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iren [92.7K]
2 years ago
13

Find the Surface Area of the cone.

Mathematics
1 answer:
Snezhnost [94]2 years ago
7 0

Answer:

\sf \huge{\boxed{\sf area = 653.1 cm^2}}

<u>Explanation</u>:

\sf \boxed{\sf area \ of  \ cone=\pi r^2 +\pi rl }

<u>Given:</u>

  • radius: 8 m
  • slant height: 18 m

<u>using this formula:</u>

\hookrightarrow \sf \pi r^2 + \pi rl

\hookrightarrow \sf (3.14)(8)^2 +(3.14)(8)(18)

\hookrightarrow \sf 653.1 cm^2

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Please help me with this please actually help me please and thank you
Westkost [7]

Answer:

C.   (x, y) → (x, -y)

Step-by-step explanation:

The algebraic representation that correctly describes a reflection over the x-axis is (x, y) → (x, -y)

Here's an example to show understanding

Plot A is (4,6) and the reflection over the x-axis would be (4,-6)    

8 0
2 years ago
if a cylinder with height 9 inches and radius r is filled with water, it can fill a certain pitcher. how many of these pitchers
dalvyx [7]

Answer:

4 pitchers

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

V=\pi r^{2}h

step 1

Find the volume of the cylinder  with height 9 inches and radius r

substitute the given values

V_1=\pi r^{2}(9)

V_1=9\pi r^{2}\ in^3

step 2

Find the volume of the cylinder  with height 9 inches and radius 2r

substitute the given values

V_2=\pi (2r)^{2}(9)

V_2=36\pi r^{2}\ in^3

step 3

we know that

The volume of the cylinder 1 can fill a certain pitcher,

so

The volume of the pitcher is the same that the volume of cylinder 1

therefore

the number of pitchers that can be filled by the second cylinder is equal to divide the volume of the second cylinder by the volume of the first cylinder

\frac{36\pi r^{2}}{9\pi r^{2}}=4\ pitchers

3 0
3 years ago
Convert to factored form <br> y = x² + 6x
steposvetlana [31]

<em><u>Convert to factored form is:</u></em>

y = x(x + 6)

<em><u>Solution:</u></em>

Given that,

y = x^2 + 6x

We have to convert to factored form

Factored form means writing terms in multiplication. i.e as a product

From given,

y = x^2 + 6x

Factor out x from above given expression

y = x(x + 6)

Here, the given equation is written as product of "x" and (x + 6)

Thus the factored form is found

8 0
3 years ago
-2 1/3 divided by -3/5
Aleonysh [2.5K]

Answer:

나는 대답이 글꼴 알고 있다고 생각한다.나는 대답이 글꼴 알고 있다고 생각한다.

7 0
2 years ago
Hello again! This is another Calculus question to be explained.
podryga [215]

Answer:

See explanation.

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>

Functions

  • Function Notation
  • Exponential Property [Rewrite]:                                                                   \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Property [Root Rewrite]:                                                           \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

We are given the following and are trying to find the second derivative at <em>x</em> = 2:

\displaystyle f(2) = 2

\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}

When we differentiate this, we must follow the Chain Rule:                             \displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]

Use the Basic Power Rule:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]

Simplifying it, we have:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]

We can rewrite the 2nd derivative using exponential rules:

\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}

To evaluate the 2nd derivative at <em>x</em> = 2, simply substitute in <em>x</em> = 2 and the value f(2) = 2 into it:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}

When we evaluate this using order of operations, we should obtain our answer:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

5 0
2 years ago
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