10^13 ) / ( 3.65 x 10^2 )  =

( 10.14 / 3.65)  x (10^13 / 10^2)  ≈  2.8 x 10^11 pounds per day

Second one

2x + y   ≥   -4     rearrange as

y  ≥  -2x  - 4

This graph is a solid line  with a positive slope and a y intercept of -4

y  ≥ 2x

This is a solid line with a positive slope  going through the origin

y - 3  >  (1/2)x

y > (1/2) x + 3

This is a dashed  line with a positive slope  and a y intercept of 3

Thus the graphs on the top right and  bottom left can be eliminated since they contain lines with negative slopes

Pick the point (0, 6)  = (x , y )

Notice that this point will satisfy all three inequalities

Since this point is in the shaded area of the graph on  the bottom right  and not in the shaded area of the graph on the top left, then the graph on the bottom right must be correct

First one

y  < -(3/4)x + 1

This graph will have a negative slope and will be a  dashed line going through the y intercept of -1

y > (2/3)x  - 3

This graph will be a  dashed line with a positive slope  and  going  through the y intercept of  - 3

Thus....either graph on the top right or the one on the bottom right are correct

Pick a point  say  (0, 0)  = (x , y)

Notice that this point will satisfy both inequalities

Since this point is in the shaded region of the one on the bottom right...thus...this one is correct

Plugging the numbers into Desmos shows that D (the lowest one) is the correct answer.

https://www.desmos.com/calculator/g8myhppttv

(insert a long and drawn out disclaimer here)

n  = 27

The divisors  are

1  3   9  27

And their product   is   1 * 3 * 9 * 27  =   27 * 27  = 27^2   =  729

6. Solve for x.

-14 < 3x + 5 or 1/2x + 5 > 7

-14 < 3x     divide both sides by 3

-14/3 < x

(1/2)x +  5 > 7     multiply through by 2

x + 10  > 14    subtract 10 from both sides

x >   4

So

x > - 14/3   or   x > 4

We must choose the  most restrictive interval that solves both equations

This  is    x > 4

5. Solve for x.

-14 < 3x -  2x < 7

-14 < x < 7

In interval notation

(-14, 7)

4. Plot the inequality on the number line

x < -2 or x > 5

3. What is the interval notation for the compound inequality?

-5 > a or a > 4

a < - 5   or   a  > 4

( -infinity, -5) or (4, infinity )

2. Heather is 6 years younger than 5 times her daughter's age. The sum of their ages is greater than 90.

What is the youngest age Heather's daughter can be?

Let her daughter's age  =  D

Heather's age  is 5D - 6

And we have that

D + 5D - 6 > 90    simplify

6D - 6 > 90     add 6 to both sides

6D  > 96       divide both sides by 6

D > 16

Her daughter  must  be at least 17

1.

2x – 5y = 14     multiply through by 6  →  12x - 30y   = 84     (1)

7x + 6y = -2      multiply through by 5 →   35x + 30y  = -10    (2)

Add  (1)  and (2)

47x  = 74

x = 74 / 47

And using  2x  - 5y  = 14     we have

2(74/47) - 5y  = 14

148 / 47  - 5y  = 14

148/47  - 14   = 5y

148 /47  - 658 / 47  =  5y

-510 / 147  = 5y    divide both sides by 5

-102 / 147  = y

Note that this function only approaches 0  from the right

lim              8√x  / x   =

x→ 0⁺

lim              8  / √x

x → 0⁺

As  x   approaches  0,  √x  is  an extremely small positive number  [but not 0 ]

So      8  /  [ an extremely small number ]  =  infinity

So.....since the limit is infinite....this  limit doesn't actually exist