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3 years ago

Find the ratio of the volume of the triangular prism

Mathematics

1 answer:

lana [24]3 years ago

3 0

Answer:

The ratio of the volume of the triangular prism to the volume of the cuboid is $\frac{3}{20}$ .

Step-by-step explanation:

Geometrically speaking, the volume of the prism is equal to the product of the area of the base and its height. Then, the volumes of the triangular prism and the cuboid are, respectively:

Triangular prism

$V_{tp} = \frac{1}{2}\times 5\,cm \times 4\,cm \times 9\,cm$

$V_{tp} = 90\,cm^{3}$

Cuboid

$V_{c} = 6\,cm\times 5\,cm \times 20\,cm$

$V_{c} = 600\,cm^{3}$

Lastly, the ratio of the volume of the triangular prism to the volume of the cuboid is:

$r = \frac{V_{tp}}{V_{c}}$

$r = \frac{3}{20}$

The ratio of the volume of the triangular prism to the volume of the cuboid is $\frac{3}{20}$ .

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What is the equation of this line in standard form? 8x−7y=−25 8x−9y=23 8x−9y=−23 9x−8y=23 Number graph ranging from negative fiv

Gnoma [55]

Answer:

The equation of line is:

$8x-9y=-23$

Step-by-step explanation:

We are given that a graph is a that passes through two points:

$(-4,-1)$ and $(\dfrac{1}{2},3)$

We know that the equation of line passing through two points:

$(a,b)$ and $(c,d)$ is given by:

$y-b=\dfrac{d-b}{b-a}\times (x-a)$

Here we have:

$(a,b)=(-4,-1)$ and $(c,d)=(\dfrac{1}{2},3)$

Hence, the equation of line is:

$y-(-1)=\dfrac{3-(-1)}{\dfrac{1}{2}-(-4)}\times (x-(-4))\\\\y+1=\dfrac{3+1}{\dfrac{1}{2}+4}\times (x+4)\\\\y+1=\dfrac{4}{\dfrac{9}{2}}\times (x+4)\\\\y+1=\dfrac{4\times 2}{9}\times (x+4)\\\\y+1=\dfrac{8}{9}\times (x+4)\\\\9\times (y+1)=8\times (x+4)\\\\9y+9=8x+8\times 4\\\\9y+9=8x+32\\\\8x-9y=9-32\\\\8x-9y=-23$