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Yanka [14]
2 years ago
9

Find the diameter of a sphere with a surface area of 196π square centimeters

Mathematics
1 answer:
aleksandr82 [10.1K]2 years ago
7 0

\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}

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if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?
diamong [38]

Answer:

All the right triangles will be similar.

Step-by-step explanation:

See the attached diagram.

Let us assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.

Since the slope of the line OP is constant and assume that it makes x° with the positive x-axis.

Hence, \tan x = \frac{AC}{BC} = \frac{A'C'}{B'C'}

⇒ \frac{AC}{A'C'} = \frac{BC}{B'C'}

Therefore, the sides of the two right triangles are in the same ratio and hence, Δ ABC and Δ A'B'C' are similar.

Hence, all the right triangles will be similar. (Answer)

4 0
3 years ago
A bowling alley has a fixed base cost and charges a variable per game rate. It costs $20.50 for five games and 28.50 for nine ga
lbvjy [14]


As ordered pairs ( g , C ) where g is the number of games and C is the cost

( 5, 20.50) and ( 9, 28.50)

the slope M = ( 28.50 - 20.50 ) / (9-5)

= 8/4

= 2

So the slope M=$2 per game

Using (5, 20.50)
The intercept B = y - m* g
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So the fixed base cost, or FLAT RATE is $10.50.
That is if they played ZER0 games, they still have
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The linear function is C (g) = 2*g + 10.50

8 0
3 years ago
Numbers nearest ten<br> 48393<br> 1549<br> 37,519<br> 65,810<br> 2175
erastova [34]

Answer:

48,390

1,550

37,520

65,810

2,180

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4 years ago
Colin wants to set up an aquarium.. He already has a tank, but needs to purchase fish, filters, and plants. If the cost of the f
ahrayia [7]

Answer:

340.65

Step-by-step explanation: Add 84.79+44.75+18.66=148.2

148.2-$488.85= 340.65

7 0
3 years ago
Read 2 more answers
. The circumference of Earth’s moon is about 1,091,500,000 cm. Write this number in scientific notation. *
kondaur [170]

1.0915 x 10{9} <----Exponet

7 0
3 years ago
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