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Julli [10]
1 year ago
12

A rectangle has a length four more than

Mathematics
1 answer:
torisob [31]1 year ago
8 0
L ≥ 5w + 4
2(L+w) ≥ 32

L+w ≥ 16

6w + 4 ≥ 16
6w ≥ 12
w ≥ 2

L ≥ 5w + 4
L ≥ 14

If L = 14 and w = 2 then the perimeter is 32.
These are the smallest dimensions that fit the criteria.

Note: If we raise the width by 1 to w = 3
then the length is at least 19. At 19 by 3 we have P = 44
Like would be appreciated!!
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812,000 gallons of water in an olympic training center's pool. express this number in scientific notation.
frez [133]
8.12×10^5
... i got this by taking the first number 8 and then counting the places behind the 8 which would be 5 so than you move the decimal place by 5 so you get 8.12 then you show theirs 5 places behind the 8 by adding the 10^5 so youbget 8.12×10^5
4 0
3 years ago
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What is the solution set of the equation<br> x + 6 = 2(x + 3) - x?
Svetach [21]

Answer:

<em>x</em> = all real numbers

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Distributive Property

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

x + 6 = 2(x + 3) - x

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Addition Property of Equality] Add <em>x</em> on both sides:                                     2x + 6 = 2(x + 3)
  2. [Distributive Property] Distribute 2:                                                                 2x + 6 = 2x + 6

Here we see that both sides are identical.

∴ our solution is all real numbers.

6 0
3 years ago
Anonymous 3 years ago
scZoUnD [109]
I'm in 7th grade and I need help with my math homework
8 0
3 years ago
Explain<br> how u subtract 247 from 538
VashaNatasha [74]
247- 538 = -291
If you line them up in that order 247 you'll have to borrow. Your answer would be -291
                                                  -538

The only way to not get -291 is to flip the two numbers.
6 0
3 years ago
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Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
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