(i think i know it just checking) which function has a period equal to half the period of the function in y=5cos(3/5x-pi)+4.. the period is 10pi/3

i think its the first one.

1. y=5sin(6/5x-pi)-4
2. y=-5/2sin(6/10x-2pi)+1/2
3. y=-4cos(5/6x-2pi)+5
4. y=2cos(3/10x-pi)-5/2

Step-by-step explanation:

The given function is

Where

Notice half the period is

Now, in the first function

Notice that this function is in the form:

Where , which definition is

Replacing this value, we have

Which means the first function is has half the period of the given function.

step-by-step explanation:

b and c

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)