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notsponge [240]
3 years ago
9

The height of one solid limestone square pyramid is 25 m. A similar solid limestone square pyramid has a height of 30 m. The vol

ume of the larger pyramid is 16,200 m3. Determine each of the following, showing all your work and reasoning.
(a) The scale factor of the smaller pyramid to the larger pyramid in simplest form
(b) The ratio of the area of the base of the smaller pyramid to the larger pyramid
(c) Ratio of the volume of the smaller pyramid to the larger
(d) The volume of the smaller pyramid
Mathematics
1 answer:
kotykmax [81]3 years ago
5 0
<span>Answers:
(A) </span>Scale factor = 5/6 or 0.833
(B) Area ratio is 25:36
(C) Volume ratio is 125:216
(D) Volume of smaller pyramid = 9375m^3


<span>Explanation:
A) The formula for the scale factor for pyramids is:
Scale factor = Height of small pyramid/Height of large pyramid
</span>Scale factor <span>= 25/30 
</span>Scale factor <span>= 5/6 or 0.833

B) </span><span> The ratio of the area of the base of the smaller pyramid to the larger pyramid = (25)^2/(30)^2 </span><span>
Hence area ratio is 25:36

C) </span><span>Ratio of the volume of the smaller pyramid to the larger = (25)^3/(30)^3
</span><span>
Therefore volume ratio is 125:216

D) Volume of smaller pyramid is 125/216 times the volume of the larger pyramid, from above,

Therefore volume of smaller pyramid=</span>125/216 * 16200 = 9375m^3
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marin [14]

Answer:

y=-3x+5

Explanation:

Given a line L such that:

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,

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We want to find the equation of the line in the slope-intercept form.

The slope-intercept form of the equation of a straight line is given as:

\begin{equation} y=mx+b\text{ where }\begin{cases}m={slope} \\ b={y-intercept}\end{cases} \end{equation}

Comparing the given line with the form above:

y=\frac{1}{3}x+1\implies Slope,m=\frac{1}{3}

Next, we find the slope of the perpendicular line L.

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Let the slope of L = m1.

Since L and y=(1/3)x+1 are perpendicular, therefore:

\begin{gathered} m_1\times\frac{1}{3}=-1 \\ \implies Slope\text{ of line L}=-3 \end{gathered}

The y-intercept of L is at (0,5), therefore:

y-intercept,b=5

Substitute the slope, m=-3, and y-intercept, b=5 into the slope-intercept form.

\begin{gathered} y=mx+b \\ y=-3x+5 \end{gathered}

The equation of line L is:

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7 0
1 year ago
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?
jarptica [38.1K]

Answer:

Option B is correct

Left 1 unit.

Explanation:

According to the graph theory of transformation:

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Given the parent function: f(x)=x^2

and the function g(x)=x^2+2x+1

we can write it as:

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Therefore, vertex of the graph of the function g(x)=(x+1)^2 is 1 units to the left of the vertex of the graph of the function f(x)=x^2 .




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3 years ago
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I think it’s f (x)= 1
3 0
3 years ago
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romanna [79]
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Answer:

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4 0
3 years ago
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