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3 years ago

Solve the equation!3 tan^3θ = tan θ

1 answer:

8 0

3 tan³ t(theta) = tan t(theta)
3 tan³ t - tan t = 0
tan t ( 3 tan² t - 1 ) = 0
tan t = 0
t 1 = k π , k ∈ Z
3 tan ² t - 1 = 0
3 tan ² t = 1
tan ² t = 1/3
tan t = +/- √3/3
t 2 = π / 6 + k π
t 3 = - π / 6 + k π , k ∈ Z

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Three stamps can be attached to each other in various ways.how many ways might three stamps be attached?

ivanzaharov [21]

Let's call the stamps A, B, and C. They can each be used only once. I assume all 3 must be used in each possible arrangement.
There are two ways to solve this. We can list each possible arrangement of stamps, or we can plug in the numbers to a formula.
Let's find all possible arrangements first. We can easily start spouting out possible arrangements of the 3 stamps, but to make sure we find them all, let's go in alphabetical order. First, let's look at the arrangements that start with A:
ABC
ACB
There are no other ways to arrange 3 stamps with the first stamp being A. Let's look at the ways to arrange them starting with B:
BAC
BCA
Try finding the arrangements that start with C:
C_ _
C_ _
Or we can try a little formula; y×(y-1)×(y-2)×(y-3)...until the (y-x) = 1 where y=the number of items.
In this case there are 3 stamps, so y=3, and the formula looks like this: 3×(3-1)×(3-2).
Confused? Let me explain why it works.
There are 3 possibilities for the first stamp: A, B, or C.
There are 2 possibilities for the second space: The two stamps that are not in the first space.
There is 1 possibility for the third space: the stamp not used in the first or second space.
So the number of possibilities, in this case, is 3×2×1.
We can see that the number of ways that 3 stamps can be attached is the same regardless of method used.

8 0

3 years ago

Amelia needs to buy some cat food. At the nearest store, 2 bags of cat food cost $4.50. How much would Amelia spend on 6 bags o

marissa [1.9K]

Answer:

$13.50

Step-by-step explanation:

2 bags of cat food = $4.50

1 bag of cat food = 2/4.50

= 2.25

6 bags of cat food = 2.25*6

=13.50

7 0

2 years ago

Read 2 more answers

Maggie is displaying paperback and hardback books on her book shelf. The ratio of hardback books to total books is 5 to 13. Whic

lubasha [3.4K]

Answer:

Total Paperback books = 8x , where x is any positive number

Step-by-step explanation:

Let

The total books are = 13x ; where x is any positive number

As given,

The ratio of hardback books to total books is 5 to 13.

⇒Hardback books = $\frac{5}{13}$ × Total books

⇒Hardback books = $\frac{5}{13}$ × 13x = 5x

So, Paperback books = Total books - Hardback books

= 13x - 5x

= 8x

⇒Total Paperback books = 8x

8 0

2 years ago

THE VALUE OF (-3)raised to 4 is

Finger [1]

Step-by-step explanation:

I think this should be the answer

7 0

3 years ago

Jose has scored 562 points on his math test so far this this semester. To get an A for the semester, he must score at least 650

I am Lyosha [343]

Answer:

562 + x ≥ 650

x ≥ 88

Step-by-step explanation:

He has 562 points. He needs x points to get an A. He must get at least 60 points to get an A.

562 + x ≥ 650

To solve this, we subtract 562 from each side

562-562 + x ≥ 650-562

x ≥ 650-562

x ≥ 88

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2 years ago