Thrice the difference between x and 4 is less than9 what's the inequality

1 answer:

4 0

(x-4)•2 < 9
the difference between x and 4 means to subtract
and twice that means to double or times by 2
and all that’s LESS than 9
so the sign opens up towards the 9

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La tabla muestra la cuenta en el nuevo kit de cuentas de Jenny los seis amigos de Jenny tienten el mismo kit de cuentas cuántas

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3 years ago

NEED HELP HERE ASAP 6. Find the cube roots of 27(cos 330° + i sin 330°).

VLD [36.1K]

we have that

the cube roots of 27(cos 330° + i sin 330°) will be
∛[27(cos 330° + i sin 330°)]

we know that
e^(ix)=cos x + isinx
therefore
∛[27(cos 330° + i sin 330°)]------> ∛[27(e^(i330°))]-----> 3∛[(e^(i110°)³)]
3∛[(e^(i110°)³)]--------> 3e^(i110°)-------------> 3[cos 110° + i sin 110°]

z1=3[cos 110° + i sin 110°]

cube root in complex number, divide angle by 3
360nº/3 = 120nº --> add 120º for z2 angle, again for z3
therefore

z2=3[cos ((110°+120°) + i sin (110°+120°)]------ > 3[cos 230° + i sin 230°]

z3=3[cos (230°+120°) + i sin (230°+120°)]--------> 3[cos 350° + i sin 350°]

the answer is

z1=3[cos 110° + i sin 110°]

z2=3[cos 230° + i sin 230°]

z3=3[cos 350° + i sin 350°]

7 0

3 years ago

Determine the angles made by the vector v = (67)i + (-15)j with the positive x- and y-axes. write the unit vector n in the direc

vivado [14]

Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j


Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j