Answer:
see explanation
Step-by-step explanation:
Using De Moivre's theorem
Given
[ 4(cos15° + isin15° ) ]³, then
= 4³ [ cos(3 × 15°) + isin(3 × 15°) ]
= 64 (cos45° + isin45° )
= 64 (
+ i )
= 64 ( (1 + i) )
= 32
(1 + i)
= 32 + 32 i
Since the motor boat left the dock 2 hours before the tour boat, their meeting point will be 27 miles from the dock from which both boats departed after 3 hours.
<h3>What is the distance?</h3>
Distance is the movement of an object regardless of direction. The distance can be defined as the amount of length an object has covered, regardless of its starting or ending position
We know that r × t = d
r = rate of speed
t = time
d = distance
For the motor boat
9 × t = d = rate × time
For the tour boat
27 × (t - 2) = d = rate × time
When they both cover the same distance in the same amount of time, they will eventually cross paths.
They both cover the same d-mile distance, so:
9 ×t = 27 × (t - 2)
Simplify to get:
9 × t = 27 × t - 54
18 t = 54
t = 3
The motor boat will have traveled at 9 mph for 3 hours to make a distance of 9 × 3 = 27 miles.
The tour boat will have traveled at 27 mph for 1 hour to make a distance of 1 × 27 = 27 miles.
Since the motor boat left the dock 2 hours before the tour boat, their meeting point will be 27 miles from the dock from which both boats departed after 3 hours.
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Answer:
90 possible outcomes.
Step-by-step explanation:
In order to find the total number of combinations possible you simply need to multiply the total number of each options with one another. For example, the number of options in each category are the following
types: 5
toppings: 6
size: 3 (small, medium, large)
Now we simply need to multiply all three of these numbers together to find the total number of possible outcomes.
5 * 6 * 3 = 90 possible outcomes.
(x+y=31)2
2x-y=11
2x+2y=62
- 2x -y=11
3y=51
y=17
x+17=31
x=14
y-x=3
Answer:
Step-by-step explanation:
Multiplying x+6y=-3 with 2 so its equal to first eqn,
Eliminating,
2x + 3y = 3 (1)
2x +12y = -6 (2) (because subtracting)
------------------
-9y =9
∴y=-1
eq. y in 1
2x -3=3
2x=3+3
x=6/2
=3
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