Use Pythagorean theorem:
9i-j = sqrt (9^2 - 1^2) = sqrt(81-1) = sqrt80
now divide both terms in V by that:
u = 9/sqrt(80)i - 1/sqrt(80)j
see attached picture:
Answer:
See below.
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336).. (Answer).
Answer:
J (7, 10)
K (3, 2)
Formula for midpoint:
x - coordinate for M:
y - coordinate for M:
Therefore, M (5,6).
Hope this helps :)
Step-by-step explanation:
If we say:
x = the number we want to find
Then, we can formulate an equation using the information given:
1414 - 4x/5 = 4
Now, we just solve for x:
4x/5 + 4 = 1414
4x/5 = 1410
4x = 7050
x = 1762.5
An inequality that represent the number of cans, c, that Jacob must still collect is 
.
<u>Step-by-step explanation:</u>
Here we have , Jacob needs to collect at least 120 cans for a food drive to earn community service credit. He has already collected 64 items. We need to solve the following :
<u>Part A:
</u>
Write and solve an inequality to represent the number of cans, c, that Jacob must still collect.
Jacob has collected 64 cans . Jacob need to collect at least 120 cans for a food drive to earn community service credit , Let Number of cans that Jacob have to collect is c , So following is the inequality for above scenario:
⇒ 
⇒ 
⇒
Therefore , An inequality that represent the number of cans, c, that Jacob must still collect is .
