The sum of 3 consecutive multiples of 4 is 120. Find the numbers.
1 answer:
Answer:
The required numbers are: 36, 40, 44
Step-by-step explanation:
Let first number = 4x
Second number = 4(x+1)
Third number = 4(x+2)
There sum = 120
We need to find the numbers
We can write:
So, we get x = 9
Now, finding the numbers:
first number = 4x = 4(9) =36
Second number = 4(x+1) = 4(9+1) = 4(10) = 40
Third number = 4(x+2) = 4(9+2) = 4(11) = 44
So, The required numbers are: 36, 40, 44
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The remainder theorem says that dividing a polynomial by
leaves a remainder of
. Here,
, then
.
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:
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:
<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>
Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j
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:
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:
<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>
Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j