Call the center of the circle \(L\)
\(SL=r\)
\(KL=r\)
\(OL=45-r\)
By pythagorean theorem:
(Hypotenuse of Triangle SOK)^2 - (Longer side of triangle SOK)^2= (Hypotenuse of triangle KOL)^2 - (Shorter side of triangle KOL)^2
\(52^2-45^2=r^2-(45-r)^2\)
Now it's your turn to solve.
500L x 0.75 =375 L - being 75% of the water in the bathtub 375L - 5.79 L =369.21 L of water needed to fill 75% of the bathtub. 369.21 L / 2 L per minute =184.605 minutes needed to fill 75% of the bathtub. 184.605 minutes / 60 minutes =3.07675 - hours needed to fill 75% of the bathtub Or: 3 hours, 4 minutes and 36 seconds
It looks like a standard question that you could find in any school.
There is nothing unusual about this question.
Alien 2 and 3 sit on a side. While Alien 1 and 4 sit on the other side. So yes, these playful aliens can do it!
Since the square root goes on for infinity:
\(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x...}}}}=\sqrt{x+\sqrt{x+\sqrt{x...}}}\)
Let us set \(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x...}}}}=y\)
This means: \(y=9\)
This also means: \(\sqrt{x+y}=9\)
Substitute \(y\): \(\sqrt{x+9}=9\)
Square both sides: \(x+9=81\)
\(\boxed{x=72}\)
A + B = 180
(30 + 5X) + (15 + 10X) = 180
45 + 15X = 180
15X = 180 – 45
15X = 135
x = 9
wow, just wow, a very thoughtful explanation!
How did you bold your question?
Since it is a parallelogram, consecutive angles are supplementary.
Yes.
i think if its postitve r then it will be in the same direction as and that's for one of the answers right
?
You'll end in the second quadrant (if you were on the regular x-y coordinates, it wuld be the point (-2.6, 1.5).
Checking back, I see that I made an error
It should not say the volume is "pi times the area of the base times the height"
It should say "the area of the base times the height"
pi Is already figured in to the area
I know that I'm susceptible to clumsy errors like this, and I promise I proofread it several times before I finally clicked the publish button. ~ sigh ~
.
where will i end up
On your polar-coordinate graph paper, first find the ray from the center point that represents 5pi/6 (it's to the upper left).
Going from the pole outward in this direction, take 3 steps and place your point.
Draw vector A, placing its tail at (0,0) and its head at (-3,-5)
To subtract vector B, add its additive inverse <-1,-4>. Place the tail of this vector at (-3,-5) and its head at (-4,-9).
The resultant vector goes from (0,0) to (-4,-9).
The top rectangular box has a volume of 4 x 4 x 3.
The bottom cylinder has a volume of pi x 3.52 x 6
Finish those calculations and add them together ...
I don't think so.
The odd-numbered aliens must either both sit in the 1m or 2m seats; but there is no combination that works.
Yes, your'e taking the geometry course on AoPs.
By the way, all AoPs problems have dollar signs next to each expression or phrase
https://www.desmos.com/calculator/zurnxjuzkv
if you square it,
x+ \(\sqrt{x+\sqrt{x+...}}\)=81
so x=72
This question is answered here. https://web2.0calc.com/questions/cube-question-help
210/360*12pi=21.99...-->22.0-->A
Hope this helps
Do u take algebra 2 classes at Santa Clara AOPS, because this looks like one of the homework questions.
Hey Rudram592, I know this is a question from AOPS...please refrain from posting them here.
