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3 years ago

Graph f (x)=tan 3x. Identify period, x-intercepts and asymptotes

1 answer:

5 0

Well the period of the tan(x) function is π. It means that when you add π on X axis you will get the same y axis value.

There is a little trick to find the period of functions like yours.
You just divide period of basic tan(x) function with, in your case 3.
So this mean you have
To = π/3

Function intercepts x axis when function is equal to 0.

tan(3x) = 0
3x = k * π
x = k * (π / 3)

There are only vertical asymptotes in tangent function.
You can easily see it if you look at the graph

tan(x) = ∞ , (π/2 + kπ)
tan(x) = -∞ (-π/2 + kπ).
x = π/2 + kπ
x = - π/2 + kπ

tan(3x) = ∞

3x = π/2 + kπ
x = π/6 + kπ/3

tan(3x) = -∞

3x = -π/2 + kπ
x = -π/6 + kπ/3

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The bookstore sells packages of 15 pens

AlexFokin [52]

Considering the definition of least common multiple, this means that smallest number of packages of each they can buy is 60.

<h3>Least common multiple</h3>

A number is a multiple of another when it contains it exactly n times. In other words, the multiples of a number are the ones you get when you multiply one number by another.

The least common multiple allows us to know what is the smallest number that is a multiple of a certain set of numbers.

One procedure for calculating the least common multiple is to break each number into prime factors. Then the common and uncommon factors are raised to the highest exponent, which must be multiplied.

<h3 /><h3>Smallest number of packages</h3>

To calculate the smallest number of packages of each they can buy, you calculate the least common multiple.

First, the decomposition of the numbers into prime factors is carried out:

15= 3×5

12= 2×2×3= 2²×3

Then, the least common multiple is calculated as 2²×3×5

Solving, the least common multiple between 12 and 15 is 60.

Finally, this means that smallest number of packages of each they can buy is 60.

Learn more with this similar problems:

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8 0

2 years ago

Evaluate5− t/3 when t=12

Novosadov [1.4K]

Answer:

$1$

Step-by-step explanation:

$5 - \frac{t}{3} = \frac{5}{1} - \frac{12}{3} = 5 - 4 = 1$

$5 - \frac{t}{3} = \frac{5}{1} - \frac{12}{3} = \frac{15 - 12}{3} = \frac{3}{3} = 1$

Hope this helps ;) ❤❤❤

8 0

3 years ago

Read 2 more answers

The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, square

Iteru [2.4K]

Answer:

(x-2)(x+3)(x+6)

Step-by-step explanation:

Given the polynomial function p(x)=x^3+7x^2-36

We are to write it as a product of its linear factor

Assuming the value of x that will make the polynomial p(x) to be zero

Let x = 2

P(2) = 2³+7(2)²-36

P(2) = 8+7(4)-36

P(2) = 8+28-36

P(2) = 0

Since p(2) = 0 hence x-2 is one of the linear factors

Also assume x = -3

P(-3) = (-3)³+7(-3)²-36

P(-3) = -27+7(9)-36

P(-3) = -27+63-36

P(-3) = 36-36

P(-3) = 0

Since p(-3) = 0, hence x+3 is also a factor

The two linear pair are (x-2)(x+3)

(x-2)(x+3) = x²+3x-2x-6

(x-2)(x+3) = x²+x-6

To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.

x^3+7x^2-36/x²+x-6 = x+6

Hence the third linear factor is x+6

x^3+7x^2-36 = (x-2)(x+3)(x+6)

8 0

3 years ago

Read 2 more answers

Please help with my guided practice

qaws [65]

it's 88 I've been getting so mix up forgive me So the area of the square is 64. When you find the area of the triangle you multiply the base by its height, which is 6 by 8 and then you divide by two. 64+24=88

7 0

3 years ago

Solve this equation 2x - 3=2x - 5

Alex

When you calculate 2x-3=2x-5 it’s going to lead as -3=-5, therefore this statement is inaccurate and doesn’t have a value of x, it doesn’t even have a solution.

5 0

3 years ago