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4 years ago

What is the second term of the sequence generated by the formula an = 3n?

Mathematics

2 answers:

Drupady [299]4 years ago

8 0

Answer:

Option D is correct that is 6 is 2nd term of the sequence.

Step-by-step explanation:

We are given with a formula which generates the terms of a sequence,

$a_n=3\times n$

we have to find 2nd term,

For the second term we put value of n = 2

Thus,

$a_2=3\times2$

$a_2=6$

Therefore, Option D is correct that is 6 is 2nd term of the sequence.

astraxan [27]4 years ago

6 0

I think b.3 i am not sure but it should be b

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Sal owns a clothing store that sells shorts and graphic T-shirts. He sells the

oee [108]

Answer:

You have a thing on there saying the answer is c. If you got the answer there is no point of asking it.

7 0

3 years ago

Verify that:

Lelu [443]

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to verify that:

$\displaystyle \left(\cos(x)\right)\left(\cot(x)\right)=\csc(x)-\sin(x)$

Note that cot(x) = cos(x) / sin(x). Hence:

$\displaystyle \left(\cos(x)\right)\left(\frac{\cos(x)}{\sin(x)}\right)=\csc(x)-\sin(x)$

Multiply:

$\displaystyle \frac{\cos^2(x)}{\sin(x)}=\csc(x)-\sin(x)$

Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:

$\displaystyle \frac{1-\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)$

Split:

$\displaystyle \frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)$

Simplify:

$\csc(x)-\sin(x)=\csc(x)-\sin(x)$

Problem 2)

We want to verify that:

$\displaystyle (\csc(x)-\cot(x))^2=\frac{1-\cos(x)}{1+\cos(x)}$

Square:

$\displaystyle \csc^2(x)-2\csc(x)\cot(x)+\cot^2(x)=\frac{1-\cos(x)}{1+\cos(x)}$

Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:

$\displaystyle \frac{1}{\sin^2(x)}-\frac{2\cos(x)}{\sin^2(x)}+\frac{\cos^2(x)}{\sin^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}$

Factor out the sin²(x) from the denominator:

$\displaystyle \frac{1}{\sin^2(x)}\left(1-2\cos(x)+\cos^2(x)\right)=\frac{1-\cos(x)}{1+\cos(x)}$

Factor (perfect square trinomial):

$\displaystyle \frac{1}{\sin^2(x)}\left((\cos(x)-1)^2\right)=\frac{1-\cos(x)}{1+\cos(x)}$

Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:

$\displaystyle \frac{(\cos(x)-1)^2}{1-\cos^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}$

Factor (difference of two squares):

$\displaystyle \frac{(\cos(x)-1)^2}{(1-\cos(x))(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}$

Factor out a negative from the first factor in the denominator:

$\displaystyle \frac{(\cos(x)-1)^2}{-(\cos(x)-1)(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}$

Cancel:

$\displaystyle \frac{\cos(x)-1}{-(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}$

Distribute the negative into the numerator. Therefore:

$\displaystyle \frac{1-\cos(x)}{1+\cos(x)}=\displaystyle \frac{1-\cos(x)}{1+\cos(x)}$

3 0

3 years ago

Please help me asap!!

agasfer [191]

C) 5; ASA

A <C = <E

S CB = BE

A <B = <B

4 0

4 years ago

8th Grade Functions: Bike Race

Arturiano [62]

Answer:

Juan wins the race

Step-by-step explanation:

The graph is shown in attached image.

The black line is Juan's graph.

The green line is Antonio's graph.

The graph shows the distance (y-axis) with time (x-axis).

The end of the curve(s) means the end of the race. Both curve's ending point in y-axis is 4 miles so the end of the race is 4 miles.

But in x-axis, we see the time:

Juan finishes at 13 minutes

Antonio finishes at 15 minutes

Definitely Juan wins the race

5 0

3 years ago

Read 2 more answers

Olivia ties 2.5 feet of ribbon onto oneballo. how many yards of ribbon does olivia need for 18 ballons

Ksivusya [100]

1 yard = 3 feet
2.5×18=45 feet
45÷3= 15 yards

3 0

4 years ago