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2 years ago

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For each of these sequences below: (a) describe the term-to-term rule (b) calculate the tenth term 4.1) 3 6 9 12 15 4.2) 5 11 17

23 29

1 answer:

ratelena [41]2 years ago

6 0

Answer: The term to term rule is an Arithmetic progression for the two question. B) 1Oth term for the first is 30 and for the second series is 59

Step-by-step explanation:

4.1) 3 6 9 12 15

For the sequence above, we can see that the next term is gotten by addition of 3 with the previous term and so It is an Arithmetic progression.

Having in mind the nth term of an AP as Tn = a + (n - 1)d.

where a is the first term =3

And d common difference =3(6-3,9-6,12-9)

10th term=

T10 = 3+ (10 - 1)3.

T10 = 3+ (9)3.

T10 = 3+ 27.

T10 =30

4.2) 5 11 17 23 29

For the sequence above, we can see that the next term is gotten by addition of 6 with the previous term and so It is an Arithmetic progression.

Having in mind the nth term of an AP as Tn = a + (n - 1)d.

where a is the first term =5

And d common difference =6 (11-5, 17-11,23-17)

10th term=

T10 = 5+ (10 - 1)6.

T10 = 5+ (9)6.

T10 = 5+ 54.

T10 =59

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Answer:

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Step-by-step explanation:

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$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

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$2\theta = \cos^{-1}0$

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$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

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The solutions listed from the smallest to the greatest are:

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2 years ago

A gift box is a rectangular prism. The box measures 12 in by 14 in by 7 in.

Olin [163]

Answer:

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Step-by-step explanation:

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3 years ago

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dangina [55]

Answer:

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Surface Area = 747.7 cm²

Step-by-step explanation:

Volume = πr² h

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V = π(49)(10)

V = 490π

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2 years ago

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Sphinxa [80]

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Step-by-step explanation:

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3 years ago

Help! If you know this can you tell me how to do it?

aleksandr82 [10.1K]

Answer:

c

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:

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In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

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Put everything over the common denominator now:

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Since $sin^2(x)+cos^2(x)=1$ , we will make that substitution:

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We could separate that fraction into 2:

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Therefore, the simplification is

sec(x)csc(x)

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3 years ago