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erma4kov [3.2K]
3 years ago
6

Write a rule for the nth term of the sequence 2,20,50,92?

Mathematics
2 answers:
Tomtit [17]3 years ago
7 0

Answer:

482

Step-by-step explanation:

Their 2nd difference is 12

Aneli [31]3 years ago
4 0

2,20,50,92,...\\ \\ a_1 = 2\\ a_2 = a_1+18=a_1+6\cdot 3 \\ a_3 = a_2+30=a_2+6\cdot 5\\ a_4 = a_3 +42 = a_3+6\cdot 7\\ a_5 =a_4+54 = a_4+6\cdot 9\\...\\a_n = a_{n-1}+6\cdot (2n-1) \\ \\ a_1+a_2+...+a_n = \\ =a_1+a_2+...+a_{n-1}+2+6\cdot \Big(3+5+7+...+(2n-1)\Big)\\ \\ a_n = 2+6\cdot \Big(3+5+7+...+(2n-1)\Big)\\ a_n = 6\cdot \Big(1+3+5+7+...+(2n-1)\Big)-4 \\ a_n = 6\cdot n^2-4 \\ \\ \Rightarrow \boxed{a_n = 6n^2-4}

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15. A cylindrical glass 10 cm tall and 8 cm in diameter is filled to 1 cm
ANTONII [103]

Answer:

No. The new height of the water is less than the height of the glass(6.33 cm<10 cm)

Step-by-step explanation:

-For the water in the glass to overflow, the volume of the inserted solid must be greater than the volume of the empty space or the ensuing height of  water >height of glass.

#Volume of the golf ball:

V=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\pi \times 4^3\\\\\approx 268.08\ cm^3

#The volume of the water in the glass:

V=\pi r^2 h\\\\=\pi \times 4^2\times 10\\\\\approx 50.27\ cm^2

We then equate the two volumes to the glass' volume to determine the new height of the water:

V=\pi r^2h\\\\(206.08+50.27)=\pi r^2 h\\\\h=318.35/(\pi \times 4^2)\\\\=6.33\ cm

Hence, the glass will not overflow since the new height of the water is less than the height of the glass(6.33 cm<10cm).

4 0
3 years ago
6. Use synthetic substitution to evaluate the polynomial P(x) = x - 4x² + 4x – 5 for x = 4
Tatiana [17]

Answer:

When x=4

P(x) =4 - 4(4)^2 + 4(4) -5

=4 - 4(16) + 16 -5

=4 - 64 +11

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8 0
3 years ago
8. In AABC, LA is a right angle and mzB = 45°. Find BC.
Margaret [11]

Answer:

BC = 11\sqrt{2}

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin45° = \frac{1}{\sqrt{2} } , then

sin 45° = \frac{opposite}{hypotenuse} = \frac{AC}{BC} = \frac{11}{BC} = \frac{1}{\sqrt{2} } ( cross- multiply )

BC = 11\sqrt{2}

7 0
2 years ago
What is the missing blank?
bekas [8.4K]

Answer:

<1 and <8 are alternate exterior angles

Step-by-step explanation:

Alternate means on the opposite side of the transversal

Exterior means outside the parallel lines

<1 and <8 are alternate exterior angles

4 0
3 years ago
Find the 12th term for the arithmetic sequence:
Sav [38]
68 should be the answer... Sorry if I'm wrong
4 0
3 years ago
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