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The smalles value of  t    will be given by   -b/2a     where b = -9    and a = 1 for this bowl shaped parabola

   NOTE:   this is the smalles value of t    NOT the smallest value of the function ....you find THAT by putting in the 't' value and calculating.

https://web2.0calc.com/questions/help-please_67220#r2

I'm a bit confused. Why do we want the fraction to be undefined? Could you please explain this to me?

Thanks

Steps: 

1) Find the equation of the straight line first

2) Substitute y = 0 into the equation, solve for x.

3) The answer is the x-intercept.

Thank you. Have a nice day

\(rT = \displaystyle\sum_{k=0}^\infty kr^{k + 1} = \sum_{k = 1}^\infty (k - 1)r^k = \sum_{k = 1}^\infty kr^k -\sum_{k = 1}^\infty r^k = T - S + 1\)

\(T = \dfrac{1 - S}{r - 1}\)

\(T = \dfrac{1 - \dfrac{1}{1 - r}}{r - 1} = \dfrac{r}{(1 - r)^2}\)

\(\dfrac{7 - y}{-1 - (-6)} = \dfrac{-2 - y}{3 - (-6)} \text{ (why?)}\\ \dfrac{7 - y}5 = \dfrac{y + 2}{-9}\\ 9y - 63 = 5y + 10\\ 4y = 73\\ y = \dfrac{73}4 \)

100% probability means that you can be 100% sure that it will happen.

Example: The Sun rises from the East

0 probability means that it won't happen.

Example: The Sun rises from the West

I will give you some hints for the other problems.

b) What has 2 sides?

c) What has 6 faces?

Using the formula to find the volumes, we have

\(V_{\text{cylinder}} = \pi r^2 \cdot 2r = 2\pi r^3\\ V_{\text{sphere}} = \dfrac43 \pi r^3\\ V_{\text{cone}} = \dfrac13 V_{\text{cylinder}} = \dfrac23 \pi r^3\)

We have \(V_{\text{cylinder}} = 2\pi r^3\) and \(V_{\text{cylinder}} + V_{\text{cone}} = \dfrac43 \pi r^3 + \dfrac23 \pi r^3 = 2\pi r^3\), so the two choices gives the same amount of chocolate.

\(BM = MA\) (why?)

\(BA = \sqrt{6^2 + 8^2} = 10\)

\(\angle BMA = 90^\circ\text{ and } BM = MA \Longleftrightarrow \triangle BMA\text{ is a right isosceles triangle (with angles }90^\circ,45^\circ , 45^\circ )\)

\(BM^2 + MA^2 = BA^2\\ 2BM^2 = 10^2\\ BM = MA = 5\sqrt 2\)

The numbers denote the area of each part. 

In the fullest details:

\(\dfrac{x + 2}{x^2 - 2x} - \dfrac2{x - 2} = -1\\ \dfrac{x + 2}{x(x - 2)} - \dfrac{2}{x - 2} = -1\\ \dfrac{x + 2}{x(x - 2)} - \dfrac{2\color{blue}x\color{black}}{\color{blue}x\color{black}(x - 2)} = -1\\ \dfrac{(x + 2) - 2x}{x(x - 2)} = -1\\ -x + 2 = -x(x - 2)\\ -x + 2 = -x^2 + 2x\\ x^2 -3x + 2 = 0\\ (x - 1)(x - 2) = 0\\ x = 1 \text{ or } x = 2\text{ (rejected)}\)

(d - e)^2 = d^2 - 2de + e^2 = (d + e)^2 - 4de

By Vieta's formula, if p and q are the roots of the quadratic equation ax^2 + bx + c = 0, then p + q = -b/a, pq = c/a.

So, in this case \(\begin{cases}d + e = -\dfrac{7}4\\ de = \dfrac{-1}{4}\end{cases}\).

You can do the rest from here.

Square of binomial <=> Discriminant = 0

\(s^2 - 4(9)(4) = 0\\ s^2 = 144\\ s = \pm12\)

s = -12 is also a solution.

Thank you!

You can enter the numbers as follows:

1 4 7 10

2 5 8 11

3 6 9 12

Then there are 3! = 6 ways of arranging the numbers in each column, so the number of ways is 6^4 = 1296.

HInt: If they are perpendicular, then their slopes are the negative reciprocrals of each other. 

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x = sgrt3+y     sub into second equation

sqrt3 +y + y = 2

2y = 2 - sqrt 3

y = 1 - 1/2 sqrt3 

x + 1- 1/2sqrt3  = 2

x = 1 + 1/2 sqrt3

You can multiply them for the answer.......

We know that the rule for divisibility by 3  is that the digits of the number must add up to a multiple of  3. So, it's clear that there are no other such two-digit numbers beyond the ones listed in the problem. Every number divisible by 3  between 100  and 99 is in the sequence, so that gets us through the 39th term of the sequence. Using the rule for divisibility by 3 , it is fairly simple to list out the remaining 11 terms of the sequence: 201, 210. 213, 216, 219, 231, 261, 291, 312, 315, 318. Thus, the 50th term is 318.

thank you!

The broken pole forms a RIGHT triangle with the ground

the slanted portion we will cal 'h'    (as in 'hypotenuse' )

the vertical portion is   5 - h

and the other leg of the triangle (the ground ) = 3

(5-h)^2 + 3^2 = h^2

h^2 -10h+25+9 = h^2

-10h = -34

h = 3.4                      the pole broke 3.4 meters from the top .... AC is thus: 5-3.4 = 1.6 meters

Look here for answer #2:  https://web2.0calc.com/questions/need-help-please_46#r2

Hmmmm..... I am not sure this is possible....

  sqr (x^2-9)  will always be positive     which would mean  |x-3| must be NEGATIVE for the terms to ADD to 0......absolute values cannot be negative.....  Did you enter your question correctly?