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LuckyWell [14K]
3 years ago
8

Would you rather have a cup of ice cream that hold last a volume of 21.21 inches or a cone that has a radius of 1.5 inches and h

eight of 3 inches?
Mathematics
1 answer:
blagie [28]3 years ago
6 0

Answer:

I will prefer the cone having volume 21.21 cubic inches.

Step-by-step explanation:

A cup of ice cream holds ice cream = 21.21 cubic inches

Since volume of a cone = Capacity of the cone to hold the ice cream

Volume of an another cone having radius (r) = 1.5 inches and height (h) = 3 inches will be,

         V = \frac{1}{3}(\pi)(r^{2} )(h)

           = \frac{1}{3}(\pi )(1.5)^{2}(3)

           = 7.069

           ≈ 7.07 cubic inches

Since the volume of the second cone is less than the first cone, I will prefer the first cone with volume = 21.21 inches³

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Find the distance from point A(−14, 5) to the line −x+2y = 14.
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Answer:

The distance from point A to given line is: 2√5 or 4.472 units

Step-by-step explanation:

Given equation of line is:

-x+2y= 14

And the point is:

A = (x_1,y_1) = (-14,5)

The standard form of equation of line is:

Ax+By+C = 0

Converting the given equation into standard form

-x+2y-14=0

The distance of a point (x1,y1) from a line is given by the formula:

d = \frac{|Ax_1+By_1+C}{\sqrt{A^2+B^2}}

In the given details,

A = -1, B = 2, C = -14

x1 = -14, y1 = 5

Putting the values in the formula

d = \frac{|(-1)(-14)+(2)(5)-14|}{\sqrt{(-1)^2+(2)^2}}\\d = \frac{14+10-14}{\sqrt{1+4}}\\d = \frac{10}{\sqrt{5}}\\d = \frac{5*2}{\sqrt{5}}\\d = \frac{\sqrt{5}*\sqrt{5}*2}{\sqrt{5}}\\d = 2\sqrt{5}\\d = 4.472\ units

Hence,

The distance from point A to given line is: 2√5 or 4.472 units

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3 years ago
The graph shows vectors w and z.
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