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3 years ago

Ml

Mathematics

1 answer:

Tanya [424]3 years ago

8 0

Answer:

<em>The gold vein is 96 miles away from the farthest gold dust strike.</em>

Step-by-step explanation:

<u>Distance Between two Points in the Plane </u>

Given two points A(x,y) and B(w,z), the distance between them is:

$d=\sqrt{(z-y)^2+(w-x)^2}$

The prospector positioned the gold vein at (-2,9) and the farthest gold dust strike at (94,9). We are required to calculate the distance between these two points. Use the formula:

$d=\sqrt{(9-9)^2+(94-(-2))^2}$

$d=\sqrt{0^2+96^2}$

$d=\sqrt{96^2}=96$

The distance is 96 units, but we know each unit on the graph represents 1 mile, thus the gold vein is 96 miles away from the farthest gold dust strike.

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3 years ago

A line with slope 3 passes through the point (0,10). What is the y-coordinate of the point on the line with x-coordinate 2?

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Hello!

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4 years ago

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3 years ago

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3 years ago

Michael has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3 π in3. One day, his sink is clogged. He ha

pashok25 [27]

Answer:

A. 14 times

B. 5 times.

Step-by-step explanation:

We know the volume of the sink, now we need to find the volume of the cup(s) he's using to empty it out.. to find out how many scoops he'll have to do.

We'll assume he can actually empty it all, even if it's unlikely he can scoop the last 5%-10% of it due to the shapes/sizes of the sink and the cup. We'll also assume he completely fills the cup (which is impossible due to angles).

The volume of the sink is 3000/3 π cubic inches, let's simplify that as 1000 π cubic inches.

a - Cylindrical cup, diameter 6 inches, height: 8 inches.

We remember the volume of a cylinder is found using this formula:

V = π r²h

So, we have:

V = π * 3² * 8 = 72π

So, how many times does Michael has to scoop (S):

$S = \frac{1000 \pi }{72 \pi } = 13.88$

Of course, he can't scoop 0.83 times... so we'll round it up.

So, Michael will have to scoop 14 times with this first cup.

b - Cylindrical cup, diameter 10 inches, height: 8 inches.

We remember the volume of a cylinder is found using this formula:

V = π r² h

So, we have:

V = π * 5² * 8 = 200π

So, how many times does Michael has to scoop (S):

$S = \frac{1000 \pi }{200 \pi } = 5$

So, Michael will have to scoop 5 times with this second cup, which is not surprising since the volume of the second cup is nearly the triple of the first one.

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4 years ago