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3 years ago

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Lisa is on a trip of 2,792 miles. She has already traveled 146 miles. She has 6 days left in her trip. How many miles does she n

eed to travel each day to complete the trip?
2,646
441
587
2,205

1 answer:

Verizon [17]3 years ago

5 0

The answer is 441 because 2,792-146/ (divided) by6= 441

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(b) 5.2m + 5 = 2.9m – 3 – 4.1m

ohaa [14]

Answer:

m =-1.25

Step-by-step explanation:

5.2m + 5 = 2.9m – 3 – 4.1m

Combine like terms

5.2m + 5 = -1.2m – 3

Add 1.2m to each side

5.2m +1.2m +5 = -1.2m +1.2m -3

6.4m +5 = -3

Subtract 5 from each side

6.4m +5-5 = -3-5

6.4m = -8

Divide each side

6.4m/6.4 = -8/6.4

m =-1.25

7 0

3 years ago

Determine the lateral surface area and the total surface for the pyramid. Round your answer to the nearest whole number.

777dan777 [17]

Answer:

$L = 704$

$S = 832$

Step-by-step explanation:

Given

$H = 22$ --- Height

$W = 8$ --- Width

$L=8$ ---- Length

Solving (a): The lateral surface area (L)

This is calculated as:

$L = 2 * (L + W) * H$

This gives:

$L = 2 * (8 + 8) * 22$

$L = 2 * 16 * 22$

$L = 704$

Solving (b): The total surface area (T)

This is calculated as:

$S = 2 * (LW + WH + LH)$

This gives:

$S = 2 * (8*8 + 8*22+ 8*22)$

$S = 2 * (64 + 176+ 176)$

$S = 2 * 416$

$S = 832$

3 0

3 years ago

If DC is about 12 units, what other length(s) can you determine? Please don’t put a link as an answer.

anyanavicka [17]

Answer:

How is DC 12 units if all the sides are congruent and AB clearly states that it is 9 units long?

Doesnt make sense

5 0

3 years ago

The contrapositive of a given statement is equivalent to the original statement? True or False

bija089 [108]

True, for a contrapositive you switch the parts and then make them opposite, but the statement is still true.

4 0

3 years ago

Help with num 1 please.

KengaRu [80]

Answer:

(i) $\displaystyle y' = (6x - 1)ln(2x + 1) + \frac{2x(3x - 1)}{2x + 1}$

(ii) $\displaystyle y' = \frac{2x}{ln(x)} - \frac{x^2 + 2}{x(lnx)^2}$

(iii) $\displaystyle y' = \frac{e^x[xln(2x) + 1]}{x}$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

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 [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

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

Exponential Differentiation

Logarithmic Differentiation

Step-by-step explanation:

(i)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = (3x^2 - x)ln(2x + 1)$

<u>Step 2: Differentiate</u>

Product Rule: $\displaystyle y' = (3x^2 - x)'ln(2x + 1) + (3x^2 - x)[ln(2x + 1)]'$
Basic Power Rule/Logarithmic Differentiation [Chain Rule]: $\displaystyle y' = (6x - 1)ln(2x + 1) + (3x^2 - x)\frac{1}{2x + 1}(2x + 1)'$
Basic Power Rule: $\displaystyle y' = (6x - 1)ln(2x + 1) + (3x^2 - x)\frac{2}{2x + 1}$
Simplify [Factor]: $\displaystyle y' = (6x - 1)ln(2x + 1) + \frac{2x(3x - 1)}{2x + 1}$

(ii)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = \frac{x^2 + 2}{lnx}$

<u>Step 2: Differentiate</u>

Quotient Rule: $\displaystyle y' = \frac{(x^2 + 2)'lnx - (x^2 + 2)(lnx)'}{(lnx)^2}$
Basic Power Rule/Logarithmic Differentiation: $\displaystyle y' = \frac{2xlnx - (x^2 + 2)\frac{1}{x}}{(lnx)^2}$
Rewrite: $\displaystyle y' = \frac{2xlnx}{(lnx)^2} - \frac{(x^2 + 2)\frac{1}{x}}{(lnx)^2}$
Simplify: $\displaystyle y' = \frac{2x}{ln(x)} - \frac{x^2 + 2}{x(lnx)^2}$

(iii)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = e^xln(2x)$

<u>Step 2: Differentiate</u>

Product Rule: $\displaystyle y' = (e^x)'ln(2x) + e^x[ln(2x)]'$
Exponential Differentiation/Logarithmic Differentiation [Chain Rule]: $\displaystyle y' = e^xln(2x) + e^x(\frac{1}{2x})(2x)'$
Basic Power Rule: $\displaystyle y' = e^xln(2x) + e^x(\frac{1}{2x})2$
Simplify: $\displaystyle y' = e^xln(2x) + \frac{e^x}{x}$
Rewrite: $\displaystyle y' = \frac{xe^xln(2x) + e^x}{x}$
Factor: $\displaystyle y' = \frac{e^x[xln(2x) + 1]}{x}$

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

Unit: Differentiation

Book: College Calculus 10e

6 0

3 years ago