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2 years ago

Determine the amplitude or Period as requested. Period of y= -2 sin x

Mathematics

1 answer:

Alex Ar [27]2 years ago

5 0

amplitude: 2

period: 2pi

The equation for a sin function is:

$y = a \sin(b(x - c) ) + d$

a = the amplitude

b = the period

c = the horizontal shift

d = the vertical shift

the equation to find the period of a sin function is:

$period = \frac{2\pi}{b}$

note: the amplitude is always a positive number, if there is a negative sign in front of it then that means it reflects over the x-axis.

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What is the slope passing through the points (11,-5) and (1,20)

tia_tia [17]

Answer:

-2.5 or -5/2

Step-by-step explanation:

To find the slope we need to find the change in y and divide it by the change in x:

m = change in y ÷ change in x

m = (-5 - 20) ÷ (11 - 1)

m = 25 ÷ -10

m = -2.5 or -5/2

Hope this helps!

4 0

2 years ago

5. Simplify the expression and find its value when p= 4 and q = -5:

Ierofanga [76]

<u>Answer</u>: -180

Step-by-step explanation:

$\bf \blue{ \boxed{ \bf p = 4 \: \: and \: \: q = - 5 \Rightarrow pq = 4 \times ( - 5) = - 20}}$

3(p2q + pq2 - pq) - 6pq + 3pq2 =

3[-20 × 2 + (-20) × 2 - (-20)] - 6 × (-20) + 3 × 2 × (-20) =

3[-40 + (-40) + 20] - 6 × (-20) + 3 × 2 × (-20) =

3(-40 - 40 + 20) - 6 × (-20) + 3 × 2 × (-20) =

3(-80 + 20) - 6 × (-20) + 3 × 2 × (-20) =

3 × (-60) - 6 × (-20) + 3 × 2 × (-20) =

-180 + 120 + 6 × (-20) =

-180 + 120 + (-120) =

-180 + 120 - 120 =

-60 - 120 = -180

7 0

2 years ago

Read 2 more answers

The largest prime factor of twelve is _____. user: identify the fractions as proper, improper, or mixed; however, if the fractio

andrew-mc [135]

The prime factors of 12 are : 2 x 2 x 3.....and 3 is the largest

4 1/3 is a mixed number because it has a whole number and a fraction.

6 0

3 years ago

Read 2 more answers

What are the types of roots of the equation below?<br> - 81=0

Tju [1.3M]

Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0. This can be obtained by finding root of the equation using algebraic identity.

<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,

⇒ x⁴ - 81 = 0

⇒ (x² + 9)(x² - 9) = 0

(x² - 9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

⇒ [x² - 3x + 3x - 9][x² - 3xi + 3xi - 9i²] = 0

⇒ (x² +0x - 9)(x² +0xi - 9(- 1)) = 0

⇒ (x² - 9)(x² + 9) = 0

⇒ x⁴ - 9x² + 9x² - 81 = 0

⇒ x⁴ - 81 = 0

Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

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1 year ago

In a bag of trail mix, there are 5 cups of nuts for every 2 cups of chocolate candies. If there are 12 cups of nuts in a bag of

Katyanochek1 [597]

Answer:

Step-by-step explanation:

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2 years ago