geno3141

Let  PA = x.

PA · PB  =  PC · PD     --->     x(x+ 35)  =  (30)(30 + 20)

                                               x² + 35x  =  1500

                                    x² + 35x - 1500  =  0

                                     (x + 60)(x - 25)  =  0

                                                           x  =  25

The unit's digit must be either a 4 or a 6 for the square to end in 6; all other possibilites can be excluded by trial.

If you are squaring a two-digit number, you can represent this number as  10a + b  (knowing that b must be

either 4 or 6).

(10a + b)²  =  100a² + 20ab + b²

The  100a²  can be ignored for it does not affect the ten's digit.

20ab  must be even; an even number, 20, times either an even number or an odd number results in an even number.

To this term (20ab) must be added the carry of the b² term.

If  b = 4,  the carry is 1.

If  b = 6,  the carry is 3.

Adding an odd number (either 1 or 3) to an even number (20ab) results in an odd number.

By trying various possibiliteis, you will discover that the ten's digit can be any of the odd digits.

The formula for the surface area of a sphere is:  Area  =  4·pi·r².

If the basketball has a diameter of 24 cm, its radius is 12 cm.

Area  =  4·pi·r²   --->   Area  =  4·pi·12²  =  1809.56 sq cm.

If the cost is  $71.62  per sq m, the cost, per square cm is  $71.62 / 100²  =   $ 0.007162.

Final cost:  $ 0.007162 x 1809.56  =  $12.96.

Hint:  divide the area into an equilateral triangle and three congruent segments.

The ten's digit can be any odd number.

There are 7 choices for the first digit:  3, 4, 5, 6, 7, 8, and 9; only 0, 1, and 2 are not acceptable.

After the first digit, there are 8 choices for the second, third, and fourth digits (only 1 and 2 are not acceptable).

This means that there are  7 x 8 x 8 x 8  =  3584  possibilities.

If you use the rules of the sequence, you will get the first six elements to be unique elements.

When you continue the sequence, you will find that:

     a₆  =  -a_o     a₇  =  -a₁     a₈  =  - a₂     a₉  =  -a₃     a₁₀  =  -  a₄     a₁₁  =  -a₅ 

Continuing, you find that:

     a₁₂  =  a₀     a₁₃  =  a₁     a₁₄  = a₂     ...

Etc.

Knowing this, can you calculate the value of a₁₀₀?

The perimeter is AB + BC + AC.

BC  =  AK + KB  =  6 + 8  =  14

Since AK is an altitude, triangle(ABK) is a right triangle. 

Its bases are AK = 6 and KB = 8.

To find AB, use the Pythagoren Theorem:  AB²  =  AK² + KB²  =  6² + 8²

Complete this equation to find the value of AB.

Also, triangle(AKC) is a right triangle.

Its bases are KC = 6 and AK = 6.

To find AC:  AC²  =  KC² + AK²  =  6² + 6²

Complete this equation to find the value of AC.

Now, use:  AB + BC + AC to find the perimeter.

There are 7 + 4 + 9 = 20 balls altogether.

You can pick two balls of the same color if you:

1)  pick two red balls:  (7/20) x (6/19) = ........

2)  pick two yellow balls:  (4/20) x (3/19) = ......

or

3)  pick two green balls:  (9/20) x (8/19) = ........

You'll need to do the three individual calculations and add their answers together ...