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intensity₁      =  distance₂⁴

intensity₂            distance₁⁴     

25/x  =  900⁴ / 225⁴

x = .09766 uW       9.77 x 10^-2  uW        ( I think !)

Thanks for the kind words guys 

(also, sorry, I made a typo: I meant "Notice that triangles ABO and OCD are similar", not  "Notice that triangles ABO and ODD are similar")

"The area of the triangle formed by points of intersection of parabola y=a(x-3)(x+2) with the coordinate axes is 12. Find a if it is known that parabola opens upward."

Let 

f(x)  = k(x) if x > 3

f(x) = (x - 3)^2 + 3 if x <= 3                                 x<=3,  y>3

Find k(x) such that f is it's own inverse.

y=(x - 3)^2 + 3

make x the subject

\(x=\pm\sqrt{y-3}+3\\ \text{For the inverse, swap x and y}\\ y=\pm\sqrt{x-3}+3 \qquad \\but \quad y\le3 \quad and \quad x>3\\ \text{ Since y is negative it must be the - sign}\\ y=-\sqrt{x-3}+3 \qquad where \qquad x>3 \)

so 

\(k(x)=-\sqrt{x-3}+3 \qquad where \qquad x>3\)

The Question says: 4t + 5s = 375

The Question also says: s = t+12

Now, we can substitute the value of s and our equation will become:

4t + 5(t+12) = 375.

We can easily solve this:

4t + 5(t+12) = 375

4t + 5t + 60 = 375

9t = 375-60

9t = 315

t = 35

Therefore, a tie cost $35.

deleted

Nice!!! 👍 

Find an equation of the line passing through the pair of points (4.9) and (3,5). Write the equation in the form

Hello Guest!

\(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-9}{3-4}\)

\(m=4\)

\(y=m(x-x_1)+y_1\)

\(y=4(x-4)+9=4x-16+9\)

\(y=4x-7\)

\(Ax + By = C\\ corresponds\\ 4x-y=7 \)

  !

Agreed. I didn't think of that!

I meant 2 x 3 x 3 x 3 x 5

typo?

This is a simple Permutation.

For the first choice, you have 5 options.

And As you can repeat flavours, you will again have 5 options.

Now you multiply that and you get:  $5^2=25$

Hope that helps!!! :)

🙃🙃👌

An easy way is to look at it as a co-ordinate geometry problem.

Suppose that A is the origin, (with AB as the x-axis), and that the square has a side length of 2.

The point on the circle at the midpoint of DC, call it E, will have co-ordinates (1, 2).

The centre of the circle, call it F, will be on the line AC, suppose that it has co-ordinates (k, k).

Then, if the radius of the circle is r, 

AF^2 = FE^2 = r^2,

and using Pythagoras,

k^2 + k^2 = (1 - k)^2 + (2 - k )^2,

2k^2 = 1 - 2k + k^2 + 4 - 4k + k^2,

6k = 5,

k = 5/6.

r^2 = k^2 + k^2,

etc..

There are: 9999 - 1000 + 1 =9000 4-digit numbers

There are: 9000 / 4 =2250 number that ARE divisible by 4

There are: 9000 / 5 =1800 numbers that ARE divisible by 5

There are: 9000 /20 =450 numbers that ARE divisible by 20 AND are counted twice

Since you want ALL 4-digit numbers that ARE NOT divisible by 4 or 5, then we have:

9000 - [2250 + 1800 - 450] ==9000 - 3,600 = 5400 4-digit numbers that are NOT divisible by 4 or 5.

f(9)=7

f(2*4.5)=7

If x=4.5

then

\(2y=\frac{7}{2}+2\\ y=\frac{11}{4}\\ y=2.75\)

4.5+2.75 =  7.25

BD = sqrt(8² + 6²)

DF = sin(29º) * 13

∠x = sin^-1(DF / BD)

Here is a graph, now count them.

Your answer is brilliant!!! Kudos! 

5 choices for the first scoop and 5 for the second scoop = 25 choices altogether.

A town has a population of 12000 and grows at 3.5% every year. What will be the population after 7 years, to the nearest whole number? 

When you start with 12,000 and add 3.5%, after the 1st year you have (12,000) • (1.035)  

Then you start with that new amount and add 3.5%, so after the 2nd year you have [(12,000) • (1.035)] • (1.035)   

You can continue that progression to demonstrate that after "n" years, you will have (12,000) • (1.035)ⁿ  

So after 7 years, the population will be (12,000) • (1.035)⁷  

You can multiply that out by hand or use a scientific calculator to get the answer 15,267.  

_.

[DEF]/[ABC] = 4/17.

t=35

The answer is wrong but thanks for answering.

The sum of the coordinates is 5 + (-7/2) = 3/2.