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3 years ago

5

acme movers charges $150 plus $30 per hour to move household goods across town. hanks movers charges $55 per hour. for what leng

ths of time does it cost less to hire banks movers?

1 answer:

Fittoniya [83]3 years ago

4 0

Answer:

For the length of time less than 6 hours cost less to hire Hanks movers

Step-by-step explanation:

Let

x -----> the time in hours

y ----> the total cost in dollars

we know that

<em>Acme movers</em>

$y=30x+150$ ----> equation A

<em>Hanks movers</em>

$y=55x$ ----> equation B

Equate equation A and equation B and solve for x

$55x=30x+150$

$55x-30x=150$

$25x=150$

$x=6\ hours$

That means-----> For x= 6 hours The cost in both companies is the same

<u><em>Verify</em></u>

For x=6 hours

<em>Acme movers</em>

$y=30(6)+150=\$330$

<em>Hanks movers</em>

$y=55(6)=\$330$

If x < 6 hours ----> It cost less to hire Hanks movers

If x > 6 hours ----> It cost less to hire Acme movers

therefore

For the length of time less than 6 hours cost less to hire Hanks movers

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Answer:

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Step-by-step explanation:

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The mean number of calls that reach a working cell number can be calculated by computing mean of binomial distribution using the given information.

Mean of binomial distribution=E(x)=np

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4 years ago

Hi, could someone help me differentiate Q6 b with the use if ln

Lady bird [3.3K]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{-(2x - 3)(6x - 43)}{(3x + 4)^4}$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Equality Properties

<u>Algebra II</u>

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

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation
Implicit Differentiation

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:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = \frac{(2x - 3)^2}{(3x + 4)^3}$

<u>Step 2: Rewrite</u>

[Equality Property] ln both sides: $\displaystyle lny = ln \bigg[ \frac{(2x - 3)^2}{(3x + 4)^3} \bigg]$
Expand [Logarithmic Property - Dividing]: $\displaystyle lny = ln(2x - 3)^2 - ln(3x + 4)^3$
Simplify [Logarithmic Property - Exponential]: $\displaystyle lny = 2ln(2x - 3) - 3ln(3x + 4)$

<u>Step 3: Differentiate</u>

Implicit Differentiation: $\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ 2ln(2x - 3) - 3ln(3x + 4) \bigg]$
Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle \frac{1}{y} \ \frac{dy}{dx} = 2 \bigg( \frac{1}{2x - 3} \bigg)\frac{dy}{dx}[2x - 3] - 3 \bigg( \frac{1}{3x + 4} \bigg) \frac{dy}{dx}[3x + 4]$
Basic Power Rule: $\displaystyle \frac{1}{y} \ \frac{dy}{dx} = 4 \bigg( \frac{1}{2x - 3} \bigg) - 9 \bigg( \frac{1}{3x + 4} \bigg)$
Simplify: $\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{4}{2x - 3} - \frac{9}{3x + 4}$
Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = y \bigg( \frac{4}{2x - 3} - \frac{9}{3x + 4} \bigg)$
Substitute in <em>y</em> [Derivative]: $\displaystyle \frac{dy}{dx} = \frac{(2x - 3)^2}{(3x + 4)^3} \bigg( \frac{4}{2x - 3} - \frac{9}{3x + 4} \bigg)$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{(2x - 3)^2}{(3x + 4)^3} \bigg[ \frac{4(3x + 4) - 9(2x - 3)}{(2x - 3)(3x +4)} \bigg]$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-(2x - 3)(6x - 43)}{(3x + 4)^4}$

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

Unit: Differentiation

Book: College Calculus 10e

8 0

3 years ago

Question 3 of 8. Step 1 of 1

natali 33 [55]

308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

<h3><u>Combination</u></h3>

Since a dairy needs 385 gallons of milk containing 6% butterfat, to determine how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 385 gallons, the following calculation must be performed:

385 x 0.06 = 23.1
300 x 0.07 + 85 x 0.02 = 22.7
310 x 0.07 + 75 x 0.02 = 23.2
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Therefore, 308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

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2 years ago