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Thank you, CPhill !

A "rational" number has nothing to do with sensibility.  It means a number that can be expressed as a ratio.

Regarding A and B, since I can see at a glance the answer is D I'm not going to waste my time with them.

The square root of 3 cannot be expressed as a ratio, so multiplying it by 0.5 won't change that. 

Assuming only one answer is correct, that answer is D.  1/3 x 0.5 = 0.5/3 = 1/6 

                                             x/7 = 3 

multiply both sides by 7        (x/7)(7) = (3)(7)

multiply it out                         x          = 21

LOL!!!....mystery solved !!!!

Here are some other possibilities using WolframAlpha

https://www.wolframalpha.com/input/?i=derivative+%5B+sec+x+*+tan+x+%5D

You might try some of the other ones....!!!

Nevermind.  I'm the biggest idiot ever.  I had to replace "x" with "theta" because I put x's wherever there was a theta.

I have no clue what the answer is.  I got a different answer and I put the answer you got in and it still says it's wrong.  I'm assuming there must be one way they will take the answer. 

Set the y's equal  and we have 

x^2−2x+4  = -2x + 4      subtract  4 from each side

x^2 - 2x = - 2x     add  2x to both sides

x^2 = 0

x = 0

One solution

(0, 4)

Break even is where R = C

So we have

10 + 30 h =  5h^2 - 25     simplify

5h^2 - 30h - 35 = 0        divide through by 5

h^2 - 6h - 7 = 0         factor

(h - 7) ( h + 1) = 0

Set both factors = 0  and solve for h and we get that

h = 7         or       h = -1

Only the first makes sense...so....Alan breaks even after 7 hours

The time, t, at which the projectile reaches the max height is

-32/ [ 2 * -16 ] =    1 second

And at this time, the max height is

-16(1)^2 + 32(1) + 50 =

16 + 50 =

66 ft

f(x)  =  sec(θ) tan(θ) 

f ' (x) = sec(θ)*tan (θ) * tan (θ)  + sec(θ)sec^2(θ)  =   sec(θ) [ tan^2 (θ) + sec^2 (θ) ]

Note : other answers are possible 

Although some stuff will be to diffcult!!

So please just feel free to give a question!

Let the no. of liters of 5% solution= x

So...the no. of liters of 25% solution is (10 - x)

So.....we have this

5 % solution * amt +  25% solution * amt =  10% solution * 10 liters

.05 x + .25(10 - x) = .10 * 10   simplify

05x  + 2.5 - .25x +  1

-.20x + 2.5 = 1     subtract 2.5 from both sides

-.20x = - 1.5         divide both sides by .20

x = 7.5 liters of 5%  solution

And

10 - x =  10 - 7.5 =    2.5 liters of 25% solution

Answer " C "

The total salt in the final solution has to equal the salt from the component solutions

x = liters of 25%        salt content = .25x

10-x = liters of 5 %    salt content = .05(10-x)

final solution salt content =  .1 (10) = 1

.25x+ .05(10-x) = 1

.25x + .5 - .05x = 1

.20x = .5

x = 2.5 liters of 25%       and  10 -2.5 = 7.5 liters of 5 %

All we know....after substitution....is that

x1 + x3 = 0       so

x1 =   - x3

That's as much as we can do....

Cool I find other moderators who care!

Well.....you won't get in any trouble with me.....LOL!!!!

Whoops it looks like other people got answers to hope all these answers help!

LOL!!!

I think it would be 11.6 feet!

[ 12^2 - 3^2 ]  =

√ 144 - 9 ]   =

then we get 135

√135 and then we get

=11.6 that is how it would be hope this helps!

No problem.....just a slight mistake....easy to make those !!!!

Okay - this has to do with modulo arithmetic. The upper bound on this will be (8-1)*15 = 105, since after 7*15 you can get any number mod 15 by choosing (0 to 7) 15-boxes + as many 8-boxes as you need. (Since 15 and 8 are relatively prime, 15n is guaranteed to get every value mod 8.) 

There should be one value between 6*15 and 7*15 that doesn't work, and that should be the number that has the same value mod 8 as 7*15 mod 8. So the answer will be 7*15 - 8 = 97. 

Checking: 
8 does not go into 97 or 97 - (2n * 15) 
8 does not go into 97-15 = 82 
8 does not go into 97-45 = 52 
8 does not go into 97-75 = 22 

Now, looking at the next values: 
98 = 15*6 + 8 
99 = 15*5 + 8*3 
100 = 15*4 + 8*5 
101 = 15*3 + 8*7 
102 = 15*2 + 8*9 
103 = 15 + 8*11 
104 = 8*13 
105 = 15*7 

Any larger numbers can be made by adding boxes of 8 to the numbers above.