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3 years ago

How many solutions does the system below have? y=1/2x+1 2y - x = 2

Mathematics

1 answer:

kvasek [131]3 years ago

3 0

Answer:

infinitely many

Step-by-step explanation:

Rewrite these equations as

y = (1/2)x + 1

2y = x + 2

and then solve the second for y: y = (1/2)x + 1. Note that these end results are identical. The two lines coincide; that is, one lies right on top of the other. Thus, there are infinitely many solutions.

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Tiana has already taken 1 page of notes on her own, and she will take 1 page during each hour of class. In all, how many hours w

Novosadov [1.4K]

Answer:

<u>42 Hours.</u>

Step-by-step explanation:

As an equation where y is the total pages and x is hours of class:

y=1+1x since she started with 1 page and does 1 page per hour.

Setting the total pages she needs as 43 (y=43) we get:

43=1+1x

Subtract one on both sides

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3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so: