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3 years ago

Combine the like terms to make a simpler expression −4p+(−6p)

2 answers:

8 0

First, we have to remove the parenthesis.
$=-4p-6p$
We then combine the like terms...
$=-10p$

The expression is now simplified.
Have a nice day! :)

Zina [86]3 years ago

7 0

<span>−4p+(−6p) = - 10p .........combine like terms

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Which of the following numbers is between - 3/4 and 5/8?

SVETLANKA909090 [29]

Answer:

The correct answer is B.

Step-by-step explanation:

If you place all of them on a number line the order from least to greatest would be:

-1, -3/4, -1/2, 5/8, 7/8, 0.9

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3 years ago

HELP ME PLEASE THIS IS DUE VERY SOON

Zarrin [17]

Answer:

5/12

Step-by-step explanation:

Divide both numbers in one of the ratios by their highest common factor.

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3 years ago

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OleMash [197]

Answer:

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Step-by-step explanation:

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3 years ago

∑∞ n=1 (n^2n)/(1+n)^(3n)

kvv77 [185]

Answer:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

<h2>Step-by-step explanation: PHEW THAT TOOK A WHILE LOL IM A FAST TYPER</h2>

3 0

3 years ago

You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material fo

zepelin [54]

Answer:

The dimensions of the box are:

x = 8,93 cm and h = 5,95 cm

C(min) = 850,69 cents

Step-by-step explanation:

The volume of the box is:

V = x²*h where x is the side of the square base and h the height

then h = V/ x² ⇒ h = 475 / x²

The total cost of box C is:

C = C₁ + 4*C₂ Where C₁ and C₂ are the costs of the base and one lateral side respectevily

Then cost C = 8*x² + 4* 6*h*x

The cost C as a function of x is

C(x) = 8*x² + (24* 475 /x² )*x

C(x) = 8*x² + 11400/x

Tacking derivatives on both sides of the equation

C´(x) = 16*x - 11400/x²

C´(x) = 0 ⇒ 16*x - 11400/x² = 0

16*x³ = 11400 ⇒ x³ = 11400/16

x³ = 712,5

x = 8,93 cm

and h = 475 / (8,93)² ⇒ h = 5,95 cm

C(min) = 8*79,77 + 4* ( 8,93)*5,95

C(min) = 638,16 + 212,53

C(min) = 850,69 cents

To check if value x = 8,93 would make C(x) minimum we go to the second derivatives

C´´(x) = 16 + 22800/x³ > 0

Then we have a minimum of C at x = 8,93

4 0

4 years ago