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Find the distance between C and midpoint of AC with the \(\sqrt{(χ2-χ1)^2+(y2-y1)^2}\) And with this resault is equal with \(\sqrt{(χ3-χ2)^2+(y3-y2)^2}\) (the distance between midpoint of AC and A) and you have x3,y3 unknowns and you have and the equation 7𝑥 + 2𝑦 = 11 so 2 equations and 2 unknowns.So you solve it! Try it alone!

Hope this helps! 

\(\frac{10π}{5}= 2π \) so for >10π we start from 0 again.The same and with -10π

So \(-\frac{16π}{5}= -\frac{10π}{5}-\frac{6π}{5}= -2π - \frac{6π}{5} = -\frac{6π}{5} \)

Correct answer is \(-\frac{16π}{5}\)

Hope this helps! 

Yes!

\(-\frac{π}{12}= - \frac{180}{12}= -15\) degrees

This is a line so the equation is like \((y-y1)=\frac{(y1-y2)}{(x1-x2)}(x-x1) \),\((x1,y1)=(0,0) , (x2,y2)=(20,15) \)

\((y-0)=\frac{(0-15)}{(0-20)}(x-0) <=> y=\frac{15}{20}x\)

The equation is \(y=\frac{15}{20}x \)

Hope this helps!

This ^

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They have to mutlipy together to -10 and add to to t

5   -2      t=3

10   -1        9

-5     2       -3

-10   1      -9

When t=1

h= -16(1^2) +64(1) = 48 FT

Max = c- b^2/4a  = 0 - (64^2/(4(-16)) = 64 ft

t max    64 = -16t^2 +64t        -t^2 +4t -4 = 0       or  t^2 -4t+4 = 0       (t-2)(t-2)     = 0     so t max = 2 sec

h= 0

 0 = -16t^2 + 64t

16t = 64

t= 4 sec

Change it to y = mx + b form   where m = slope (gradient)

3x+5y=8

5y=-3x + 8

y = -3/5 x + 8/5        gradient =  - 3/5

You calculate perfect cubes as follows:

Take the exponent / 3 (use integer part only) + 1 = 5/3 + 1 =2, and 10/3 + 1 = 4. Then multiply them together:

So, 2 x 4 = 8 perfect Cubes in 3^5 x 5^10 as follows: (1^3, 3^3, 5^3, 15^3, 25^3, 75^3, 125^3, 375^3) =8

P.S. These Perfect Cubes are divisors(factors) of 3^5 * 5^10.
 

Just multiply: Length x Width x Height =7/8 x 8/9 x 9 = 7 cubic inches.

is it 36(3.14) inches ??

Thank you!!

I see a total of 4 as follows:
When n=1, the GCD=6
When n=2, the GCD=1
When n=3, the GCD=2
When n=4, the GCD=3
And this pattern repeats after n = 7

\(200 = R + P + C = \\ \\ R + (3R+4) + C =\\ \\ 4(R+1)+C\\ \\ C = 196-4R\)

\(E[C] =\\ E[196-4R]=\\ 196-4E[R] = \\ 196-4(2) = 188 \)

\(Var[C] = Var[196-4R] = \\ 4^2 Var[R] = \\ 16Var[R] =\\ 16(1.2) = 19.2\)

I think yes especially if you are in sports or theatre club.

Yes, you got it!.

y = 250 * 4^x - That is your equation for the growth of bacteria.

Here is my jab at this!!

10C3 * 7C2 * 5C2 * 3! =151,200 / 6^10 =0.00250057 =0.250057%.

Because the last "456" are fixed, they can only appear in 3! ways =456, 465, 546, 564, 645, 654.

P.S. There is bound to be a "screw up" somewhere! After all, it is based on "Probability Theory" invented by some Italian and a couple of French mathematicians for the purpose of gambling, according to my understanding of it!.

\(E[a X + b] = a E[X] + b\\ \\ Var[a X + b]= a^2 Var[X]\\ \\ E[Y] = E[100X-50] = 100E[X]-50\\ \\ Var[Y] = Var[100X-50] = 10000Var[X]\)

I bet you have E[X] and Var[X] from some other part of the problem so plug those in.

Expanding the terms, 

\((x^2+2xh+h^2)+(y^2+2yh+y^2)=(a^2+2ab+b^2) \)

Using Pythagorean Theorem,

\(x^2+h^2=a^2\\ y^2+h^2=b^2\)

We could subsitute the values in, and rewrite the equation

\(a^2+2xh+b^2+2yh=a^2+2ab+b^2\\ 2xh+2yh=2ab\\ h(x+y)=ab \)

\([ABC]=\frac12 AB\cdot CH = \frac12 BC \cdot AC\\ \frac12 (x+y)h=\frac12 ab\\ h(x+y)=ab\)

I hope this helped,

Gavin

Expanding the terms, 

\((x^2+2xh+h^2)+(y^2+2yh+y^2)=(a^2+2ab+b^2) \)

Using Pythagorean Theorem,

\(x^2+h^2=a^2\\ y^2+h^2=b^2\)

We could subsitute the values in, and rewrite the equation

\(a^2+2xh+b^2+2yh=a^2+2ab+b^2\\ 2xh+2yh=2ab\\ h(x+y)=ab \)

\([ABC]=\frac12 AB\cdot CH = \frac12 BC \cdot AC\\ \frac12 (x+y)h=\frac12 ab\\ h(x+y)=ab\)

I hope this helped,

Gavin

\(Var[a X + b] = a^2 Var[X]\)

\(Var[3Y+2] = 9 Var[Y] = 11.61\\ \\ Var[1-2Y] = 4 Var[Y] = 5.16\)

\(E[aX + b] = aE[X] + b\\ V[a X + b] = a^2V[X]\)

\(\tilde{R} = 1-3R\\ E[\tilde{R}] = E[1-3R] = \\ 1 - 3E[R] =\\ 1-3\left(\dfrac{24}{11}\right)=\\ 1-\dfrac{72}{11} = -\dfrac{61}{11}\)

\(V[\tilde{R}] = V[1-3R] = \\ (3)^2 V[R] = 9\left(\dfrac{95}{121}\right) = \dfrac{855}{11} \)

Try to expand the terms! 

y=60/x     which is the same as dimitris