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Anton [14]
3 years ago
12

Find the side of a square whose diagonal is of the given measure. Given = 8 miles

Mathematics
2 answers:
ss7ja [257]3 years ago
8 0
Use the Pythagorean theorem. Since sides of squares are all equal 2a^2=8^2. 2a^2=64, so a^2=32. The sides are equal to the square root of 32
sasho [114]3 years ago
5 0
The diagonal is solved by a^2+b^2=c^2
c=8 in this problem, so c^2=64
Since the figure is a square, a must equal b.
64/2=32, each side is root of 32 units
the square root of 32 is approximately 5.66.
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How do I solve the length of AC?​
Crank

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∆ABC and ∆ADE are similar triangles.

Thus ;

\frac{AD}{AC}  =  \frac{DE}{BC}  =  \frac{AE}{AB}  \\

So :

\frac{5}{3 + 2x}  =  \frac{4}{8}  \\

\frac{5}{3 + 2x}  =  \frac{1}{2}  \\

Inverse both sides

\frac{3 + 2x}{5}  =  \frac{2}{1}  \\

\frac{2x + 3}{5}  = 2 \\

Multiply sides by 5

5 \times  \frac{2x + 3}{5}  = 5 \times 2 \\

2x + 3 = 10

Thus ;

AC = 2x + 3 = 10

AC = 10

Done...

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7 0
2 years ago
A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t
Vlad1618 [11]

Answer:

 185553.7\text{ feet}^3

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is 84\text{ feet}, and the total height of the building up to the top of the dome is 91\text{ feet}.

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be h\text{ feet}

As the dome hemispherical.

circumference of a hemisphere =\frac{1}{2}\times2\pi\times radius

                                                    =\pi\times radius

                                                    \frac{22}{7}\times radius=84

                                                    radius=26.75\text{ feet}

total height of the building up to the top of the dome =\text{radius of hemisphere}+\text{height of mountaintop}

=26.75+h=91

h=64.25\text{ feet}

Volume of building =\text{volume of cylindrical mountaintop}+\text{volume of dome}

                                =\pi(radius)^2h+\frac{2}{3}\pi(radius)^3

as radius of mountain top is same as dome

putting values

                                =3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3      

                               =145484.6+40069.1

                               185553.7\text{ feet}^3

Hence the total volume of the building is 185553.7\text{ feet}^3                                      

5 0
3 years ago
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Tomtit [17]

Answer:

$7,865,000 + (Claire's cases)

Step-by-step explanation:

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$5040000 + $2825000 = $7865000

3 0
3 years ago
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liq [111]

Answer:

x=1

Step-by-step explanation:

Simplify:

24x-12=12

add 12 on both sides:

24x=24

divide both sides by 24

x=1

Hope this helps!

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Answer:

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Step-by-step explanation:

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