All Answers 356007 Answers

Thanks Omi!

Strange, AoPS has some wrong answers....

Can you solve using this informaion?

Guest's solution doesn't use calculus, it uses triginometry.

But you get what I mean.

A simple knowledge of 30 60 90 well help!

its a ti-84.

except the one in the picture is a rando from google images.

Thank you!

Using the method that CalculatorUser said, you split the triangle into two 30-60-90 triangles. We get that the height of the isosceles triangle is simply just 2, and the base is 4sqrt3. Using the formula for triangle area, we get that the area of the triangle 4sqrt3.

(That calculus method looks hard!)

Very nice solution!

This is why there is a controversy to whether someone should learn calculus at a young age.

In my opinion, it is not good to learn calculus. Because the extra knowledge my blur your vision on seeing simple solutions.

The internet is the source of all my dark magic, without it I will be powerless.

btw, how did you know that lol. 

Wow thanks! it worked!! 

Here is my attempt:

Good job on finding \( 0=-3j+jk-3k\) guys, we can work from here?

We factor:

\(0=j(-3+k)-3k\)

Simplifies to:

\(0=j(k-3)-3k\)

We add 9 to both sides, this allows us to factor better:

\(9=j(k-3)-3k+9\)

We factor once again

\(9=j(k-3)-3(k-3)\)

We then simplify:

\(9=(j-3)(k-3)\)

Now that we have a binomial expression, we can list the factors of 9 to guess solutions.

1 and 9

3 and 3.

So for 1 and 9, we set them equal

\(j-3=1\)

\(k-3=9\)

Solving this, we get J=4 and k=12, since they can be reversed, the values of K and be 4 or 12.

Now we solve 3 and 3

\(j-3=3\)

\(k-3=3\)

Solving this, we get J=6 and K=6, since they can be reversed, the values of K can only be 6.

So the possible values for K can be 4, 6, and 12.

The sum of that is \(\boxed{22}\)

A factor of 9 is also -3 and -3. But do you know why it doesn't work?

Much better solution!! 

Notice that if you divided that isosceles triangle into two congruent parts, they form 30-60-90 triangles.

You can easily solve from there.

You can use any bookmark currently.

Edit may not appear because you aren't using Chrome. It depends on the browser you have.

Just paste the code into the URL section.

1. By similar triangles, CE = 22/3.

3. By similar triangles, DE = 8.5.

963

https://www.quora.com/How-many-times-is-digit-0-written-when-listing-all-numbers-from-1-to-3333 

More than 1 explanation there. Hope that helped! 

Thanx, Guest...... you should check to see if you think your answer is 'reasonable'....121 cm^2  seems wwwwaaaayyyy high doesn't it?  (even a square of 4cm sides has but 16 cm^2 area)

Area of isoceles triangle = 1/2 s² sin (theta)  =  1/2 4² sin 120 = 6.93 cm^2

First, we want to find the volume of the barrel. The formula for the volume of a cylinder is h* π * r^2. Substituting 15 in for h and 10 in for r, we get that the volume of the barrel is 1500π. Now, we must find the area fo the bucket. The formula for the volume of a hermisphere is (2/3)* π  * r^3. Substituting 10 in for r, we get that the volume of the bucket is 2000/3π. We divide 1500π by 2000/3π to get 9/4, but Brad can't make 1/4 of a trip to the well and get water, so the answer is 3 trips.

It is a triangle inside a circle.. 

Notice both sides of the triangle (Left and right) are radii of the circle so they are equal in length. 

The angle 120 is between both sides (4cm each) 

If we want the area, there is 2 ways to find it.. 

We can really just constract a right angle triangle from the 120 degrees and use trig to find the rest. 

Other method (I prefer) Is to find the opposite side of 120 degrees, and then apply Heron's formula. 

First of all let's label the sides 

Let the side opposite to angle 120 be c, 

Let the side on the left be b,

Let the side on the right be a. 

Using the law of cosines, we know that:

c^2=a^2+b^2-2ab*cos(x) , Let the angle 120=x 

So just applying the formula we get,

c^2=16+16-32*cos(120)

cos(120)=-0.5 

32-32(-0.5)=48 

c^2=48

c=sqrt(48) Positive or negative but since we are finding a side it must be positive. 

Now let's apply heron's formula 

which is:

Area=sqrt((s(s-a)(s-b)(s-c)) where s=(a+b+c)/2 

we know that,

a=4

b=4

c=sqrt(48)

adding these together we get:

4+4+sqrt(48) =14.928203 approx.=15

so s=15

just subsituiting, 

sqrt((15(15-4)(15-4)(15-sqrt(48))=121.038469 approx=121

So the area is 121 cm^2

I am pretty sure there is a faster solution.

Maybe using inscribed theorem etc..  

Some questions, 

1- I already have a bookmark, do i still need to create a new one? If so how? (Google chrome tho) 

2-I click right click on the bookmarks that i have but no "edit button shows..) 

great solution! Exactly what I did too :)) 

But apart from "must satisfy the equation 2x+3y=5" 

we already found that 5/xy=?? (Minimum value) 

therefore, 5=xy :) 

so 5/5=1 

An arc of 55 degrees on circle A has the same length as an arc of 40 degrees on circle B. What is the ratio of the area of circle A to the area of circle B? Express your answer as a common fraction.

https://www.desmos.com/calculator 

Type your question here but let k=x and j=y or vice versa and notice that k=j at 6 

also when k or j = 4 the other = 12 

Also notice that it will approach 3 but can't equal to 3 as it will be undefined. 

1) The graph of the parametric equations x= 2-3t, y= -1+5t is a line. What is the slope of this line? 

2)Find the value of c such that the point (3,c) is on the graph of the parametric equations x = 6 + 2t, y = -2 +5t

3)At what point does the graph of the parametric equations x = 3-2t, y= -2 + 5t, intersect the graph of the parametric equations x = -1+3s, y=5-9s?