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Mathematics

1 answer:

kicyunya [14]3 years ago

4 0

Great job was is you strategies

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20 POINTS, 2 questions ( answer with both explanations !! )

andrew11 [14]

A) 275+12d=1091
b) 275+12d=1091
-275 on both sides
12d=816
÷12 on both sides
d=68

6 0

3 years ago

Find the volume of this cone

frosja888 [35]

Answer:

$\frac{6400\pi}{3}\approx 6702.06\:\mathrm{cm^3}$

Step-by-step explanation:

The volume of a cone is given by $V=\frac{1}{3}\cdot r^2\pi\cdot h$ .

In this specific cone, the entire height of the cone is not given. However, we do see that it is broken up into two separate cones. Since one cone is inside/part of the other, these cones must be similar. Therefore, we can set up the following proportion to find the height of the smaller cone.

Let $h_s$ be the height of the small cone:

$\frac{5}{h_s}=\frac{20}{12+h_s},\\\\20h_s=5(12+h_s),\\\\20h_s=60+5h_s,\\\\15h_s=60,\\\\h_s=4$

Therefore, the height of the largest cone is $12+4=16$ . Now we have all necessary information to find the volume of the cone:

$V=\frac{1}{3}\cdot 16\cdot 20^2\cdot \pi =\frac{6400\pi}{3}\approx \boxed{6702.06\:\mathrm{cm^3}}$

3 0

3 years ago

Find the centrroid of the triangle with the given vertices F(1, 5), G(-2, 7) and H(-6, 3)

jekas [21]

$\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} F(\stackrel{x_1}{1},\stackrel{y_1}{5})\\\\ G(\stackrel{x_2}{-2},\stackrel{y_2}{7})\\\\ H(\stackrel{x_3}{-6},\stackrel{y_3}{3}) \end{cases} \\\\\\ \left( \cfrac{1-2-6}{3}~~,~~\cfrac{5+7+3}{3} \right)\implies \left( \cfrac{-7}{3}~~,~~\cfrac{15}{3} \right)\implies \left( -2\frac{1}{3}~~,~~5 \right)$