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zheka24 [161]
3 years ago
10

I'm not sure where to begin, can someone help me begin?

Mathematics
1 answer:
VLD [36.1K]3 years ago
7 0
First, convert the mixed number into an improper fraction.
To convert a mixed number into an improper fraction, find the product of the whole number and the denominator and then add the numerator.
Then the denominator will be the original denominator from the mixed number.

1 \frac{1}{3} = \frac{4}{3}

Now the fraction \frac{4}{3} is being raised to the third power negative.
When an exponent is negative, it means to take the reciprocal of the number then raise it to the power of the absolute value of the exponent.

In a mathematical expression: x^{-n} = \frac{1}{x^n}

So, first take the reciprocal of \frac{1}{3} which is 3.

Then raise 3 to the absolute value of the exponent. The exponent is -3.
The absolute value of -3 is 3.

3^3 = 3 * 3 * 3 = 27

So, the answer is 27.
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Can someone please help me​
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Answer:

square 20 has 44 green squares

square 21 has 45 green squares

Step-by-step explanation:

To solve the problem, we need to observe the cases, and determine/define a rule for each case (odd number of sides, or even number of sides).

For square one, we note that the centre square is shared by two diagonals, so we saved one square from the two diagonals.

The side length is 3 for square 1, 4 for square 2, and so on.

Let

n= square number (1, 2,3...)

L = side length (3,4,5...)

G1(n) = function that gives the number of green squares for square n, n=odd

G2(n) = function that gives the number of green squares for square n, n=even

side length, L=n+2   ................(1)

G1(n) = twice the side length less one, as discussed above

G1(n) = 2L-1       now substitute L=n+2

G1(n) = 2(n+2) -1    simplify

G1(n) = 2n + 3

Check:

for n=1, square 1 has 2*1+3 = 5 green squares ... checks

for n=3, square 3 has 2*3+3 = 9... checks

for n=5, square 5 has 2*5+3 = 13 ....checks

For even squares, it is even easier, because

G2(n) = 2L = 2(n+2)

check:

for n=2, square 2 has 2(2+2) = 8 green squares........checks

for n=4, square 4 has 2(4+2) = 12 green squares........checks.

Fincally, we apply our formula to n=20 and n=21

square 20 : G2(20) = 2(n+2) = 2(20+2) = 44 green quars

square 21 : G1(21) = 2n+3 = 2(21)+3 = 45 green squares

5 0
2 years ago
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