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3 years ago

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Mathematics

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timofeeve [1]3 years ago

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A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is c

svetoff [14.1K]

1. Consider the pyramid ABCDE in the figure 1 attached:

Each side of the square base equals $\sqrt{20} = \sqrt{4*5} = \sqrt{4}* \sqrt{5}=2 \sqrt{5}$ (units)

Area of 1 lateral side of pyramid ABCDE is $\frac{1}{2}* 2 \sqrt{5}*x=\sqrt{5}x$

so the total lateral area is $4\sqrt{5}x$ (units squared)

and the total surface area is $20+4\sqrt{5}x$ (units squared)

2. Now consider the second figure KLMNP, Sydney's pyramid:

The lateral area is $4* \frac{1}{2}* 4 \sqrt{5} *2x=16 \sqrt{5}x$

so the total area of the second pyramid is $20+16 \sqrt{5}x$

So 2 things can be said about the areas:

i) the lateral area of Sydney's pyramid is $\frac{16 \sqrt{5}x}{4\sqrt{5}x} =4$ times larger than the lateral area of the original pyramid.

ii) The total area of Sydney's pyramid is $(20+16 \sqrt{5}x)-(20+4\sqrt{5}x)=12\sqrt{5}x$ units squared larger than the total area of the original pyramid.

5 0

3 years ago

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Using compatible number to estimate the quotient 2116÷7

DerKrebs [107]

Answer:

302

Step-by-step explanation:

7 goes into 21 3 times, so the first digit of the quotient is 3. There's no remainder. Bringing down the second "1," we find this indivisible by 7, and so bring down the 6.Thus, Remember that 7 goes into 14 2 times. Thus, a good estimate would be 302.

3 0

3 years ago

A company recently downsized its number of employees by 30%. If there are still 84 employees, how many employees were there prio

Sloan [31]

Answer:

There were 120 employees prior to the layoffs.

Step-by-step explanation:

x is original amount of employees

0.7x=84

divide by 0.7 both sides

x=120 employees

downsize 30% is 36, 120-36=84

6 0

3 years ago

What is 2.5 x 200(what does it equal)

Nastasia [14]

Answer:

500

Step-by-step explanation:

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3 years ago

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Solve two-step equations<br> 2 = 4s + –10 i need it ASAP

saveliy_v [14]

Answer:

s=3

Step-by-step explanation:

4 0

3 years ago

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