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3 years ago

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Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party. 4 inches 7 inches Find the volum

e of one paper cone if the diameter is 4 inches and the height is 7 inches. Round your answer to the nearest cubic inch.

1 answer:

madreJ [45]3 years ago

3 0

The volume of one cone would be 29 in³.

The formula for the volume of a cone is V=(1/3)πr²h. Substituting our information we have:

V=(1/3)(3.14)(4/2)²(7)

We divide the diameter by 2 because the radius is half of the diameter. This gives us:
V=1/3(3.14)(28) = 29.306 ≈ 29in³

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Answer:

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Step-by-step explanation:

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2 years ago

When testing the difference between two population means and the population variances are unknown and unequal, the degrees of fr

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Answer: 34 degrees of freedom should be used to find the p-value of the test .

Step-by-step explanation:

Degrees of Freedom relates to the maximum number of independent values, that have independence to vary in the sample.

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3 years ago

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3 years ago

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

<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>

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

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

<em>Find 1st Derivative</em>

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate <em>y'</em> terms: $-xy' - 2y' = y$
[Algebra] Factor <em>y'</em>: $y'(-x - 2) = y$
[Algebra] Isolate <em>y'</em>: $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

<u>Step 3: Find </u><em><u>y</u></em>

Define equation: $-xy - 2y = -4$
Factor <em>y</em>: $y(-x - 2) = -4$
Isolate <em>y</em>: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

<u>Step 4: Rewrite 1st Derivative</u>

[Algebra] Substitute in <em>y</em>: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

<u>Step 5: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

<u>Step 6: Find Slope at Given Point</u>

[Algebra] Substitute in <em>x</em>: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

6 0

3 years ago

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©<br>Find the area of a circle with radius, r = 6.53m.<br>Give your answer rounded to 2 DP.

natita [175]

Answer:

133.96 meters squared

Step-by-step explanation:

To calculate the area of a circle, simply multiply the radius squared, by pi.

A = pi x r^2

A = pi x 6.53^2

A = pi x 42.6409

A = 133.9603382

The area of the circle is approximately 133.96 meters squared.

Hope this helps! :)

7 0

3 years ago

Read 2 more answers