Answer:
![\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960](https://tex.z-dn.net/?f=%5Csin%20253.740%5E%7B%5Ctextdegree%7D%20%3D%20-%5Cfrac%7B24%7D%7B25%7D%20%3D%20-0.960)
![\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280](https://tex.z-dn.net/?f=%5Ccos%20253.740%5E%7B%5Ctextdegree%7D%20%3D%20-%5Cfrac%7B7%7D%7B25%7D%20%3D%20-0.280)
![\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429](https://tex.z-dn.net/?f=%5Ctan%20253.340%5E%7B%5Ctextdegree%7D%20%3D%20%5Cfrac%7B24%7D%7B7%7D%20%3D%20%203.429)
Step-by-step explanation:
The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.
The angle is:
![\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20180%5E%7B%5Ctextdegree%7D%2B%5Ctan%5E%7B-1%7D%5Cleft%28%5Cfrac%7B24%7D%7B7%7D%20%5Cright%29)
![\theta \approx 253.740^{\textdegree}](https://tex.z-dn.net/?f=%5Ctheta%20%5Capprox%20253.740%5E%7B%5Ctextdegree%7D)
The values of the trigonometrical functions are computed below:
![\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960](https://tex.z-dn.net/?f=%5Csin%20253.740%5E%7B%5Ctextdegree%7D%20%3D%20-%5Cfrac%7B24%7D%7B25%7D%20%3D%20-0.960)
![\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280](https://tex.z-dn.net/?f=%5Ccos%20253.740%5E%7B%5Ctextdegree%7D%20%3D%20-%5Cfrac%7B7%7D%7B25%7D%20%3D%20-0.280)
![\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429](https://tex.z-dn.net/?f=%5Ctan%20253.340%5E%7B%5Ctextdegree%7D%20%3D%20%5Cfrac%7B24%7D%7B7%7D%20%3D%20%203.429)
Answer:
8
Step-by-step explanation:
hypotenuse = c = 17 feet
Height = a = 9 feet + 6 feet = 15 feet
Children's space = b
a^2 + b^2 = c^2
15^2 + b^2 = 17^2
225 + b^2 = 289 Subtract 225 from both sides
225-225+b^2=289-225
b^2 = 64 Take the square root of both sides.
sqrt(b^2) = sqrt(64)
b = 8
Since each child takes up 1 foot, 8 children can sit on side b.
The value in this case would be going up. Since .75 being multiplied by an increasing number would only increase, the value must be doing the same.
However, if that t were an exponent, the value would be decreasing. The more a number between 0 and 1 is multiplied by itself, the smaller it gets.
By De Moivre's formula, the <em>cubic</em> roots of the <em>complex</em> number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
<h3>How to find the cube root of a complex number</h3>
Herein we have a <em>complex</em> number in <em>rectangular</em> form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The <em>root</em> formula is introduced below:
, for k ∈ {0, 1, ..., n - 1} (1)
Where n is the grade of the complex root.
The magnitude and direction of the <em>complex</em> number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:
k = 0
z₁ = 2.997 + i 4.002
k = 1
z₂ = - 4.964 + i 0.595
k = 2
z₃ = 1.967 - i 4.597
By De Moivre's formula, the <em>cubic</em> roots of the <em>complex</em> number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
To learn more on complex numbers: brainly.com/question/10251853
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Answer:
4-3
Step-by-step explanation:
solve for x