All Answers 356001 Answers

If  PQ = 5,QR = 2x, and PR = 7x, what is PR?

As  x  goes to infinity,  x²  goes to infinity;

as  x²  goes to infinity,  1/x²  goes to zero.

So the  lim (as x goes to infinity)  of  7 - 1/x²  is  7 - 0  which is  7.

To divide by a fraction, multiply by its inverse:

(1/2) / (3/5)  =  (1/2) x (5/3)  =  (1x5) / (2x3)  =  5/6

To find out how long it takes an amount to double, you can use this formula:  t  =  ln(2) / r

where  t = time  and  r = rate (written as a decimal).

For example, if you want to know how many years that it takes a population of 22,350,000 to double if the yearly population rate increase is 9%, use:  t  =  ln(2) / 0.09   --->   t = 7.7 years (approximately).

The beginning population is not used in the calculation.

Was this answer correct? Also, is this the final exam for Geometry?

Ok, Alan, you're right. I've got something confused.

If the grids is composed of unit squares then h(7) = 5, h(h(7)) → h(5) = -1

.

f^-1(x) = (x - 5)/4

f^-1(9) = 1

f^-1(f^-1(9)) → f^-1(1) = -1

.

solve (C*((U*(e^-(t/(R*C))))^2)-(V^2))/2=A for t

The dot product is a scalar Omi.

u.v = -7*0 + (-1)*8 + 8*2 → 8

.

Find the vector z, given u= (3,−2,−3) and v= (4,3,−5). 

z = 2u + 5v 

Approximate the limit 

-6  ?

solve (С*(((2.7^-(t/(R*C)))-G)^2))/2=A for t

\(\begin{align}(С*([(2.7^{-(t/(R*C))})-G]^2))/2&=A\\~\\ \frac{С\;[(2.7^{-(t/(R*C))})-G]^2}{2}&=A\\~\\ \;[(2.7^{-(t/(R*C))})-G]^2&=\frac{2A}{C}\\~\\ (2.7^{-(t/(R*C))})-G&=\pm\sqrt{\frac{2A}{C}}\\~\\ 2.7^{-(t/(R*C))}&=G\pm\sqrt{\frac{2A}{C}}\\~\\ log[2.7^{-(t/(R*C))}]&=log\left[G\pm\sqrt{\frac{2A}{C}}\;\right]\\~\\ -(t/(R*C))log[2.7]&=log\left[G\pm\sqrt{\frac{2A}{C}}\;\right]\\~\\ t/(RC)&=\frac{-log\left[G\pm\sqrt{\frac{2A}{C}}\;\right]}{log(2.7)}\\~\\ t&=\frac{-RClog\left[G\pm\sqrt{\frac{2A}{C}}\;\right]}{log(2.7)}\\~\\ \end{align}\)

so its exponential

Find the magnitude of the vector described below. Initial point: (–8, –9, –5)
Terminal point: (–2, –4, –3) 

\(d^2=(-2--8)^2+(-4--9)^2+(-3--5)^2\\ d^2=(-2+8)^2+(-4+9)^2+(-3+5)^2\\ d^2=(6)^2+(5)^2+(2)^2\\ d^2=36+25+4\\ d^2=65\\ d=\sqrt{65}\; units\\\)

Find a unit vector in the direction of the vector described below. Initial point: (–8, 9, –1)
Terminal point: (1, 5, 0) 

This clip is quite good :0

Determine the octant(s) in which (x,y,z) is located so that the conditions are satisfied.

x > 0, y < 0, z > 0

I just had to look up octants myself.  They are not that difficult

With 2 dimensions you have quadrants.

With 3 dimensions you have octants becasue you also have to consider whether y is positive or negative.

The first four octants are the same as above only z must be positive

the next four (5,6,7,8) are also the same as above but z is negative.

Here is an artical on it.

Find the coordinates of the point located 5 units behind the yz-plane,      x=-5

6 units to the right of the xz-plane,    y=+6

and 8 units above the xy-plane.     z=+8

(-5, 6, 8)

3(x+2y)-3(4x-3y)-2y

There are 3 brackets to expand - the most important thing to remember is that a negative sign always belongs to the number behind it.

3(x+2y)           -3(4x-3y)             -2y

3*x+3*2y          -3*4x  - 3*-3y      -2y

3x+6y               -12x+9y              -2y

3x-12x    +6y  +9y   -2y

And you can finish it :)

Ask if you do not fully understand :)

Find the dot product of u and v.

u= (−7,−1,8) ,v= (0,8,2)

Find u × v.
u= (5,6,2) ,v=( −8,−4,2)

how do i set it up ? 

As follows:

.

.

Find out from your State Capital what the population growth of your State was in the previous 10 years and project it for the next 10 years. Example: If the population grew by 10% in the previous 10 years, then the population will grow to 1.10 x 945,934=~1,040,527 roughly. That is all you can do, unless your State has the population growth for the previous 20, 30 or even 100 years. That would be a much better predictor of the population growth in next 10 years.

The temperature should be:

9 - (4 x 7) = -19 F. by 7pm.