Mathematics, 03.08.2019 05:40 hanahspeers

What is the value of x? sin(x+11)°=cos(2x+22)°

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Answer from: Gabilop

$\sin(x+11) = \cos(2x+22)$ answers: $\begin{aligned} x & = 19 + 360n\\ x & = 139 + 360n\\ x & = 259 + 360n \end{aligned}$ where n is an integer.======the stuff inside the cosine can be factored. $\sin(x+11) = \cos\big(2(x+11)\big)$ cosine double angle identity can be used, with x+11 as the angle being doubled.we can use the alternate form of the cosine double angle identity that uses sine only, since the other part of the equation involves sine. $\begin{aligned} \cos(2a) & = 1 - 2\sin^2 a \\ \cos\big(2(x+11)\big) & = 1 - 2\sin^2(x+11) \end{aligned}$ hence $\begin{aligned} \sin(x+11) & = \cos\big(2(x+11)\big) \\ \sin(x+11) & = 1 - 2\sin^2(x+11) \end{aligned}$ if we move all terms to one side, we get $\begin{aligned} 2\sin^2(x+11) + \sin(x+11) -1 & = 0 \end{aligned}$ this can be factored and solved like a quadratic.if we let $a = \sin(x+11)$ then $\begin{aligned} 2\sin^2(x+11) + \sin(x+11) -1 & = 0 \\ 2a^2 + a - 1 & = 0 \end{aligned}$ because $\sin^2(x+11) = \big[\sin(x+11) \big]^2$ find two numbers that multiply to get -2 and add to get 1.these two numbers are 2 and -1 $\begin{aligned} 2a^2 + a - 1 & = 0 \\ 2a^2 + 2a - a - 1 & = 0\\ 2a(a + 1) - (a+1) & = 0 \\ (2a - 1)(a+1) & = 0 \end{aligned}$ zero factor property: either factor can be equal to zero to satisfy this equation. and remember that a is sin(x+11)for (2a-1), we have $\begin{aligned} 2a - 1 & = 0 \\ 2a & = 1 \\ a & = \frac{1}{2} \\ \sin(x + 11) & = \tfrac{1}{2} \\ x + 11 & = \sin^{-1} \left(\tfrac{1}{2}\right) \end{aligned}$ $\sin^{-1} \left(\tfrac{1}{2}\right)$ gives the angles that have a sine ratio of 1/2.two angles have a positive sine ratio of 1/2: 30 degrees and 150 degrees (refer to unit circle, etc.)therefore, for 30 degrees: $\begin{aligned} x + 11 & = \sin^{-1} \left(\tfrac{1}{2}\right) \\ x + 11 & = 30 + 360n, n\text{ an integer} \\ x & = 19 + 360n, n\text{ an integer} \end{aligned}$ because co-terminal angles.for 150 degrees, do the same steps to get $x = 139 + 360n, n\text{ an integer}$ for (a+1) $\begin{aligned} a+1 & = 0\\ a & = -1 \\ \sin(x+11) & = -1 \\ x + 11 & = \sin^{-1}(-1) \end{aligned}$ $\sin^{-1}(-1)$ gives the angles with a sine ratio of -1.this is 270 degrees $\begin{aligned} x + 11 & = 270 + 360n \\ x & = 259 + 360n, n\text{ an integer} \end{aligned}$ your answers are $\begin{aligned} x & = 19 + 360n\\ x & = 139 + 360n\\ x & = 259 + 360n \end{aligned}$ where n is an integer.

Answer from: Quest

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v

Answer from: Quest

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15