Answer:
1640
Step-by-step explanation:
Even, positive integers
2+4+6+8+10+12+14+16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50+52+54+56+58+60+62+64+66+68+70+72+74+76+78+80 = 1640
Answer:
v=−27
Step-by-step explanation:
Since v is on the right side of the equation, switch the sides so it is on the left side of the equation.
−6(3v−4)+8v=4(v+7)
Simplify −6(3v−4)+8v
−10v+24=4(v+7)
Simplify 4(v+7).
−10v+24=4v+28
Move all terms containing v to the left side of the equation.
−14v+24=28
Move all terms not containing v to the right side of the equation.
−14v=4
Divide each term by −14 and simplify.
v=−27
The result can be shown in multiple forms.
Exact Form:
v=−27
Answer:
1) w₁=4 - i w₂= -4 + i
2) w₁= 3 - i w₂= -3 + i
3) w₁= 1 + 2i w₂= - 1 - 2i
4) w₁= 2- 3i w₂= -2 + 3i
5) w₁= 5 - 2i w₂= -5 + 2i
6) w₁= 5 - 3i w₂= -5 + 3i
Step-by-step explanation:
The root of a complex number is given by:
![\sqrt[n]{z}=\sqrt[n]{r}(Cos(\frac{\theta+2k\pi}{n}) + i Sin(\frac{\theta+2k\pi}{n}))](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bz%7D%3D%5Csqrt%5Bn%5D%7Br%7D%28Cos%28%5Cfrac%7B%5Ctheta%2B2k%5Cpi%7D%7Bn%7D%29%20%2B%20i%20Sin%28%5Cfrac%7B%5Ctheta%2B2k%5Cpi%7D%7Bn%7D%29%29)
where:
r: is the module of the complex number
θ: is the angle of the complex number to the positive axis x
n: index of the root
1) z = 15 − 8i ⇒ r=17 θ= -0.4899 rad
w₁=
=4-i
w₂=
=-1+i
2) z = 8 − 6i ⇒ r=10 θ= -0.6435 rad
w₁=
= 3 - i
w₂=
= -3 + i
3) z = −3 + 4i ⇒ r=5 θ= -0.9316 rad
w₁=
= 1 + 2i
w₂=
= -1 - 2i
4) z = −5 − 12i ⇒ r=13 θ= 0.4426 rad
w₁=
= 2- 3i
w₂=
= -2 + 3i
5) z = 21 − 20i ⇒ r=29 θ= -0.8098 rad
w₁=
= 5 - 2i
w₂=
= -5 + 2i
6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad
w₁=
= 5 - 3i
w₂=
= -5 + 3i
Answer: 24,000 / 6,200 = x years
Step-by-step explanation:
The car is valued at $24,000.
Yearly payments are $6,200.
The year that it will be paid off can be dtermined by calculating how long it would take $6,200 to get to $24,000.
You can do that by dividing $24,000 by $6,200.
Assume the number of years for the car to be paid off is x:
24,000 / 6,200 = x years
<em>When solved:</em>
<em>= 24,000 / 6,200</em>
<em>= 3.87 years </em>