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Juanita's saving = 15x       Dan's = 100 + 12x

15 x   >   100 + 12 x   solve for x

3x > 100

x > 33.33 wks        so  at 34 weeks Juanita will have more money than Dan

btw the answer is not 3

v and u are at right angles, so v projected onto u is a zero length vector (i.e. the dot).

.w is in the opposite direction to u so the projection will be facing the opposite way from u (i.e. a)

x is a small amount in the same direction as u so its projection will be small and in the same direction as u (i.e. c)

I'll leave you to reason about te projection of y onto u.

I get the following:

11 oz/ hr   *   24 hr /day  *  1 gal / 128 oz = ..........gal / day

I can see only one such number that is divisible by 72 =32256. There isn't really anything to explain! You simply try every combination of 2 and 3 until you find it !.

The prime factorization of 72 is $2^3*3^2$, and so in order of 32x5y to be divisable by 72, it's prime factorization must include $2^3*3^2$.

Use the pythagorean theorum to find the perpendicular height, 

then use Pythagoras again and find the other side.

I want you to look at f'(x)

f'(x) is the GRADIENT of the tangent to the curve 

So just thinking about the gradient, which choices could be correct?

Anyway, now that I have looked at it properly, you do not understand it because it does not make any sense.

None of the answers are correct.

Hi asinus,

the memo I have on this sum uses a way different approach, and comes up with 9,22 or 99,22 deg..?

I see you have reposted and Hectictar is answering.

You should only have one question per post anyway.

Let a side of a hexagon be equal to the height (or length) of a solid.

Solid A          A = 28 cm²

I'm gonna use this formula to calculate a² ( and b²)

2(3√3*a²/2) + 6a² = 28         a² = 2.5008485          a = 1.581407127

V_(A) = 3√3/2 * a = 10.27502675 cm³ 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solid B          A = 40.32 cm²

2(3√3*b²/2) + 6b² = 40.32         b² = 3.601221843         b = 1.897688553

V_(B) = 3√3/2 * b = 17.75524625 cm³

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

V_(B)  :  6912  =  V_(A)  :  x

x = 4000 grams  

Hi AoPS! This answer was actually written by me! Thanks!

38. If a block has a mass of 25-g and a volume of 29.5-mL. What is the
density of the block?

Hello maximusaurelius!

\(\rho=\frac{m}{V}\)

\(\rho=\frac{25g}{29.5ml}\times \frac{ml}{cm^3}\)

\(\rho=0.847g/cm^3\)

  !

i dont understand

but it is a different type of question

we have equation:

25 = (1--3)^2 + (y-3)^2

solve for y, then the result of y will be 6 or 0 :)

The answer is in 7 weeks.

The set of possible values of xyz is -2, -1, 1, and 2.

you should use mathway.com realy helpful.

use desmos.com it helps me alot... might help you too

Really? If you can do more then 3, I'll give you 2 ++

Only four integers can be used: 2, 3, 4 and 5

1st  Δ    2, 5, 5

2nd Δ    3, 4, 5

3rd Δ    4, 4, 4

Given that g + 7f = 12f - 5g evaluate \(\sqrt{\frac{17g^2}{2f^2+8g^2}}\)

Hello Guest!

\(g + 7f = 12f - 5g\\ f=\frac{6g}{5}\\ f^2=\frac{36g^2}{25}\)

\(\sqrt{\frac{17g^2}{2f^2+8g^2}}=\sqrt{\frac{17g^2}{2(\frac{36g^2}{25})+8g^2}}=\sqrt{\frac{17g^2\cdot25}{2\cdot 36g^2+200g^2}} =\sqrt{\frac{425g^2}{272g^2}}\color{blue}=1.25\)

  !

3x-29      +   6x-7   = 180^o      Solve for 'x'

then use this value of x :       6x-7 = 8y+17   to solve for y