Question 2:

Draw:

We draw TO, OU, and OA so that they meet at the center as radii.

Plan with what you know:

Since angle QTA = 41 and angle RUA = 63, we can use that information to find angle TOU.

TO, OA, and OU are all congruent as they are radii. Because of this, isosceles triangles TOA and UOA are formed.

Solving:

PUA = 180 - RUA = 117

PTA = 180 - QTA = 139

OUA = PUA - 90 = 27

OTA = PTA - 90 = 49

UOA = 180 - 2(OUA) = 126

TOA = 180 - 2(OTA) = 82

TOU = 360 - (UOA + TOA) = 152

QPR = 360 - 90 - 90 - TOU = \(\boxed{\text{Now you do the rest!}}\)

Shouldn't be that hard, considering that you read my solution.

Question 1:

(I drew this)

AD = 10 - 7 = 3

Through a series of proofs, we know that ADB is similar to BEC by AA.

We set up a proportion.

1. \(\frac{AD}{AB}=\frac{BE}{BC}\)

Subsitute in known values.

2. \(\frac{3}{17}=\frac{7}{BC}\)

Can you solve for BC?

The following hints are not the best way to do it, but the best way to understand it.

For the first problem:

Consider:

Perimeter = 2L + 2W

Set Up:

"The length of a rectangle is five meters less than twice the width​"

L = 2W - 5

Equation: 44 = 2L + 2W

Now solve!

Using this method, you can solve the rest.

This is just to find the polynomial. I believe you need to use Pascal Triangle to find the rest.

Consider:

Standard form:

ax² + bx + c = 0

Use your information:

(1)    a(-4)² + b(-4) + c = -22

(2)    a(-1)² + b(-1) + c = 2

(3)    a(2)² + b(2) + c = -1

Simplify:

(1)    16a -4b + c = -22

(2)    a - b + c = 2

(3)    4a + 2b + c = -1

These equations are solvable because there are 3 variables with 3 equations.

Solving:

(1) - (2) = 15a -3b = -24

(2) - (3) = -3a - 3b = 3

Subtract the two resulting equations

18a = -27

a = (-3/2)

From here, it is basic algebra to find the rest of the variables.
a=-(3/2) b=(1/2), c=4

Our quadratic polynomial is:

\(-\frac{3}{2}x^2+\frac{1}{2}x+4=0\)

I never asked a question. But from what I've seen on this website (I've dugged through a lot of posts out of interest):

It depends on:
(1) Who is online

(2) The difficulty of the question

(3) The reputation of the question asker

(4) The legitimacy of the question.

Cphill, EP, and Cal tend to answer the question as soon as possible. While other answerers (like Melody, Heureka, and Alan) usually look for harder problems that may interest them. They also tend to come online a little less. The question difficulty is determines a lot too. College level math or competition math (especially olympiad level) take the longest. Intermediate to basic level competition math take some time. The fastest are easy competition problems to school level problems. The reputation of the question asker may motivate some to answer the question. Question's posted by Melody or CPhill gain attention, while Guest questions are the lowest priority. The question needs to be legit. Questions like long chains of homework usually takes a long time. A single simply formatted question takes less time.

Hint: The angle formed by a tangent line and the circle's radius when is a 90 degree angle

Using this info, can you find the slope?

Another hint: The slopes of perpendicular lines are negative reciprocals of each other.

Example of a negative reciprocal:

\(2\) and \(-\frac{1}{2}\) 

"If you could have a superpower what would it be?"

Be careful for what you wish! That superpower may ruin your life and make your life miserable in ways you can never imagine! Try some thought experiments and imagine what would happen with your super power. Can you keep it secret? How would you deal with the media? How would you deal with the SOCIAL media?

"If you could be an animal what would it be?"

Once again, be careful for what you wish. You never could imagine the horrible things that can happen to you as an animal. If you were to retain your human intelligence, how would you deal with all that attention?

But of course. I would probably have the power to control time only after I do ten pushups. The reason why ten pushups is because I would rather put the trigger on a physical action than a mental one. An accidental or not thoughtful will to travel through time can lead to accidents or unwanted events.

I'd stay human. I like being the most developed creature on earth :)

Elegant!

To obtain the largest value, you have to make the two values wrapped in paranthesis as close as possible.

To obtain the smallest value, you have to make the two values wrapped in paranthesis as far as possible.

No I don't think so. I think they have to approve it first?