Solve sin2x + 2sinx = 0 for 0 ≤ x < 2π. ...?

1 answer:

3 0

Sin 2 x + 2 sin x = 0
2 sin x cos x + 2 sin x = 0 / : 2
sin x cos x + sin x = 0
sin x ( cos x + 1 ) = 0
sin x = 0, cos x + 1 = 0, cos x = - 1;
Answer:
x = 0, or x = π

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A total of 750 tickets were sold for the school play. They were either adult tickets or student tickets. There were 50 more stud

Vlada [557]

Answer:

350 adult tickets were sold.

Step-by-step explanation:

Let's set up some values:

x = adult tickets

x + 50 = student tickets, since there were 50 more student tickets than adult tickets.

Now, let's set up our equation. If these two values add up to 750 tickets, then we can conclude the following:

(x) + (x + 50) = 750

2x + 50 = 750

2x = 700

x = 350 adult tickets. This means there were 400 student tickets sold.

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A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the plate, including t

vredina [299]

You're looking for the extreme values of $x^2+3y^2+13x$ subject to the constraint $x^2+y^2\le1$ .

The target function has partial derivatives (set equal to 0)

$\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2$

$\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0$

so there is only one critical point at $\left(-\dfrac{13}2,0\right)$ . But this point does not fall in the region $x^2+y^2\le1$ . There are no extreme values in the region of interest, so we check the boundary.