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3 years ago

Calculate s62 for the arithmetic sequence

Mathematics

1 answer:

masha68 [24]3 years ago

4 0

Answer:

A) 10, 013/6

Step-by-step explanation:

The given arithmetic sequence {an } = {5/6 n + 2/3}

We need to find the 62th term, so plug in n = 62 in the above sequence, we get

S62 = { $\frac{5}{6} .62 + \frac{2}{3}$

= {310/6 + 2/3}

= {155/3 + 2/3}

= (155 + 2)/3

S62 = 157/3

Now let's find the first term.

S1 = [5/6 (1) + 2/3]

S1 = [5/6 + 2/3]

S1 = (5 + 4)/6

S1 = 9/6

s1 = 3/2

The sum of the terms S62 = 62(3/2 + 157/3) divided by 2

= 31(9 + 314)/6

= 31(323)/6

= 10, 013/6

So the answer is A)10,013/6

Thank you.

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Simplify the expression to a polynomial in standard form: (4x+5) (x^2-3x-2) PLEASE HLEP

pickupchik [31]

Answer:

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Step-by-step explanation:

So we have the expression:

$(4x+5)(x^2-3x-2)$

Distribute. Multiply (4x+5) to each term:

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Distribute:

$=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)$

Combine like terms:

$=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)$

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3 years ago

The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Area of a Rectangle: A = lw

l is length
w is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

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

Step-by-step explanation:

Step 1: Define

$\displaystyle l = 10 \ meters$

$\displaystyle \frac{dl}{dt} = 4 \ m/day$

$\displaystyle w = 23 \ meters$

$\displaystyle \frac{dw}{dt} = 1 \ m/day$

Step 2: Differentiate

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

Step 3: Solve

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
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[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

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

Unit: Implicit Differentiation

Book: College Calculus 10e

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4 years ago

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Answer:

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DaniilM [7]

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Learn more on Trigonometry here: brainly.com/question/22099203

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Alika [10]

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Your answer is C.

Hope this helps!

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