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Irina-Kira [14]
3 years ago
8

Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6in. The height of the prism i

s 10in

Mathematics
1 answer:
vesna_86 [32]3 years ago
8 0

ANSWER

211.2 {in}^{2}

EXPLANATION

The surface area of a triangular prism is

equal to the area of two triangular faces

plus the area of the three rectangular faces.

The area of the equilateral triangle is calculated using the formula:

= 2 \times \frac{ \sqrt{3} }{4}  {s}^{2}  + 3 \times  \: bh

where s=6 is the length of one side.

and b=6 is the breadth of the rectangle and h=10 is the height of the rectangle.

Surface area

= 2 \times \frac{ \sqrt{3} }{4}  \times  {6}^{2}  + 3 \times  \: 6 \times 10

= 18\sqrt{3} + 180

=211.2square inches.

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Trig: A sector of a circle has area 25 cm2 and centralangle
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Park rangers tagged fish in a state park to track their population. The function f(x)=200(1.05)x can be used to find the populat
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The given exponential function can be used to determine the

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2. 0.05

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4. Range; [0, ∞)

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which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

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2. The rate of growth of the fish from the exponential function is given as follows;

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3. Please find attached the graph of the exponential function created

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The table of values is presented as follows;

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. The domain is the possible x-values which is; 0 ≤ x < ∞

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f(11) = 200 × (1.05)¹¹ ≈ 342

  • The population of the fish after 11 years is <u>346 (fishes)</u>

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