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photoshop1234 [79]
2 years ago
12

The national park has a new kiosk which visitors pass through as they enter the park. The kiosk is in the shape of a cylinder wi

th a diameter of 5 meters and a height of 3 meters and a conical roof that measures 2 meters in height. What is the volume of the kiosk? Round your answer to the nearest cubic meter
Mathematics
1 answer:
posledela2 years ago
5 0

Answer:

72 m^3

Step-by-step explanation:

volume of the kiosk = volume of cylinder + volume of cone

volume of a cylinder = nr^2h

n = 3.14

r = radius = 5/2 = 2.5

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

3.14 x (2.5^2) x 3 = 58.88  

Volume of a cone = 1/3(nr^2h)

3.14 x 1/3 x (2.5^2) x 2 = 13.08

13.08 + 58.88 = 71.96

To round off to the nearest cubic meter, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

= 72 m^3

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January through

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Since both terms are perfect squares, factor using the difference of squares formula.

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3 years ago
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What is the approximate area of the shaded portion of the diagram? (Use 3.14 as an estimate for pi.)
Nadusha1986 [10]

Answer:

218

Step-by-step explanation:

first find the area of the circle-

A=\pi r^{2} \\A=\pi 10^{2} \\A=100\pi \\A=314

to find the area of the triangle, we need the base and the height. The base we know is 16, since we don't know the height yet, use the Pythagorean theorem to find the height. One leg is 16 the hypotenuse is 20 (2* the radius).

a^{2} +b^{2} =c^{2} \\a^{2} +16^{2} =20^{2} \\a^{2} +256=400\\a^{2} =144\\a=12

Now I know the height is 12. Find the area of the triangle

A=\frac{1}{2} bh\\A=\frac{1}{2} (16)(20)\\A=96

subtract the area of the triangle from the area of the circle

314-96=218

6 0
2 years ago
Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points) Part B: Find an irrational nu
max2010maxim [7]
A rational number can always be represented as a fraction.
5.2 = 52/10 
5.5 = 55/10

A number between them would be 54/10 since 54 is between 52 and 55.

An irrational number cannot be represented as a fraction. A good example of an irrational number is the square root of a number.
sqrt(5.2^2) = 5.2  ----> 5.2^2 = 27.04
sqrt(5.5^2) = 5.5  ----> 5.5^2 = 30.25

The square root of a number between 27.04 and 30.25 will be an irrational number between 5.2 and 5.5
sqrt(28) = 5.2915...
3 0
2 years ago
If -y-2x^3=Y^2 then find D^2y/dx^2 at the point (-1,-2) in simplest form
algol13

Answer:

\frac{d^2y}{dx^2} = \frac{-4}{3}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Factoring

<u>Calculus</u>

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Product Rule: \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Chain Rule: \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Quotient Rule: \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

-y - 2x³ = y²

Rate of change of tangent line at point (-1, -2)

<u>Step 2: Differentiate Pt. 1</u>

<em>Find 1st Derivative</em>

  1. Implicit Differentiation [Basic Power Rule]:                                                  -y'-6x^2=2yy'
  2. [Algebra] Isolate <em>y'</em> terms:                                                                              -6x^2=2yy'+y'
  3. [Algebra] Factor <em>y'</em>:                                                                                       -6x^2=y'(2y+1)
  4. [Algebra] Isolate <em>y'</em>:                                                                                         \frac{-6x^2}{(2y+1)}=y'
  5. [Algebra] Rewrite:                                                                                           y' = \frac{-6x^2}{(2y+1)}

<u>Step 3: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

  1. Differentiate [Quotient Rule/Basic Power Rule]:                                          y'' = \frac{-12x(2y+1)+6x^2(2y')}{(2y+1)^2}
  2. [Derivative] Simplify:                                                                                       y'' = \frac{-24xy-12x+12x^2y'}{(2y+1)^2}
  3. [Derivative] Back-Substitute <em>y'</em>:                                                                     y'' = \frac{-24xy-12x+12x^2(\frac{-6x^2}{2y+1} )}{(2y+1)^2}
  4. [Derivative] Simplify:                                                                                      y'' = \frac{-24xy-12x-\frac{72x^4}{2y+1} }{(2y+1)^2}

<u>Step 4: Find Slope at Given Point</u>

  1. [Algebra] Substitute in <em>x</em> and <em>y</em>:                                                                     y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(-1)^4}{2(-2)+1} }{(2(-2)+1)^2}
  2. [Pre-Algebra] Exponents:                                                                                      y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(1)}{2(-2)+1} }{(2(-2)+1)^2}
  3. [Pre-Algebra] Multiply:                                                                                   y''(-1,-2) = \frac{-48+12-\frac{72}{-4+1} }{(-4+1)^2}
  4. [Pre-Algebra] Add:                                                                                         y''(-1,-2) = \frac{-36-\frac{72}{-3} }{(-3)^2}
  5. [Pre-Algebra] Exponents:                                                                               y''(-1,-2) = \frac{-36-\frac{72}{-3} }{9}
  6. [Pre-Algebra] Divide:                                                                                      y''(-1,-2) = \frac{-36+24 }{9}
  7. [Pre-Algebra] Add:                                                                                          y''(-1,-2) = \frac{-12}{9}
  8. [Pre-Algebra] Simplify:                                                                                    y''(-1,-2) = \frac{-4}{3}
6 0
2 years ago
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