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emmainna [20.7K]
3 years ago
12

The two guy wires supporting a flagpole are each anchored 7m from the flagpole and form an angle of 52 degrees with the ground.

What is the total length of guy wire, to the nearest meter, needed to support this flagpole?
Mathematics
1 answer:
Ulleksa [173]3 years ago
3 0
The answer to ur question is 69m
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The rate of transmission in a telegraph cable is observed to be proportional to x2ln(1/x) where x is the ratio of the radius of
sergij07 [2.7K]

Answer:

The value of x that gives the maximum transmission is 1/√e ≅0.607

Step-by-step explanation:

Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.

f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)

We need to equalize f' to 0

  • k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
  • 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
  • 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
  • ln(1/x) = x/2x = 1/2 -------  we send the natural logarithm as exp
  • 1/x = e^(1/2)
  • x = 1/e^(1/2) = 1/√e ≅ 0.607

Thus, the value of x that gives the maximum transmission is 1/√e.

7 0
4 years ago
What are the vertical asymptotes of the function f(x) = 2x + 8 / x2 + 5x + 6?
Irina18 [472]
I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.

Side Note: x^2 means "x squared"

Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)

There are no common factors between the numerator and denominator. So there is nothing to cancel out. 

Recall that you cannot divide by zero. Something like 1/0 is undefined. 
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3

The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.

4 0
3 years ago
Solve ((9-2)^2)^3/(4+3)^5
Alenkasestr [34]
=(7^2)^3/7^5
=7^6/7^5
=7
8 0
3 years ago
Amber borrows $5,000 from the bank. If she repays the loan in 5 years, the annual interest rate is 8%, compounded annually. Howe
Svetllana [295]

Answer:

The answer is (B) $1,307

Step-by-step explanation:

First you would plug the $5000, 5 Years and 8% Interest(Compound) into your Formula - A=P(1+r)t

A=5000(1+.08)5

Which the interest is $2346.64

<u>__      _________________________________________________</u>

Next you would plug $5000, 3 Years and 6.5% Interest(Compound) Into your Formula - A=P(1=r)t

A=5000(1+.065)3

Which the future value is $1039.75

<u>__       _________________________________________________</u>

Finally you would subtract $2346.64 by $1039.75 and then round the difference to the nearest dollar.      

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Chuge%5Ccolor%7Byellow%7D%5Cunderline%20%5Ccolorbox%7Bviolet%7D%20%7B%5Ccolor%7Bred%7D%7BQUE
zzz [600]

Answer:

   26. <u>c. 6 cm</u>

   27. <u>c. 70 cm³</u>

Step-by-step explanation:

<u>Question 26</u>

  • Volume = Length × Width × Height
  • 360 = 10 × 6 × Width
  • Width = 6 cm
  • <u>c. 6 cm</u>

<u></u>

<u>Question 27</u>

  • Volume = Length × Width × Height
  • Volume = 7 × 5 × 2
  • Volume = 70 cm³
  • <u>c. 70 cm³</u>

<u></u>

<u>Question 28 (not entirely visible)</u>

3 0
2 years ago
Read 2 more answers
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