3 years ago

A multiplication problem is shown 789 times what equals 8679 what the missing number

Mathematics

1 answer:

navik [9.2K]3 years ago

5 0

Answer:

789

Step-by-step explanation:

8679/789 = 11

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Jade had the following system of equations to help her with a physics problem, but she only needed to know what the sum of x and

pav-90 [236]

From the second:

2x-y=4

x=(4+y)/2 and applying this to first:

4+y+3y=12

4y+4=12

4y=8

y=2 and since x=(4+y)/2, x=3 so

x+y=2+3=5

8 0

3 years ago

Solve using algebraic equation: <br> 5sin2x=3cosx<br><br> (No exponents)

DaniilM [7]

$5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x$

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

$10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0$

Now the zero product property tells us that there are two cases where this is true,

$\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}$

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of $\dfrac\pi2$ , so $x=\dfrac{(2n+1)\pi}2$ where $n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}$

which occurs twice in the interval $[0,2\pi)$ for $x=\arcsin\dfrac3{10}$ and $x=\pi-\arcsin\dfrac3{10}$ . More generally, if you think of $x$ as a point on the unit circle, this occurs whenever $x$ also completes a full revolution about the origin. This means for any integer $n$ , the general solution in this case would be $x=\arcsin\dfrac3{10}+2n\pi$ and $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .