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The ONLY answer that has the correct units is A    33.5  in³       No calculation necessary.

y= mx+b      m = slope

y = 1/3 x + b     sustitute in the point given to calc 'b

4 = 1/3 (-3) + b      b =  5

y = 1/3  x + 5

Well just plug in r, because you know that the radius is 2.

So it should be 4/3pi2^3

4/3pi8

It should be 33.5in^3

AC || FD    so  angle C = 3x    (=  Angle D)

x + 8x +3x = 180^o      Solve for 'x'

Square area would be   side length x side length      4.5  x 4.5 cm²

    added to triangle area   1/2 bh    =   1/2 (4.5)(4.5) cm²

Use law of cosines to find missing side length

   then use Heron's Rule to calculate the area....

if the commer is a decimal point then its 0.1806829816707153

if its not then its 0.0001806829816707

Volume of a cone is        (1/3) • pi • radius² • height 

Substitute values            (1/3) • 3.14 • 8.5² • 18 

Do the arithmetic            (1/3) • 3.14 • 72.25 • 18  =  1361.19 

And the answer, rounded, is                                      1361.2 cubic feet  

_.

wait what... hmmm thats confusing...

Yes you are right LOL  :)

I have no idea...

lets see if my math teacher can do it...

Wouldn't they be 0 meters apart.... The cable is 10 m above the gound and half the cable is 40 m long. SInce the cable is 10 m above the gound, that means that the cable is 40 m above the ground. If the length of half the cable is 40 m and the cable is 40 m above the ground, wouldn't the cable have to be folded in half? If the cable is folded in half, then the 2 poles are 0 meters apart.

🔥🔥🔥

Edit:

Since my previous answer is a total mess, I'll try to clarify.

The problem tells us that the bottom of the cable is 10 m above the gound. Since the poles holding up the cable are 50 m tall, that means that the top of the cable is 50 m above the ground. If we cut the cable in half, there are 40 m on the left and right side. Taking the right side only, the cable is 40 m long. Since the cable is 10 m above the gound, it is 40 m tall. This is the most confusing part that I can't explain well... In order for the cable to be the same length as it is tall, the cable must be right on the pole. For the cable to be on the pole, then the cable must have been folded exactly in half meaning that the distance between the two poles is 0 m.

What is the lateral area of the cone?

Looks like there are 19 possible finite roots!!  Use a numerical technique like Newton-raphson to find them:

Find the area of the shaded polygons

This relates to the Collatz conjecture.  For the specific numbers quoted there are 15 different integers involved (that is, if I've interpreted the question correctly!), namely: 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

One question per post!

Try to do them yourself. These are very basic questions.

Surely you could do some of them yourself

See https://web2.0calc.com/questions/what-is-the-polar-form-of-the-equation-of-x-6-2-y-2-36#r2 

As follows:

Haven't done a problem like this in a while but from what I remember:

Find how many play 1 sport first

Basketball

Start with 17-8(baseball and basketball)-5(basketball and football)=4 students play just basketball

Baseball

Start with 21-8(both bballs) -6(football and baseball)=7 play just baseball

Football

Start with 24-6-5=13 play just Football

So far we have 13+7+4=24 students

Add that to the double sport players

24+8+5+6=43 students play sports

Another way is to take 21+17+24=6s and subtract the doubles

62-8-5-6=43

That isn't correct

No Problem! I find it easier to do these problems when you know how many you are supposed to end with first. :) 

The sum of three integers is 193. The sum of the first and second integers exceeds the third by 13. The third integer is 11 less than the first. Find the three integers.

Die Summe von drei ganzen Zahlen ist 193. Die Summe der ersten und zweiten ganzen Zahlen überschreitet die dritte um 13. Die dritte ganze Zahl ist 11 kleiner als die erste. Finden Sie die drei ganzen Zahlen.

Hello Guest!

\(x+y+z=193\\ x+y=z+13\\ \underline{z=x-11}\)

\(x+y+x-11=193\\ \underline{x+y=x-11+13}\)

\(2x+y=193+11\)

\(y=-11+13\)

\(y=2\)

\(2x+2=204\\ 2x=202\)

\(x=101\)

\(z=101-11\)

\(z=90\)

  !

Using Pythagoras theorem,

\((PL)^2=(AL)^2+(AP)^2\)

\(PL=\sqrt{(AL)^2+(AP)^2}\)

\(PL=\sqrt{64+36}=10\) units

Notice PL is the length of the rectangle.

Now,

Notice angle MPA, it is 45 degrees. Why? (PA  is perpendicular on diagonal LM) it follows, that it bisects the angle.

Notice triangle PAM is a right-angled triangle (LM is a straight line, the straight-line angle is 180 degrees, LAP is 90 so PAM is also 90 to add up to 180)

Use trigonometry to find PM

But From angle PMA (Which is also 45 degrees) (Angles in a triangle add up to 180 degrees)

\(sin(45)\frac{6}{PM}\)

Thus \(PM=\frac{6}{sin(45)}\)\(=8.485 units\)

Area of rectangle is PM*PL  (Length*width)

\(10*8.485\)

=\(84.85\) units squared, "round your final answer to the nearest hundredth" (already rounded)

let the three integers be \(x,y,z\)

It follows:

(1) \(x+y+z=193\)  (The sum of the three integers is 193)

 (2) \(x+y=z+13\) (The sum of first and second integers are more than the third by 13) 

 (3) \(z+11=x\) (The third integer is 11 less than the first) 

Substitute (3) into (2)

But first, rearrange (3) such that, \(z=x-11\)

\(x+y=x-11+13\)

\(y=2\)

Now the first equation (1)

\(x+y+z=193\)

\(x+z=191\)

We know from (3) that \(z=x-11\)

\(x+x-11=191\)\(=2x-11=191\)

\(2x=202\)

\(x=101\)

Again, the first equation (1)

\(x+y+z=193\)

\(101+2+z=193\)

\(z=90\)

So the three integers are:

\(x=101\)

\(y=2\)

\(z=90\)