The given polygons are similar. Find the value of x.

In preparing for holiday festivities, confetti is stuffed into decorative spherical containers. Each container has a diameter of

professor190 [17]

Answer:

C. 905 in³

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, sphere

We know that the volume of a sphere is expresses as

V= 4/3πr³

Given that the diameter of the sphere is 12inches

Radius r= 12/2= 6 inches

Substituting our radius we can solve for the volume

V=4/3(3.142*6³)

V= (4*3.142*216)/3

V= 2714.68/3

V= 904.9in³

Approximately V= 905in³

5 0

2 years ago

SIMPLIFY (4-74+7) A. 223 B. 9 27 C. 9+2/7 D. 9

sesenic [268]

Answer:

The correct option is D.

Step-by-step explanation:

The given expression is

$(4-\sqrt{7})(4+\sqrt{7})$

Difference of two squares property:

$a^2-b^2=(a+b)(a-b)$

Using the above property, the given expression can be written as

$(4)^2-(\sqrt{7})^2$

Applying square we get

$16-7$

$9$

Therefore the correct option is D.

6 0

3 years ago

On Monday, the theater club sells 14 tickets for the school play. On Tuesday, they sell 10 tickets. On those two days, they sell

Margarita [4]

Answer:

<h2>31 tickets</h2>

Step-by-step explanation:

Step one:

number of tickets sold

monday=14

tuesday=10

the number of tickets sold for Monday and Tuesday combined is

14+10= 24

step two:

we want to find how many tickets make 30%

so 30/100*24

0.3*24

=7.2 tickets,

Approximately 7 ticket

Therefore the total ticket is

14+10+7

=31 tickets

7 0

2 years ago

Which graph is an example of a function whose parent function is y = StartRoot x EndRoot?On a coordinate plane, a curve starts a

lbvjy [14]

Answer:

On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0)

Step-by-step explanation:

The attached graph is an example of the square root function scaled and translated.

_____

No transformation of the square root curve will turn it into a parabola or into two curves.

3 0

3 years ago

Read 2 more answers

Can you find the limits of this

Pavel [41]

Answer:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{-3}{8}$

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Constant]: $\displaystyle \lim_{x \to c} b = b$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Property [Addition/Subtraction]: $\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)$

L'Hopital's Rule

Differentiation

Derivatives
Derivative Notation

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:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

We are given the following limit:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16}$

Let's substitute in <em>x</em> = -2 using the limit rule:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{(-2)^3 + 8}{(-2)^4 - 16}$

Evaluating this, we arrive at an indeterminate form:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{0}{0}$

Since we have an indeterminate form, let's use L'Hopital's Rule. Differentiate both the numerator and denominator respectively:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \lim_{x \to -2} \frac{3x^2}{4x^3}$

Substitute in <em>x</em> = -2 using the limit rule:

$\displaystyle \lim_{x \to -2} \frac{3x^2}{4x^3} = \frac{3(-2)^2}{4(-2)^3}$

Evaluating this, we get:

$\displaystyle \lim_{x \to -2} \frac{3x^2}{4x^3} = \frac{-3}{8}$

And we have our answer.

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

Unit: Limits

6 0

2 years ago