Don't forget S is measured in thousands of units so you are solving for :

100 < 74.5 + 43.75Sin(πt/6)
25.5 < 43.75Sin(πt/6)
Sin(πt/6) >25.5/43.75 = 0.582857
ASrcSin(πt/6) > 0.62224 radians
πt/6 > 0.62224
t > 6 x 0.62224/π = 1.1884 (4dp)

This initial value occurs when the sine value is increasing and it will reach its maximum value of 1 when Sin(πt/6) = Sinπ/2, that is when t = 3.
Consequently, monthly sales exceed 100,000 during the period between t = 1.1884 and 4.8116
[3 - 1.1884 = 1.8116 so the other extreme occurs at 3 + 1.8116]

Note : on the basis of these calculations, January is 0 ≤ t < 1 : February is 1 ≤ t < 2 :....May is 4 ≤ t < 5
So the period when sales exceed 100,000 occurs between Feb 6 and May 25 and annually thereafter.

3 0

3 years ago

Find the x- and y-intercepts of the parabola y=x2+10x+4

Nuetrik [128]

Answer:

x-intercepts: -5 +/- $\sqrt{21}$ . y-intercept: 4

Step-by-step explanation:

For x-intercepts use the quadratic equation

$x= (-b +/-\sqrt{b^2-4ac} )/2a$

Fill in your values:

$x= (-10 +/-\sqrt{100-16} )/2$

And solve

$x=-5 +/- \sqrt{21}$

For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.

6 0

1 year ago

What is the value of x? x= ___ °

JulsSmile [24]

Answer:

80°

Explanation:

All angles inside a triangle must add up to 180°

6 0

2 years ago

Which ratio is equivalent to the given ratio? 8: 16 Select each correct answer. 16/31 1/3 1/2 12/24

Marrrta [24]

$8:16\implies \cfrac{8}{16}\implies \cfrac{1}{2}\implies 1:2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{16}{31}\qquad \bigotimes~\hfill \cfrac{1}{3}\qquad \bigotimes~\hfill \cfrac{1}{2}\qquad \textit{\large \checkmark}~\hfill \cfrac{12}{24}\implies \cfrac{1}{2}\qquad \textit{\large \checkmark}$

8 0

1 year ago

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