Write the first four terms in the following sequences. A(n+1)=A(n)−5 for n≥1 and A(1)=9 .

Mathematics

1 answer:

luda_lava [24]3 years ago

4 0

Answer:

Step-by-step explanation:

A(1) = 9

A(n+1) = A(n) - 5

n = 1 ; A(1+1) = A(1) - 5

A(2) = 9 - 5

A(2) = 4

n = 2 ; A(2+1) = A(2) - 5

A(3) = 4 - 5

A(3) = 1

n = 3 ; A(3+1) = A(3) - 5

A(4) = 1 - 5

A(4) = -4

n = 4 ; A(4+1) = A(4) - 5

A(5) = -4 - 5

A(5) = -9

First four terms are: 9 , 4 , 1 , -4 , - 9

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If the area of a baseball diamond (shape of a square) is 8100 ft squared, how would you find the distance from 1st base to 3rd b

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Answer:

Exact distance = $90\sqrt{2}$ feet
Approximate distance = 127.2792 feet.

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Explanation:

The area of the square is 8100 square feet, abbreviated ft^2.

Apply the square root to find the distance from any base to its adjacent counterpart (eg: from 1st to 2nd base). So we get sqrt(8100) = 90 ft as that side distance. Notice that 90*90 = 8100.

If you were to draw a line from 1st base to 3rd base, then you would split the square into two congruent right triangles. Each right triangle is isosceles (the two legs being 90 ft each).

Use the pythagorean theorem to find the hypotenuse.

$a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{90^2+90^2}\\\\c = \sqrt{2*90^2}\\\\c = \sqrt{2}*\sqrt{90^2}\\\\c = \sqrt{2}*90\\\\c = 90\sqrt{2} \ \text{ ... exact distance}\\\\c \approx 127.2792 \ \text{ ... approximate distance}\\\\$