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mestny [16]
3 years ago
9

#3 find domain and range using interval notation

Mathematics
1 answer:
kkurt [141]3 years ago
6 0

Hey there! :)

Answer:

D : [-4, ∞)

R: [-2, ∞)

Step-by-step explanation:

Notice that one end of the graphed function has a closed circle, and one end is a line. We must use specific brackets accordingly:

[ is used for closed points.

( is used for arrows or open circles.

Therefore:

This graph goes from x = -4 towards x ⇒∞. Therefore:

D : [-4, ∞)

The range of this function goes from x = -2 towards y⇒ ∞. Therefore:

R: [-2, ∞)

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Answer:

No. The new height of the water is less than the height of the glass(6.33 cm<10 cm)

Step-by-step explanation:

-For the water in the glass to overflow, the volume of the inserted solid must be greater than the volume of the empty space or the ensuing height of  water >height of glass.

#Volume of the golf ball:

V=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\pi \times 4^3\\\\\approx 268.08\ cm^3

#The volume of the water in the glass:

V=\pi r^2 h\\\\=\pi \times 4^2\times 10\\\\\approx 50.27\ cm^2

We then equate the two volumes to the glass' volume to determine the new height of the water:

V=\pi r^2h\\\\(206.08+50.27)=\pi r^2 h\\\\h=318.35/(\pi \times 4^2)\\\\=6.33\ cm

Hence, the glass will not overflow since the new height of the water is less than the height of the glass(6.33 cm<10cm).

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Step-by-step explanation:

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Step-by-step explanation:

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