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3 years ago

Simplify a - {5b - [a - (3b - 2c) + c - (a - 2b - c)]}.

Mathematics

2 answers:

densk [106]3 years ago

8 0

Asking the Math Gods...

= a-6b+4c

Allushta [10]3 years ago

3 0

Answer:

a-6b+4c

Step-by-step explanation:

a-{5b-[a-(3b-2c)+c-(a-2b-c)]}

a-{5b-[a-1(3b-2c)+c-1(a-2b-c)]}

a-{5b-[a+(-3b+2c)+c+(-a+2b+c)]}

a-{5b-[a-3b+2c+c-a+2b+c]}

a-{5b-[-b+4c]}

a-{5b+[b-4c]}

a-{5b+b-4c}

a-{6b-4c}

a+{-6b+4c}

a-6b+4c

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

What is the volume of the prism?

anygoal [31]

Answer:

78.75 cm cubed

Step-by-step explanation:

To find the volume of the prism, use the formula V = l*w*h where l = 4.5, w = 5 and h = 3.5.

So the volume is V = 4.5*5*3.5 = 78.75

7 0

4 years ago

Please help me find DOMAIN/RANGE and the EQATION

mrs_skeptik [129]

Answer:

Domain of the function → (-6, ∞)

Range of the function → (-∞, ∞)

Step-by-step explanation:

Domain of a function is the set of x-values of the function.

Similarly, Range of the function is the set of y-values.

From the graph attached,

Domain of the function → (-6, ∞)

x-values of the function starts from x = -6 (excluding x = -5) and tends to the positive infinity.

Range of the function → (-∞, ∞)

y-values starts from negative infinity and tends to positive infinity.

7 0

3 years ago

Find the SUm of the infinite series.

givi [52]

I'll do problem 13 to get you started.

The expression $4\left(\frac{2^n}{7^n}\right)$ is the same as $4\left(\frac{2}{7}\right)^n$

Then we can do a bit of algebra like so to change that n into n-1

$4\left(\frac{2}{7}\right)^n\\\\4\left(\frac{2}{7}\right)^n*1\\\\4\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{0}\\\\4\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{1-1}\\\\4\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{1}*\left(\frac{2}{7}\right)^{-1}\\\\4*\left(\frac{2}{7}\right)^{1}\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{-1}\\\\\frac{8}{7}\left(\frac{2}{7}\right)^{n-1}\\\\$

This is so we can get the expression in a(r)^(n-1) form

a = 8/7 is the first term of the geometric sequence
r = 2/7 is the common ratio

Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).

We'll plug those a and r values into the infinite geometric sum formula below

S = a/(1-r)

S = (8/7)/(1 - 2/7)

S = (8/7)/(5/7)

S = (8/7)*(7/5)

S = 8/5

S = 1.6

------------------------

Answer in fraction form = 8/5

Answer in decimal form = 1.6

7 0

3 years ago

Help pls and thank you

netineya [11]

Answer:

Step-by-step explanation:

7 0

4 years ago

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