All Answers 358270 Answers

Answer 1 is correct but there is a typo.

It is not c=121

It is the product of all possible c is 121

\(c=-9\pm\sqrt{40}\;i\)

The rate of change of the area is -6/5 in^2/sec.

The sum of the coordinates is 11 + (-3/2) = 19/2.

Thanks very much guest for finding that ancient thread  (I assume there is a newer one as well)

It seems this question has already been answered to the best ability of most, if not all, people here.

I have unlocked the linked question if anyone wants to add to it.   

Do not answer directly on this thread

A vertical pole AB measuring 5 meters snaps at point C. The pole remains in contact at C and the top of the pole touches the ground at point T, a distance of 3 meters from A. Find the length AC, in meters, the point where the pole snapped.

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

AB = 5       AT = 3       AC => x

3² + x² = (5 - x)²          x = 1.6           CT = 3.4

Find the area of the triangle with sides sqrt(13), sqrt(61), sqrt(80).

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

The triangle area, using Heron's formula, is 14 square units. 

....BUT   since b = c+ 11     b would be    132 under your scenario

x^2 + 132 x + 121    has 2 roots.....   hmmmmm.....

There are 56 possible seatings.

6 x 6 x 6 = 216 possible rolls

2 4 5

5 2 4

4 5 2

2 5 4

5 4 2

4 2 5       6 rolls will mult to 40          6 /216 = 1/36

for the polynomial to have 1 real root, its discriminant, \(\sqrt{b^2-4ac}\), must be equal to zero.

In this case, it would mean that\(\sqrt{(c+11)^2-4c}\) must be equal to zero. We can then set up an equation:

\(\sqrt{(x+11)^2-4x}=0\\ (x+11)^2-4x=0\\ x^2+22x+121-4x=0\\ x^2+18x+121=0\)

(i replaced the variable c with x to make it less confusing)

the product of the roots of a quadratic is equal to the constant term divided by the coefficient of the quadratic term. In this case, it would be equal to 121/1 = 121. 

Therefore, the answer to your question is c = 121.

I assumed you meant "SUM of its digits > 7": If that is the case, then you have:

(1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 18)>>Total = 90 such sums

Probability = 62 / 90 ==31 / 45

(by the way, I'm assuming that you mean x^2+y^2=25, because or else it wouldn't be a circle)

First, set up a system of equations:

\(x^2+y^2=25 \\ 3x+4y=6 \)

notice that the second equation, 3x+4y=6, is very close to 3x+4y=25. 

The system of equations below:

\(x^2+y^2=25 \\ 3x+4y=25 \)

would have 2 solutions: (3,4) and (-3,-4). The distance between them is 10, as it is the diameter of the circle.

therefore, as the constant 25 in the equation 3x+4y = 25 decreases by 1, the distance between the equation with the number decreasing and the original equation 3x+4y=25 will increase by 10/50 = 1/5.

the rest of the explanation is in the photo below:

Answer: \(2\sqrt{23.56}\)

Approximate form: 9.708

I hope this helped you cuz i took a long time solving this lol

The possible values of the second term are 2 and -6.

A 2 digit palindrome in any base would have to be   x  x      as in 11  22  33  44  55  66  ....99  

            which of these is a palindrome in base 2?

(the only 5 digit base two numbers are 16-31₁₀    palindromes include 17 21 27 31)

27      in base 2   =  11011

27 = 33₈

125/9   *  r   = 25/3         r = common ratio = 3/5

125/9 * (3/5)⁷ = 125/9* 2187/78125 = 0.3888      or  (243/625)

Answered here:

https://web2.0calc.com/questions/help_30050

We  have a horizontal asymptote at y  = 4

This means  that  the ratio of the coefficients on  x^2  in the  numerator and denominator =   4

So

a/-2   = 4    ⇒    a   =   -8

And since we have a vertical asymptote  at   x  = 5 , then

-2(5) + c   =  0

c = 10

And (0,0)  is on the  graph  which means that

2(0)  - b   =  0

So b = 0

So

a + b + c  =  -8  + 0  +  10    = 2

Here's a graph :  https://www.desmos.com/calculator/fnsrqu4ihg

There are 4 ways:

(4, 0, 0)

(3, 1, 0)

(2, 2, 0)

(1, 1, 2)

order doesn't matter because the boxes are indistinguishable

See the following :

We  have   30-60-90  triangle GIF   where  GI  = 3.5  and  IF =  3.5sqrt (3)

So....the  area of this triangle is  (1/2) (3.5)(3/5) sqrt (3)  = (49/4)sqrt (3)/2            (1)

And then we have   the  area  of   60°  sector   of a circle with a rdius of 7  less a triangle with sides of  7  and an included angle of 60°

So this area is    (1/2)7^2 ( pi/3)  - (1/2) ( 7)^2 sqrt (3) / 2  =  (49/2)  ( pi/3 - sqrt (3) / 2)   =

49pi/6 - (49/4) sqrt (3)     (2)

So   1/4 area  of this  shaded region  is  (1) + (2)   =    (49/6) pi - (49sqrt (3)  /8)

So....the total area is    4  [ (49/6) pi  - 49sqrt (3) / 8 '  =

(98/3) pi  - (49/2) sqrt (3)    ≈  60.19  units^2

Exactly  what Guest found   !!!

To answer this question, you will need to find the area of the chord of a circle with a radius of 7, shown in the image below, and then multiply by 2

The area of the chord is the area of the sector minus the area of the triangle:

\(\frac{49\pi}{3}-3.5\sqrt{3}\cdot3.5\cdot\frac{1}{2}\cdot2 \)

=\(\frac{49\pi}{3}-12.25\sqrt{3}\)

Now, multiply that by 2 and the answer is \(\frac{98\pi}{3}-25\sqrt{3}\)

That is roughly equal to 59.324

NO GUARANTEES:   (YOU should check my math)