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3 years ago

Locate the points of discontinuity in the piecewise function shown below.

Mathematics

2 answers:

Lesechka [4]3 years ago

6 0

Answer:

Step-by-step explanation:

There is actually no points, because if you look at the breaks, it's always filled in with a greater than or equal to. For example,

x < -1

-1 $\leq$ x

x < 2

2 $\leq$ x

Advocard [28]3 years ago

3 0

Answer: D

Step-by-step explanation:

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7 B is the midpoint of AC. AB - BV, and

aleksklad [387]

Answer:

i think G sorry if its wrong

Step-by-step explanation:

6 0

3 years ago

Cos^2 x+4sin^2 x/2=1

lana [24]

$Let\ \dfrac{x}{2}=a,\ therefore\ x=2a.\\\\\cos^2x+4\sin^2\dfrac{x}{2}=\cos^22a+4\sin^2a\\\\\text{use}\ \cos2x=\sin^2x-\cos^2x\\\\=(\sin^2a-\cos^2a)^2+4\sin^2a\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(\sin^2a)^2-2(\sin^2a)(\cos^2a)+(\cos^2a)^2+4\sin^2a\\\\=\sin^4a-2\sin^2a\cos^2a+\cos^4a+4\sin^2a\\\\=\underbrace{\sin^4a+2\sin^2a\cos^2a+\cos^4a}_{(*)}-4\sin^2a\cos^2a+4\sin^2a\\\\\text{use}\ (*)\qquad(a+b)^2=a^2+2ab+b^2$

$=\underbrace{(\sin^2a)^2+2\sin^2a\cos^2a+(\cos^2a)^2}_{(*)}-4\sin^2a(\cos^2a-1)\\\\=(\sin^2a+\cos^2a)^2-4\sin^2a(\cos^2a-1)\\\\\text{use}\ \sin^2a+\cos^2a=1\to\sin^2a=\cos^2a-1\\\\=1^2-4\sin^2a(\sin^2a)=1-4\sin^4a=1-(2\sin^2a)^2$

$\cos^22a+4\sin^2a=1\\\\1-(2\sin^2a)^2=1\qquad\text{subtract 1 from both sides}\\\\-(2\sin^2a)^2=0\to2\sin^2a=0\qquad\text{divide both sides by 2}\\\\\sin^2a=0\to\sin a=0\\\\a=k\pi\ for\ k\in\mathbb{Z}\\\\\dfrac{x}{2}=k\pi\qquad\text{multiply both sides by 2}\\\\\boxed{x=2k\pi\ for\ k\in\mathbb{Z}}$

6 0

3 years ago

Soybeans have a conversion factor of 36.744 (bu/t). How much do 45 bushels weigh?

Dahasolnce [82]

Answer:

1.22

Step-by-step explanation:

Soybeans have a conversion of 36.744

Therefore the amount in which 45 bushels weigh can be calculated as follows

= 45/36.744

= 1.22

Hence 45 bushels weigh 1.22

6 0

3 years ago

Find the coordinates of d if e (-6,4) Is the midpoint of df and f has coordinates (-5,-3)

Oksanka [162]

Answer:

Step-by-step explanation:

Let the coordinates of d be (x,y)

The midpoint of (x,y) and (-5,-3) is equal to ((-5+x)/2, (-3+y)/2)

this should be equal to the coordinates of e, (-6,4)

we have (-5/2+x/2, -3/2+y/2)

-5/2+x/2 = -6

-5 + x = -12

x = -7

-3/2+y/2 = 4

-3+y = 8

y = 11

Therefore the coordinates of d are (-7,11)

4 0

3 years ago

No fake answers please

Fiesta28 [93]

Answer: Top-Left straight line

Step-by-step explanation:

A function on a graph is a line that does not overlap itself where two coordinates on the x-axis would be the same. All of the graphs except the top left one, are curved to where there would be two of the same coordinates for x. Also, a function is where each input (x) has only one output (y). Since the x coordinate is listed twice with DIFFERENT outputs, it cannot be a function.

7 0

3 years ago