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aksik [14]
3 years ago
5

a rectangular prism has a width of 8cm, a height of 5cm and a depth of 2cm. what’s the volume of the prism

Mathematics
2 answers:
Sergio039 [100]3 years ago
6 0

Answer:

80 cm^3

Step-by-step explanation:

The volume of rectangular prism can be found using:

v=lwh

We know the length is 2 cm, the width is 8 cm, and the height is 5cm, so we can substitute them in

v=2*8*5

Multiply

v=16*5

v=80

The volume is 80 cm^3

kogti [31]3 years ago
3 0

Answer:

80 cm

Step-by-step explanation:

The formula to find the volume of a rectangular prism is V=lwh

So you multiply 8 by 5 by 2

Then end up with 80 cm

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A parabola can be drawn given a focus of (5, -3) and a directrix of y=1. Write the equation of the parabola in any form.
Anna71 [15]

Answer:

(x²-10x+33)/(-8) = y

Step-by-step explanation:

The distance between any point on a parabola from both its focus and directrix are the same.

Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,

\sqrt{(x-5)^2+(y-(-3))^2}is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.

Equating the two equations given, we have

\sqrt{(x-5)^2+(y-(-3))^2} = |y-1|

square both sides to get

(x-5)²+(y+3)²=(y-1)²

expand the y components

(x-5)² + y²+6y+9 = y²-2y+1

subtract y²+6y+9 from both sides

(x-5)² = -8y - 8

expand the x components

x²-10x+25 = -8y - 8

add 8 to both sides to isolate the -8y

x²-10x+33 = -8y

divide both sides by -8 to isolate y

(x²-10x+33)/(-8) = y

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