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3 years ago

14

How do you find the holes, vertical, and horizontal asymptote of an equation?

1 answer:

AfilCa [17]3 years ago

4 0

This is a great question, but it's also a very broad one. Please find and post one or two actual rational expressions, so we can get started on specifics of how to find vertical and horiz. asymptotes.

In the case of vert. asy.: Set the denom. = to 0 and solve for x. Any real x values that result indicate the location(s) of vertical asymptotes.

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What is the largest possible integral value in the domain of the real-valued function

kotegsom [21]

Answer:

Max Value: x = 400

General Formulas and Concepts:

<u>Algebra I</u>

Domain is the set of x-values that can be inputted into function f(x)

<u>Calculus</u>

Antiderivatives
Integral Property: $\int {cf(x)} \, dx = c\int {f(x)} \, dx$
Integration Method: U-Substitution
[Integration] Reverse Power Rule: $\int {x^n} \, dx = \frac{x^{n+1}}{n+1} + C$

Step-by-step explanation:

<u>Step 1: Define</u>

$f(x) = \frac{1}{\sqrt{800-2x} }$

<u>Step 2: Identify Variables</u>

<em>Using U-Substitution, we set variables in order to integrate.</em>

$u = 800-2x\\du = -2dx$

<u>Step 3: Integrate</u>

Define: $\int {f(x)} \, dx$
Substitute: $\int {\frac{1}{\sqrt{800-2x} } } \, dx$
[Integral] Int Property: $-\frac{1}{2} \int {\frac{-2}{\sqrt{800-2x} } } \, dx$
[Integral] U-Sub: $-\frac{1}{2} \int {\frac{1}{\sqrt{u} } } \, du$
[Integral] Rewrite: $-\frac{1}{2} \int {u^{-\frac{1}{2} }} \, du$
[Integral - Evaluate] Reverse Power Rule: $-\frac{1}{2}(2\sqrt{u}) + C$
Simplify: $-\sqrt{u} + C$
Back-Substitute: $-\sqrt{800-2x} + C$
Factor: $-\sqrt{-2(x - 400)} + C$

<u>Step 4: Identify Domain</u>

We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.

Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.

7 0

3 years ago

!!!!PLEASE HELP!!!! Tracy deposited $59 into a bank account that earned 3.5% simple interest each year. If no money was deposite

oksian1 [2.3K]

If you meant “112” years the answer is $6,839.28, if you actually meant 112112 the answer is $6,846,119.28

8 0

3 years ago

How do you use the associative property to write an expression equivalent to (w+9)+3

m_a_m_a [10]

The equivalent expression for the given expression (w+9)+3 using associative property is w + 12

<u>Solution:</u>

Given that, expression is ( w + 9 ) + 3

We have to find how do we can use the associative property to write an expression equivalent to ( w + 9 ) + 3

The associative property states that you can add or multiply regardless of how the numbers are grouped

By above definition, we get

(a + b) + c = a + (b + c)

So, now let us apply the above property to the given expression,

Then, ( w + 9 ) + 3 = w + ( 9 + 3 ) = w + 12

Hence, the equivalent expression for the given expression is w + 12

5 0

3 years ago

A force of 10 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work is done in stretching it

Troyanec [42]

Answer:

W = 15/4 ft . ib

Step-by-step explanation:

Force = 10ib

According to hooked law, f(x) = kx

x = 4inches = 4/12 ft

x= 1/3ft

f(x) = 1/3k

10 = 1/3k

k = 30 ib/ft

f(x) = 30x

Workdone = integral of f(x) with its limit

6 inches = 6/12 ft

= 1/2ft

W = integral(1/2 to 0) of 30x

W = 15x^2(1/2 to 0)

W = 15(1/2)^2 - 15(0)^2

W = 15(1/4) - 0

W = 15/4 ft. Ib

4 0

3 years ago

Lynn goes to the supermarket and purchases 6 boxes of cookies for $11.04. Each box contains 8 cookies. What is the price per coo

aksik [14]

Answer:

Step-by-step explanation:

6 x 8 = 48

11,04 x 6 = 66,24

66,24/48 = 1,38$

8 0

3 years ago