MATHEMATICS COLLEGE

What is 04.151515... into a fraction

Answers

Answer 1

Answer:

Answer:

$\displaystyle 4.\overline{15} = (137)/(33)$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \n 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)

Subtract the original number from the shifted number to eliminate the fraction part completely:

$\begin{aligned}&(100\, x) - x \n &= 15.151515\cdots\n & \phantom{=}- 0.151515\cdots\n&=15 \end{aligned}$ .

In other words:

$99\, x = 15$ .

$\displaystyle x = (15)/(99) = (5)/(33)$ .

Therefore, the original number would be:

$\displaystyle x + 4 = (5)/(33) = (132 + 5)/(33) = (137)/(33)$ .

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13x = 15x - 8

What is the value of X?

Answers

Answer:x equals 4

Step-by-step explanation:

I NEED YOUR HELP 22 POINTSA cone has a base of 30 in^2 and a height of 8.8 what is the volume of the cone?
Plz show how to do it I'm stuck

Answers

Hello from MrBillDoesMath!

Answer:

88 in^3

Discussion:

The volume of a cone of height h and base radius r is

Pi * R^2 * (h/3)

But Pi * r^2 ( = 30) is the area of the base so the volume is:

(30) * (8.8)/3 =

(30/3) ( 8.8) =

10 * 8.8 =

88 in^3

Thank you,

MrB

Answer:

8293.8in

Step-by-step explanation:

Find the limit of the formula given

Answers

Answer:

$\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 1$

General Formulas and Concepts:

Algebra II

Natural logarithms ln and Euler's number e
Logarithmic Property [Exponential]: $\displaystyle log(a^b) = b \cdot log(a)$

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_(x \to c^+) f(x)$
Left-Side Limit: $\displaystyle \lim_(x \to c^-) f(x)$

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

L’Hopital’s Rule: $\displaystyle \lim_(x \to c) (f(x))/(g(x)) = \lim_(x \to c) (f'(x))/(g'(x))$

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

We are given the following limit:

$\displaystyle \lim_(x \to 0^+) x^\big{√(x)}$

Substituting in x = 0 using the limit rule, we have an indeterminate form:

$\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 0^0$

We need to rewrite this indeterminate form to another form to use L'Hopital's Rule. Let's set our limit as a function:

$\displaystyle y = \lim_(x \to 0^+) x^\big{√(x)}$

Take the ln of both sides:

$\displaystyle lny = ln \Big( \lim_(x \to 0^+) x^\big{√(x)} \Big)$

Rewrite the limit by including the ln in the inside:

$\displaystyle lny = \lim_(x \to 0^+) ln \big( x^\big{√(x)} \big)$

Rewrite the limit once more using logarithmic properties:

$\displaystyle lny = \lim_(x \to 0^+) √(x)ln(x)$

Rewrite the limit again:

$\displaystyle lny = \lim_(x \to 0^+) (ln(x))/((1)/(√(x)))$

Substitute in x = 0 again using the limit rule, we have an indeterminate form in which we can use L'Hopital's Rule:

$\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = (\infty)/(\infty)$

Apply L'Hopital's Rule:

$\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}}$

Simplify:

$\displaystyle \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}} = \lim_(x \to 0^+) -2√(x)$

Redefine the limit:

$\displaystyle lny = \lim_(x \to 0^+) -2√(x)$

Substitute in x = 0 once more using the limit rule:

$\displaystyle \lim_(x \to 0^+) -2√(x) = -2√(0)$

Evaluating it, we have:

$\displaystyle \lim_(x \to 0^+) -2√(x) = 0$

Substitute in the limit value:

$\displaystyle lny = 0$

e both sides:

$\displaystyle e^\big{lny} = e^\big{0}$

Simplify:

$\displaystyle y = 1$

And we have our final answer.

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

Unit: Limits

What is the value of a + 4b / a + b if a = -4, b = 3

Answers

Answer:- 8

Step-by-step explanation:

-4 + 4(3)/ -4+3

-4 +12 / -1

8/-1

Marie plants 12 packages of vegetable seeds in a community garden. Each package costs $1.97. What is the total cost of the seeds?

Answers

Answer:

$23.64

Step-by-step explanation:

12 * $1.97 = $23.64

What is a description of an undefined term?

Answers

Answer:

In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined. In Geometry, we define a point as a location and no size. ... And the third undefined term is the line.

Step-by-step explanation:

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