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mafiozo [28]
2 years ago
15

g is a trigonometric function of the form g(x) = a sin(bx + c) + d. Below is the graph g(x). The function intersects its midline

at 3/4 *pi, 3) and has a maximum point at (pi,7) Find a formula for g(x). Give an exact expression.​
Mathematics
1 answer:
GalinKa [24]2 years ago
5 0

Answer:

g(x)=4sin(2x+\frac{\pi}{2})+3

Step-by-step explanation:

Because the function intersects its midline at (\frac{3\pi}{4},3), then the midline is d=3.

Additionally, the amplitude is just the positive distance between the maximum/minimum and the midline, so the amplitude is a=7-3=4.

Also, given that period is \frac{2\pi}{b} and the fact that the period is \pi-0=\pi from our given maximum, we have the equation \frac{2\pi}{b}=\pi where b=2.

Lastly, to find c, we know that the phase shift, -\frac{c}{b}, is -\frac{\pi}{4} (or \frac{\pi}{4} to the left) since \pi-\frac{3\pi}{4}=-\frac{\pi}{4}. Therefore, we have the equation -\frac{c}{2}=-\frac{\pi}{4} where c=\frac{\pi}{2}.

Putting it all together, our final equation is g(x)=4sin(2x+\frac{\pi}{2})+3

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ELEN [110]

Answer:

(- 3, 37) and (- \frac{5}{2}, \frac{63}{2} )

Step-by-step explanation:

Given the 2 equations

2x² - y + 19 = 0 → (1)

y + 11x = 4 → (2) ← subtract 11x from both sides

y = 4 - 11x → (3)

Substitute y = 4 - 11x into (1)

2x² - (4 - 11x) + 19 = 0

2x² - 4 + 11x + 19 = 0

2x² + 11x + 15 = 0 ← in standard form

(2x + 5)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - \frac{5}{2}

x + 3 = 0 ⇒ x = - 3

Substitute these values into (3) for corresponding values of y

x = - \frac{5}{2} : y = 4 + \frac{55}{2} = \frac{63}{2} ⇒ (- \frac{5}{2}, \frac{63}{2} )

x = - 3 : y = 4 + 33 = 37 ⇒ (- 3, 37 )

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3 years ago
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zmey [24]

Answer:

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4 years ago
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kozerog [31]

The nth term of an arithmetic sequence is given as:

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Answer:

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Step-by-step explanation:

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