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dimaraw [331]
2 years ago
9

Find Q, I'm not sure if it is possible however.

Mathematics
1 answer:
zmey [24]2 years ago
4 0

9514 1404 393

Answer:

  Q ≈ 0.0314148930589 radians ≈ 1.79994078613°

Step-by-step explanation:

There is no algebraic solution for the set of equations with mixed polynomial and trig functions:

  x·sin(Q/2) = 5

  1/2x^2(Q -sin(Q)) = π/12

__

However, we can use the first equation to substitute for x in the second equation. This gives ...

  \displaystyle \frac{1}{2}\left(\frac{5}{\sin{\frac{Q}{2}}}\right)^2(Q-\sin{Q})=\frac{\pi}{12}

This can be simplified using the half-angle identity and recast as a function of Q:

  \displaystyle f(Q)=\frac{25(Q-\sin{Q})}{1-\cos{Q}}-\frac{\pi}{12}

This function will have a zero at the desired value of Q. It can be solved iteratively. A graph shows an approximate value of Q is 0.314 (radians). The value can be refined by Newton's method iteration to give the angle to full calculator precision:

  Q ≈ 0.0314148930589 radians ≈ 1.79994078613°

__

The corresponding value of x is about 318.333447755. In short, this is a very narrow sector/segment in a relatively large circle.

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Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1) (2.5, 1.5) (3.5, 2.5) (1.5, 2.5) (3.5, 1.5)
Setler79 [48]

Answer:

\boxed {\boxed {\sf (1.5 , 2.5)}}

Step-by-step explanation:

The midpoint is the point that bisects a line segment or divides it into 2 equal halves. The formula is essentially finding the average of the 2 points.

(\frac {x_1+x_2}{2}, \frac {y_1+ y_2}{2})

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 endpoints of the line segment. For this problem, these are (5,4 ) and (-2, 1).

  • x₁= 5
  • y₁= 4
  • x₂= -2
  • y₂= 1

Substitute these values into the formula.

( \frac {5+ -2}{2}, \frac {4+1}{2})

Solve the numerators.

  • 5+ -2 = 5-2 = 3
  • 4+1 = 5

( \frac {3}{2}, \frac{5}{2})

Convert the fractions to decimals.

(1.5, 2.5)

The midpoint of the line segment is (1.5 , 2.5)

3 0
2 years ago
Considering the number of questions incorrect from classmates on a quiz {10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19,
IrinaK [193]

Answer:

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

Step-by-step explanation:

We are given the following data in the question:

10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{225}{15} = 15

Sum of squares of differences = 25 + 16 + 9 + 4 + 4+ 4 + 1 + 0+ 1+ 1 + 4 + 9 + 9+ 16 + 25 = 128

S.D = \sqrt{\dfrac{128}{14}} = 3.02

Empirical rule:

  • According to this rule almost all the data lies within three standard deviation of the mean for a normal distribution.
  • About 68% of data lies within one standard deviation of the mean.
  • About 95% of data lies within two standard deviations of mean.
  • Arround 99.7% of data lies within three standard deviation of mean.

Thus, by empirical rule,

\mu \pm 1\sigma = 15\pm (3.02) = (11.98,18.02)

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

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Alex_Xolod [135]
5. 
First plug the value of x into the equation
 2(-2y-12)+y=9
then solve for y
2(-2y)+2(-12)+y=9 \\ -4y+(-24)+y=9 \\ -4y-24+y=9 \\ -3y-24=9 \\ -3y=33 \\ \frac{-3y}{-3}= \frac{33}{-3} \\ y = -11

6. Do the same steps 
5(-y-1)+y=-13 \\ 5(-y)+5(-1)+y=13 \\ -5y+(-5)+y=13 \\ -5y-5+y=13 \\ -4y-5=13 \\ -4y=18 \\ \frac{-4y}{-4}= \frac{18}{-4} \\ y=-4.5 

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