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VikaD [51]
3 years ago
15

A pole is held vertically by attaching wires at a height of 13.4 m above the ground. The other end of each wire is anchored in t

he ground at a distnace of 9.54 m from the base of the pole. The pole makes a right angle with the ground. What is the length of each wire?b) 3 forces pull in different directions on an object at the origin. Once force has a magnitude of 100 newtons, and pulls at an angle 140 degrees with respect to the +x axis. The other two forces are 200 newtons at an angle of 70 degrees, and 160 newtons at an angle of 250 degress. Along what angle (in degress) could a single force of the appropriate magnitude point that would accomlish the same thing as the three factors acting together?
Mathematics
1 answer:
maks197457 [2]3 years ago
5 0

Answer:

  • 16.45 m
  • 121.7°

Step-by-step explanation:

a) The Pythagorean theorem is used to find the length of the hypotenuse of a right triangle from the the lengths of the legs:

  c² = a² + b²

  c = √(a² + b²) = √(13.4² +9.54²) ≈ 16.45 . . . meters

____

b) Using an appropriate vector calculator, you can find the sum of the given forces to be ...

  100∠140° +200∠70° +160∠250° = 119.733∠121.704°

The forces have a resultant equivalent to a force at 121.7°.

__

If you're calculating this by hand, you can add the components of the forces:

  a∠b = (a·cos(b), a·sin(b))

  100∠140° ≈ (-76.604, 64.279)

  200∠70° ≈ (68.404, 187.939)

  160∠250° ≈ (-54.723, -150.351)

(Values are shown rounded here. You never round intermediate calculations, but maintain full calculator precision until the final answer.) Then the sum of these forces is approximately ...

  resultant ≈ (-62.924, 101.866)

The (second quadrant) angle of this resultant is ...

  angle = arctan(101.866/-62.924) ≈ 121.7°

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(-2/3)^7*(3/5)^6*(5/6)^5*(1/3)^-7 simplify of law of indices ​
Wewaii [24]

Answer:

\boxed {-\frac{12}{5}}

Step-by-step explanation:

Solve the following expression:

(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Calculate -\frac{2}{3} to the power of 7:

(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Calculate \frac{3}{5} to the power of 6:

-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Multiply both -\frac{128}{2187} and \frac{729}{15625}:

-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-Calculate \frac{5}{6} to the power of 5:

-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}

-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}

-Multiply both -\frac{128}{46875} and \frac{3125}{7776}:

-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}

-\frac{4}{3645} \times (\frac{1}{3})^{-7}

-Calculate \frac{1}{3} to the power of -7:

-\frac{4}{3645} \times (\frac{1}{3})^{-7}

-\frac{4}{3645} \times 2181

-Multiply both the -\frac{4}{3645} and 2187:

-\frac{4}{3645} \times 2181

\boxed {-\frac{12}{5}}

Therefore, the final answer is -\frac{12}{5}.

3 0
3 years ago
What is the value of x and the length of segment DE?
disa [49]

Answer:

x  = 6.6 and DE = 16.2

Step-by-step explanation:

The question is incomplete as the attachment to solve segment DE is missing. However, see attached for complete question.

Given

\frac{5}{9}= \frac{9}{(2x+3)}

Required

Find x

Length of DE

To find x, we need to first simplify the given equation

\frac{5}{9}= \frac{9}{(2x+3)}

Multiply both sides by 9(2x+3)

\frac{5}{9} * 9(2x + 3) = \frac{9}{(2x+3)} * 9(2x + 3)

5(2x + 3) = 9(9)

10x + 15 = 81

Subtract 15 from both sides

10x + 15 - 15 = 81 - 15

10x  = 66

Divide both sides by 10

\frac{10x}{10}  = \frac{66}{10}

x  = \frac{66}{10}

x  = 6.6

From the attached;

DE = 2x + 3

Substitute 6.6 for x

DE = 2(6.6) + 3

DE = 13.2 + 3

DE = 16.2

Hence x  = 6.6 and DE = 16.2

3 0
3 years ago
Describe the transformation from the parent function to the function g(x)=2 times 3^x-4
azamat

Answer:

Step-by-step explanation:

The parent function of g(x) = 2*3^x-4 would be 3^x

The transformation would include: shifting parent function 4 units down (-4) and compressing the function (2)

The movement (shifting) of the graph is caused by the y-intercept. If the y-intercept is positive, the graph moves up and vice versa.

The coefficient which is multiplied determines whether the function is compressed (squeezed) or stretched. If the coefficient is less than 1, then the function is stretched. If the coefficient is greater than 1, then the function is compressed.

6 0
3 years ago
PLEASE HELP???!!!!!
Likurg_2 [28]
We'll use the Pythagorean Theorem
130^2 = side^2 +50^2
side ^ 2 = 16,900 -2,500
side ^ 2 = 14,400
side = square root (14,400)
side = 120 feet



4 0
3 years ago
Read 2 more answers
Please help!!!!!!!!!!!!!!
tiny-mole [99]

Answer:

53.1 degrees

Step-by-step explanation:

use sohcahtoa

sin(x) = 12/15

sin(x) = 0.8

sin-1(0.8) = 53.1301

5 0
3 years ago
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