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2 years ago

What is the shortest horizontal shift of a sine curve that will turn it into a cosine curve?

1 answer:

3 0

The shortest horizontal shift of a sine curve that will turn it into a cosine curve is a shift of 90°( π/2 radians).

The function y = sin x defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently. It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.

Technical analysis and trading both employ sine waves to assist spot oscillator-related patterns and cross-overs.

Similar to the sine graph, the cosine graph is an up-down graph. The sine graph and cos graph are identical except that the sine graph begins at 0, whereas the cos graph begins at 90° (or π/2). The cosine (cos) graph shown below starts at 1 and drops to -1 before rising once again.

Thus, the shortest horizontal shift of a sine curve that will turn it into a cosine curve is a shift of 90°( or π/2 radians).

Learn more about sine and cosine curves at

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Math 8: Linear Functions, Part 2

Studentka2010 [4]

Answer:

$\boxed{\text{1. y + 5 = -4(x - 3); \qquad 2. y - 8 = x + 1}}$

Step-by-step explanation:

Question 1

The point-slope formula for a straight line is

y – y₁ = m(x – x₁)

x₁ = 3; y₁ = -5; m = -4

Substitute the values

$\boxed{\textbf{y + 5 = -4(x - 3)}}$

The diagram shows the graph of equation 1 (red) with slope -4 passing through (3,-5).

Question 2

x₁ = -1; y₁ = 8; m = 1

Substitute the values

$\boxed{\textbf{y - 8 = x + 1}}$

The diagram shows the graph of equation 2 (green) with slope 1 passing through (-1,8).

3 0

4 years ago

Keiko sold 3 less than three-fourths of his sister’s sales. Which expression represents what Keiko sold?

Valentin [98]

Let’s represent his sister’s sales as x

3/4ths of his sister’s sales would be:

3/4x

3 less than 3/4ths of his sister’s sales would be:

3/4x - 3

3 0

3 years ago

What is the largest integer n such that (n^2-38) / (n +1) is an integer?

Phantasy [73]

Answer:

a. 36

Step-by-step explanation:

for (n^2-38)/(n+1) to be an integer, n+1 must completely divide, n^2-38.

we check with the options

option a n=36 sutisfies the above condition.

(36^2-38)/36+1 = 1258/37= 34 , which is an integer. Therefore, largest integer would be 36

6 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

fenix001 [56]

Answer:

2, 7, 114

Step-by-step explanation:

(3 + 0.5x)(38 - 4x)

114 + 19x - 12x - 2x²

-2x² + 7x + 114

7 0

3 years ago

50 POINTS!! Pleasee helppppp!!! A scientific journal recently reported that there are currently 2400 black rhinos in the world t

Harman [31]

Answer:

Step-by-step explanation:

So, we started out with 2,400 black rhinos.

And we know that they are declining at a rate of 10% per year.

In other words, each subsequent year will only have 90% of the previous year's rhinos.

Therefore, our function is:

$f(x)=2400(.9)^x$

We can do some elimination first.

First, the starting point or y-intercept must be 2400 since that's the number of rhinos we started out with.

Therefore, we can eliminate A and D.

From the remaining choices B or C, we can technically also eliminate B. This is because from our function, we know it's exponential decay, and exponential decay is not a straight line.

However, to double check, let's check the population after 10 years using our function. So:

$f(10)=2400(.9)^{10}$

Use a calculator:

$f(10)\approx837$

So, after 10 years, the population should be around 840.

B is definitely not 840 (at x=10). However, C is right around it.

Therefore, we can conclude that C is the right answer.

And we're done!

6 0

3 years ago