(0.2m^2n)^3 *1000m^4n^7<br> simplify

NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.

slava [35]

Answer:

<h3><u>Question 7</u></h3>

<u>Lateral Surface Area</u>

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).

$\implies \sf L.A.=2(10 \times 6)+(3 \times 6)=138\:\:m^2$

<u>Total Surface Area</u>

Area of the isosceles triangle:

$\implies \sf A=\dfrac{1}{2}\times base \times height=\dfrac{1}{2}\cdot3 \cdot \sqrt{10^2-1.5^2}=\dfrac{3\sqrt{391}}{4}\:m^2$

Total surface area:

$\implies \sf T.A.=2\:bases+L.A.=2\left(\dfrac{3\sqrt{391}}{4}\right)+138=167.66\:\:m^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)$

<h3><u>Question 8</u></h3>

<u>Lateral Surface Area</u>

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

$\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2$

<u>Total Surface Area</u>

Area of a pentagon:

$\sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2$

where a is the side length.

Therefore:

$\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)$

Total surface area:

$\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)$

8 0

1 year ago

Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.

sammy [17]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be $m = 2.$

$y = 2x + b$

We substitute the given point to find b:

$2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4$

Finally the line is:

$y = 2x + 4$

Answer:

$y = 2x + 4$

7 0

3 years ago

Read 2 more answers

Me. Silvera bought a can of paint. He used 3/8 of it to paint a fence and 1/4 to paint a table top. He painted a chair with some

LuckyWell [14K]

Well, seeing the information above, he used 5/8 of paint to paint the fence and table top. If he only had 1/8 left of the paint, he used 2/8 on the chair.

I found the 5/8 because I needed a common denominator. I multiplied the top and bottom by 2 to get 2/8. 3/8+2/8=5/8, and then I added 2/8 to the 5/8 that then gave me 7/8 of paint used, and 1/8 of paint left.

Hope I helped!

3 0

3 years ago

Write the standard form of the equation of a line if the point on the line nearest to the origin is at (6, 8).

Alchen [17]

Answer:

$\large\boxed{y=\dfrac{4}{3}x}$

Step-by-step explanation:

The line passes through the origin has an equation y = mx

m - slope

The formula of a slope of a line passes through the origin

and a point (x, y):

$m=\dfrac{y}{x}$

We have the point (6, 8). Substitute:

$m=\dfrac{8}{6}=\dfrac{8:2}{6:2}=\dfrac{4}{3}$

Finally:

$y=\dfrac{4}{3}x$

4 0

2 years ago

from a window 20 feet above the ground, the angle of elevation to the top of another building is 35 degrees. The distance betwee

NISA [10]

Answer:

56.4 ft

Step-by-step explanation:

The tangent of the angle relates the opposite side (height above the window) to the adjacent side (distance between buildings) in the right triangle that models this geometry.

Tan = Opposite/Adjacent

tan(35°) = (height above window)/(distance between buildings)

height above window = (52 ft)tan(35°) ≈ 36.4 ft

Added to the window height of 20 ft, the height of the other building is ...

20 ft + 36.4 ft = 56.4 ft

5 0

3 years ago

(0.2m^2n)^3 *1000m^4n^7 simplify