All Answers 358083 Answers

You can find the equation of a tangent line by using the following formula:

\(y-y_1=f'\left(x_1\right)\left(x-x_1\right)\)

The general area formula for a trapezoid is the following equation:

\(A_{\text{trap.}}=\frac{1}{2}(b_1+b_2)h\)

A = area of the trapezoid

b₁ = the length of a base

b₂ = the length of the other base

h = the perpendicular height from one base to the other

Generally, it helps me to remember the formula as the quantity of the average of the lengths of the bases all multiplied by the height. For some reason, I can recall a formula better when I remember the formula, in words, and then translate it into an algebraic equation.

P (three heads) =  C(8,3)(2/3)^3(1/3)^5  = 448 / 6561

P (two heads) = C(8,2)(2/3)^2(1/3)^6  = 112 / 6561

So......     448 / 112   =  4 times more likely to get 3 heads than 2 heads

Let's  look  at the expansion of the second term, first

Note that, by the binomial expansion, the fourth term of this expansion will be :

20 c^3 (1/c)^3   =  20

And note that every other term in this expansion either contains  "c"  or "1/c" - or both - to some power(s)

And in the expansion of (a + b)^4  , the  a^2b^2   term will be the third term....and its coefficient  will be 6

So.....the a^2b^2  term  in the product of both expansions will be  20 * 6   = 120

If the shaded regions have equal areas....then the chords forming part of their boundaries have equal length.....then each chord must span 60° and radii drawn from the center of the semi-circle to each of the upper vertices of the trapezoid will form three congruent equilateral triangles  whose sides will all equal 1 meter

Then the area of the trapezoid is : 

3 (1/2) sin 60  =  3 (1/2) (√3) /2   =  (3/4)√3  m^2  ≈ 1.3 m^2

Draw OA , OB and AB

Now since minor arc AB  = 80°....then, in triangle AOB,   since angle AOB is a central angle of the larger  circle  subtending minor arc AB, it  has the same measure.

And OA  = OB  since they are both radii of the larger circle....but if OA  = OB....then the angles opposite these sides in triangle AOB - namely angles OAB and OBA - are equal.... 

Thus....  OAB  = OBA  =   [ 180 - 80 ] / 2   = 50°

But angles OAB and OBA are inscribed angles in the smaller circle

And OAB  intercepts minor arc OB.....and its measure is twice that of OAB  =100°

Likewise....OBA  intercepts minor arc OA....and its measure is twice that of OBA  = 100°

Thus  minor arc OA  + minor arc OB  =  arc AOB

And    100° + 100°  =  arc AOB  = 200°

(a)

I'm not sure if this is correct but the expected value for each question is (1/10)*0+(9/10)*1=0.9. Since the expected value for one question is 0.9 and there are ten questions. The expected value for the exam is 10*0.9=9.

I was thinking, this is like putting 9 indistinguishable balls into 3 distinguishable boxes where every box must have one ball. Once you put a ball in each box then we have two but 6 balls into 3 boxes. We can use stars (are the balls) and bars (the box dividers). For example this |**||****, would be 2-0-4. So that's the same as 9C3=84.

Also...

\(\frac{(-3)^{2n+1}}{27\,\cdot\,(-3)^{2n}}=\frac{(-3)^{2n+1}}{27}\,\cdot\,\frac{(-3)^{2n+1}}{(-3)^{2n}}\)

This is not true.

If you multiply the two fractions on the right side together, you will get   \(\frac{[ (-3)^{2n+1})]^2}{27\,\cdot\,(-3)^{2n}}\)     .

\(\frac{a}{bc}\,\neq\,\frac{a}{b}\,\cdot\,\frac{a}{c}\)

But..you can distribute division the same as you distribute multiplication, like this....

\(\frac{8 + 6 +10}{2}=\frac12(8+6+10)\,=\,(\frac12)(8)+(\frac12)(6)+(\frac12)(10)\,=\,4+3+5\,=\,12\)     

I'm glad I am not the only one...

Yes, Cphill, I must concede to you and your wolframalpha...

What I was trying to do was find a number in the expression \(\frac{a}{2}\) such that\(a\in \mathbb{Z}\hspace{1mm}\text{and}\hspace{1mm}-4<\frac{a}{2}\leq -3\). And of course, the only two numbers that work is -7 and -6. 

Also it's the internet's cat

Hong Kong

Haha true but more because of that hilarious and random line in Its Everyday Bro: They buy me like a loan yeah I smell good. Is that your boys cologne? 

HAHAHAHAH

(-3⁾²ⁿ⁺¹ /(27*(-3)²ⁿ)

Note that we can write this as

(-3⁾²ⁿ⁺¹ / (-3)²ⁿ   * ( 1 /27 )

And remember that we have the property that    a^m / aⁿ  = a ^{( m - n)}

So   ...we have....

(-3) ^{[ (2n + 1) - 2n ]}  *  (1/27)  =

(-3)¹  * (1/27)  =

(-3)  / 27  =

-1 / 9

1. Because you smell good.

2. Because the cat (it's a cat, right?) in your profile picture is your cat, and it smells good.

3. You like perfume.

4. You have just made some delicious pancakes with lots of maple syrup, butter, and strawberries. 

5. Because you currently smell someone named 'Good.' 

👻

Where did you live?

-👻

I used to.

I think they want  36.869897645844°  to the nearest minute...

If so....there are 60 minutes in each degree..... so....   60 *.869897645844  ≈ 52'

So the result is     36° 52'

Thanks, Melody.....I had no clue on this one.....!!!!

Sorry, X²......I think you made a slight mistake.....your solution of -3 is correct, but not -3/2

Floor (-3/2)  = -2

But

2(-3/2) + 3  =  0

The other solution is   t  = -7/2

Floor (-7/2)  = Floor (-3.5)  =  -4

And

2(-3.5) + 3  =

-7 + 3  =   -4

Here's a graph of the solution points :

Can I have your cats autograph to please Ginger. :)

Look what you have done to your poor cat!

Thanks :))

Maybe he/she forgot to put the units.